Fifteenth award: to Emmanuel Candès for his work on compressed sensing that has revolutionized signal processing and medical imaging and his related work on computational harmonic analysis, statistics and scientific computing.

Fourteenth award: to Bjorn Engquist for his contributions to a wide range of powerful computational methods over more than three decades.

Thirteenth award: to Joel Smoller for his leadership, originality, depth, and breadth of work in dynamical systems, differential equations, mathematical biology, shock wave theory, and general relativity.

Twelfth award: to Cathleen Synge Morawetz for her deep and influential work in partial differential equations, most notably in the study of shock waves, transonic flow, scattering theory, and conformally invariant estimates for the wave equation.

Eleventh award: to John Mather for being a mathematician of exceptional depth, power, and originality; and to Charles S. Peskin for devoting much of his career to understanding the dynamics of the human heart and bringing an extraordinarily broad range of expertise to bear on this problem.

Tenth award: to Paul H. Rabinowitz for his deep influence on the field of nonlinear analysis.

Ninth award: to Ivo Babuska for important contributions to the reliability of finite element methods, the development of a general framework for finite element error estimation, and the development of p- and hp- finite element methods; and to S. R. S. Varadhan for important contributions to the martingale characterization of diffusion processes, to the theory of large deviations for functionals of occupation times of Markov processes, and to the study of random media.

Eighth award: to Elliott H. Lieb for his profound analysis of problems arising in mathematical physics.

Seventh award: to Paul R. Garabedian for his important contributions to partial differential equations, to the mathematical analysis of problems of transonic flow and airfoil design by the method of complexification, and to the development and application of scientific computing to problems of fluid dynamics and plasma physics.

Sixth award: to Clifford A. Truesdell for his outstanding contributions to our understanding of the subjects of rational mechanics and nonlinear materials, for his efforts to give precise mathematical formulation to these classical subjects, for his many contributions to applied mathematics in the fields of acoustic theory, kinetic theory, and nonlinear elastic theory, and the thermodynamics of mixtures, and for his major work in the history of mechanics.

Fixth award: to Mark Kac for his important contributions to statistical mechanics and to probability theory and its applications.

Fourth award: to Garrett Birkhoff for bringing the methods of algebra and the highest standards of mathematics to scientific applications.

Third award: to James B. Serrin for his fundamental contributions to the theory of nonlinear partial differential equations, especially his work on existence and regularity theory for nonlinear elliptic equations, and applications of his work to the theory of minimal surfaces in higher dimensions.

Second award: to Fritz John for his outstanding work in partial differential equations, in numerical analysis, and, particularly, in nonlinear elasticity theory; the latter work has led to his study of quasi-isometric mappings as well as functions of bounded mean oscillation, which have had impact in other areas of analysis.

First award: to Jürgen K. Moser for his contributions to the theory of Hamiltonian dynamical systems, especially his proof of the stability of periodic solutions of Hamiltonian systems having two degrees of freedom and his specific applications of the ideas in connection with this work.

>Twenty-fourth award: to András Vasy "for his fundamental paper `Microlocal analysis of asymptotically hyperbolic and Kerr-de Sitter spaces,' Inventiones Mathematicae, 194 (2013), 381513."

Twenty-third award: to Simon Brendle for his outstanding solutions of long standing problems in geometric analysis including the solution with R. Schoen of the differentiable sphere theorem (JAMS 22 2009) and the solution of the Lawson conjecture (to appear Acta Mathematica 2013). Brendle is also recognized for his deep contributions to the study of the Yamabe equation.

Twenty-second award: to Gunther Uhlmann for his fundamental work on inverse problems; and to Assaf Naor for introducing new invariants of metric spaces and for applying his new understanding of the distortion between various metric structures to theoretical computer science.

Twenty-first award: to Alberto Bressan for his fundamental works on hyperbolic conservation laws; and to Charles Fefferman for his many fundamental contributions to different areas of analysis; and to Carlos Kenig for his important contributions to harmonic analysis, partial differential equations, and nonlinear dispersive PDE.

Twentieth award: to Frank Merle for his fundamental work in the analysis of nonlinear dispersive equations.

Nineteenth award: to Daniel Tataru for his fundamental paper “On global existence and scattering for the wave maps equations,” Amer. Jour. of Math. 123 (2001) no. 1, 37–77; and to Terence Tao for his recent fundamental breakthrough on the problem of critical regularity in Sobolev spaces of the wave maps equations, “Global regularity of wave maps I. Small critical Sobolev norm in high dimensions”, Int. Math. Res. Notices (2001), no.6, 299–328 and “Global regularity of wave maps II. Small energy in two dimensions”, to appear in Comm. Math. Phys. (2001 or early 2002); and to Fanghua Lin for his fundamental contributions to our understanding of the Ginzburg-Landau (GL) equations with a small parameter.

Eighteenth award: to Demetrios Christodoulou for his contributions to the mathematical theory of general relativity, and to Sergiu Klainerman for his contributions to nonlinear hyperbolic equations, and to Thomas Wolff for his work in harmonic analysis.

Seventeenth award: to Leon Simon for his profound contributions toward understanding the structure of singular sets for solutions of variational problems.

Sixteenth award: to Richard M. Schoen for his work on the application of partial differential equations to differential geometry, in particular his completion of the solution to the Yamabe Problem in Conformal deformation of a Riemannian metric to constant scalar curvature, Journal of Differential Geometry, volume 20 (1984), pp. 479-495.

Fifteenth award: to Richard B. Melrose for his solution of several outstanding problems in diffraction theory and scattering theory and for developing the analytical tools needed for their resolution.

Fourteenth award: to Luis A. Caffarelli for his deep and fundamental work in nonlinear partial differential equations, in particular his work on free boundary problems, vortex theory and regularity theory.

Thirteenth award: to Alberto P. Calderón in recognition of his fundamental work on the theory of singular integrals and partial differential equations, and in particular for his paper Cauchy integrals on Lipschitz curves and related operators, Proceedings of the National Academy of Sciences, USA, volume 74 (1977), pp. 1324-1327.

Twelfth award: to Donald S. Ornstein in recognition of his paper, Bernoulli shifts with the same entropy are isomorphic, Advances in Mathematics, volume 4 (1970), pp. 337-352.

Eleventh award: to I. M. Singer in recognition of his work on the index problem, especially his share in two joint papers with Michael F. Atiyah, The index of elliptic operators. I, III, Annals of Mathematics, Series 2, volume 87 (1968), pp. 484-530, 546-604.

Tenth award: to Paul J. Cohen for his paper, On a conjecture of Littlewood and idempotent measures, American Journal of Mathematics, volume 82 (1960), pp. 191-212.

Ninth award: to Louis Nirenberg for his work in partial differential equations.

Eighth award: to Norman Levinson for his contributions to the theory of linear, nonlinear, ordinary, and partial differential equations contained in his papers of recent years.

Seventh award: to A. C. Schaeffer and D. C. Spencer for their memoir, Coefficients of schlicht functions. I, II, III, IV, Duke Mathematical Journal, volume 10 (1943), pp. 611-635, volume 12 (1945), pp. 107-125, and the Proceedings of the National Academy of Sciences, volume 32 (1946), pp. 111-116, volume 35 (1949), pp. 143-150.

Sixth award: to Jesse Douglas for his memoirs, Green's function and the problem of Plateau, American Journal of Mathematics, volume 61 (1939), pp. 545-589; The most general form of the problem of Plateau, American Journal of Mathematics, volume 61(1939), pp. 590-608; and Solution of the inverse problem of the calculus of variations, Proceedings of the National Academy of Sciences, volume 25 (1939), pp. 631-637.

Fifth award: to John von Neumann for his memoir, Almost periodic functions and groups. I, II, Transactions of the American Mathematical Society, volume 36 (1934), pp. 445-492, and volume 37 (1935), pp. 21-50.

Fourth award: to Marston Morse for his memoir, The foundations of a theory of the calculus of variations in the large in m-space, Transactions of the American Mathematical Society, volume 31 (1929), pp. 379-404; and to Norbert Wiener for his memoir, Tauberian theorems, Annals of Mathematics, Series 2, volume 33 (1932),pp. 1-100.

Third award: to J. W. Alexander for his memoir, Combinatorial analysis situs, Transactions of the American Mathematical Society, volume 28 (1926), pp. 301-329.

Second award: to E. T. Bell for his memoir, Arithmetical paraphrases. I, II, Transactions of the American Mathematical Society, volume 22 (1921), pp. 1-30, 198-219; and to Solomon Lefschetz for his memoir, On certain numerical invariants with applications to Abelian varieties, Transactions of the American Mathematical Society, volume 22 (1921), pp. 407-482.

First award: to G. D. Birkhoff for his memoir, Dynamical systems with two degrees of freedom. Transactions of the American Mathematical Society, volume 18 (1917), pp. 199-300.

First award: to Geordie Williamson for his work on the representation theory of Lie algebras and algebraic groups. His results include proofs and re-proofs of some longstanding conjectures as well as spectacular counterexamples to the expected bounds in others.

Nineteenth award: The 2015 Frank Nelson Cole Prize in Algebra was awarded to Peter Scholze for his work on perfectoid spaces which has led to a solution of an important special case of the weight-monodromy conjecture of Deligne.

Eighteenth award: The 2012 Frank Nelson Cole Prize in Algebra was awarded to Alexander S. Merkurjev for his work on the essential dimension of groups.

Seventeenth award: The 2009 Frank Nelson Cole Prize in Algebra was awarded to Christopher Hacon and James McKernan for their groundbreaking joint work on higher dimensional birational algebraic geometry.

Sixteenth award: The 2006 Frank Nelson Cole Prize in Algebra was awarded to János Kollár for his outstanding achievements in the theory of rationally connected varieties and for his illuminating work on a conjecture of Nash.

Fifteenth award: The 2003 Frank Nelson Cole Prize in Algebra was awarded to Hiraku Nakajima for his work in representation theory and geometry.

Fourteenth award: The 2000 Frank Nelson Cole Prize in Algebra was awarded to Andrei Suslin for his work on motivic cohomology, and to Aise Johan de Jong for his important work on the resolution of singularities by generically finite maps.

Thirteenth award: The 1995 Frank Nelson Cole Prize in Algebra was awarded to Michel Raynaud and David Harbater for their solution of Abhyankar's conjecture. This work appeared in the papers Revêtements de la droite affine en caractéristique p > 0, Invent. Math. 116 (1994) 425-462 (Raynaud), and Abhyankar's conjecture on Galois groups over curves, Invent. Math. 117 (1994) 1-25 (Harbater).

Twelfth award: The 1990 Frank Nelson Cole Prize in Algebra was awarded to Shigefumi Mori for his outstanding work on the classification of algebraic varieties and, in particular, for his paper Flip theorem and the existence of minimal models for 3-folds, Journal of the American Mathematical Society, volume 1 (1988), pp. 117-253.

Eleventh award: The 1985 Frank Nelson Cole Prize in Algebra was awarded to George Lusztig for his fundamental work on the representation theory of finite groups of Lie type. In particular for his contributions to the classification of the irreducible representations in characteristic zero of the groups of rational points of reductive groups over finite fields, appearing in Characters of reductive groups over finite fields, Annals of Mathematics Studies, volume 107, Princeton University Press, 1984.

Tenth award: The 1980 Frank Nelson Cole Prize in Algebra was awarded to Michael Aschbacher for his paper, A characterization of Chevalley groups over fields of odd order, Annals of Mathematics, Series 2, volume 106 (1977), pp. 353-398; and to Melvin Hochster for his paper Topics in the homological theory of commutative rings, CBMS Regional Conference Series in Mathematics, Number 24, American Mathematical Society, 1975.

Ninth award: The 1975 Frank Nelson Cole Prize in Algebra was awarded to Hyman Bass for his paper, Unitary algebraic K-theory, Springer Lecture Notes in Mathematics, volume 343, 1973; and to Daniel G. Quillen for his paper, Higher algebraic K-theories, Springer Lecture Notes in Mathematics, volume 341, 1973.

Eighth award: The 1970 Frank Nelson Cole Prize in Algebra was awarded to John R. Stallings for his paper, On torsion-free groups with infinitely many ends, Annals of Mathematics, Series 2, volume 88 (1968), pp. 312-334; and to Richard G. Swan for his paper, Groups of cohomological dimension one, Journal of Algebra, volume 12 (1969), pp. 585-610.

Seventh award: The 1965 Frank Nelson Cole Prize in Algebra was awarded to Walter Feit and John G. Thompson for their joint paper, Solvability of groups of odd order, Pacific Journal of Mathematics, volume 13 (1963), pp. 775-1029.

Sixth award: The 1960 Frank Nelson Cole Prize in Algebra was awarded to Serge Lang for his paper, Unramified class field theory over function fields in several variables, Annals of Mathematics, Series 2, volume 64 (1956), pp. 285-325; and to Maxwell A. Rosenlicht for his papers, Generalized Jacobian varieties, Annals of Mathematics, Series 2, volume 59 (1954), pp. 505-530, and A universal mapping property of generalized Jacobians, Annals of Mathematics, Series 2, volume 66 (1957), pp. 80-88.

Fifth award: The 1954 Frank Nelson Cole Prize in Algebra was awarded toHarish-Chandra for his papers on representations of semisimple Lie algebras and groups, and particularly for his paper, On some applications of the universal enveloping algebra of a semisimple Lie algebra, Transactions of the American Mathematical Society, volume 70 (1951), pp. 28-96.

Fourth award: The 1949 Frank Nelson Cole Prize in Algebra was awarded to Richard Brauer for his paper, On Artin's L-series with general group characters, Annals of Mathematics, Series 2, volume 48 (1947), pp. 502-514.

Third award: The 1944 Frank Nelson Cole Prize in Algebra was awarded to Oscar Zariski for four papers on algebraic varieties published in the American Journal of Mathematics, volumes 61 (1939) and 62 (1940), and in the Annals of Mathematics, Series 2, volumes 40 (1939) and 41 (1940).

Second award: The 1939 Frank Nelson Cole Prize in Algebra was awarded to A. Adrian Albert for his papers on the construction of Riemann matrices published in the Annals of Mathematics, Series 2, volume 35 (1934) and volume 36 (1935)

.First award: The 1928 Frank Nelson Cole Prize in Algebra was awarded to L. E. Dickson for his book Algebren und ihre Zahlentheorie, Orell Füssli, Zürich and Leipzig, 1927.

Eighteenth award: The 2017 Frank Nelson Cole Prize in Number Theory was awarded to Henri Darmon for his contributions to the arithmetic of elliptic curves and modular forms.

Eighteenth award: The 2014 Frank Nelson Cole Prize in Number Theory was awarded to Yitang Zhang for his work on bounded gaps between primes and to Cem Y. Yildirim, János Pintz and Daniel Goldston were jointly awarded the 2014 Cole Prize in Number Theory for their work on small gaps between primes.

Seventeenth award: The 2011 Frank Nelson Cole Prize in Number Theory was awarded to Chandrashekhar Khare and Jean-Pierre Wintenberger for their remarkable proof of Serre's modularity conjecture.

Sixteenth award: The 2008 Frank Nelson Cole Prize in Number Theory Manjul Bhargava for his revolutionary work on higher composition laws.

Fifteenth award: The 2005 Frank Nelson Cole Prize in Number Theory Peter Sarnak for his fundamental contributions to number theory and in particular his book Random Matrices, Frobenius Eigenvalues and Monodromy, written jointly with his Princeton colleague Nicholas Katz.

Fourteenth award: The 2002 Frank Nelson Cole Prize in Number Theory Henryk Iwaniec for his fundamental contributions to analytic number theory, and to Richard Taylor for several outstanding advances in algebraic number theory.

Thirteenth award: The 1997 Frank Nelson Cole Prize in Number Theory Andrew J. Wiles for his work on the Shimura-Taniyama conjecture and Fermat's Last Theorem, published in Modular elliptic curves and Fermat's Last Theorem, Ann. of Math. 141 (1995), 443-551.

Twelfth award: The 1992 Frank Nelson Cole Prize in Number Theory Karl Rubin for his work in the area of elliptic curves and Iwasawa Theory with particular reference to his papers Tate-Shafarevich groups and L-functions of elliptic curves with complex multiplication and The "main conjectures" of Iwasawa theory for imaginary quadratic fields and to Paul Vojta for his work on Diophantine problems with particular reference to his paper Siegel's theorem in the compact case.

Eleventh award: The 1987 Frank Nelson Cole Prize in Number Theory To Dorian M. Goldfeld for his paper, Gauss's class number problem for imaginary quadratic fields, Bulletin of the American Mathematical Society, volume 13, (1985), pp. 23-37; and to Benedict H. Gross and Don B. Zagier for their paper, Heegner points and derivatives of L-Series, Inventiones Mathematicae, volume 84 (1986), pp. 225-320.

Tenth award: The 1982 Frank Nelson Cole Prize in Number Theory Robert P. Langlands for pioneering work on automorphic forms, Eisenstein series and product formulas, particularly for his paper Base change for GL(2), Annals of Mathematics Studies, volume 96, Princeton University Press, 1980; and to Barry Mazur for outstanding work on elliptic curves and Abelian varieties, especially on rational points of finite order, and his paper Modular curves and the Eisenstein ideal, Publications Mathematiques de l'Institut des Hautes Etudes Scientifiques, volume 47 (1977), pp. 33-186.

Ninth award: The 1977 Frank Nelson Cole Prize in Number Theory Goro Shimura for his two papers, Class fields over real quadratic fields and Heche operators, Annals of Mathematics, Series 2, volume 95 (1972), pp. 130-190; and On modular forms of half integral weight, Annals of Mathematics, Series 2, volume 97 (1973), pp. 440-481.

Eighth award: The 1972 Frank Nelson Cole Prize in Number Theory Wolfgang M. Schmidt for the following papers: On simultaneous approximation of two algebraic numbers by rationals, Acta Mathematica (Uppsala), volume 119 (1967), pp. 27-50; T-numbers do exist, Symposia Mathematica, volume IV, Academic Press, 1970, pp. 1-26; Simultaneous approximation to algebraic numbers by rationals, Acta Mathematica (Uppsala), volume 125 (1970), pp. 189-201; On Mahler's T-numbers, Proceedings of Symposia in Pure Mathematics, volume 20, American Mathematical Society, 1971, pp. 275-286.

Seventh award: The 1967 Frank Nelson Cole Prize in Number Theory James B. Ax and Simon B. Kochen for a series of three joint papers, Diophantine problems over local fields. I, II, III, American Journal of Mathematics, volume 87 (1965), pp. 605-630, 631-648, and Annals of Mathematics, Series 2, volume 83 (1966), pp. 437-456.

Sixth award: The 1962 Frank Nelson Cole Prize in Number Theory Kenkichi Iwasawa for his paper, Gamma extensions of number fields, Bulletin of the American Mathematical Society, volume 65 (1959), pp. 183-226; and to Bernard M. Dwork for his paper, On the rationality of the zeta function of an algebraic variety, American Journal of Mathematics, volume 82 (1960), pp. 631-648.

Fifth award: The 1956 Frank Nelson Cole Prize in Number Theory John T. Tate for his paper, The higher dimensional cohomology groups of class field theory, Annals of Mathematics, Series 2, volume 56 (1952), pp. 294-297.

Fourth award: The 1951 Frank Nelson Cole Prize in Number Theory Paul Erdös for his many papers in the theory of numbers, and in particular for his paper, On a new method in elementary number theory which leads to an elementary proof of the prime number theorem, Proceedings of the National Academy of Sciences, volume 35 (1949), pp. 374-385.

Third award: The 1946 Frank Nelson Cole Prize in Number Theory H. B. Mann for his paper, A proof of the fundamental theorem on the density of sums of sets of positive integers, Annals of Mathematics, Series 2, volume 43 (1942), pp. 523-527.

Second award: The 1941 Frank Nelson Cole Prize in Number Theory Claude Chevalley for his paper, La théorie du corps de classes, Annals of Mathematics, Series 2, volume 41 (1940), pp. 394-418.

First award: The 1931 Frank Nelson Cole Prize in Number Theory H. S. Vandiver for his several papers on Fermat's last theorem published in the Transactions of the American Mathematical Society and in the Annals of Mathematics during the preceding five years, with special reference to a paper entitled On Fermat's last theorem, Transactions of the American Mathematical Society, volume 31 (1929), pp. 613-642.

Fourth award: to Kristin Umland for her outstanding work toward improving mathematics education at the precollege level, especially her role in the development of the nonprofit organization Illustrative Mathematics.

Third award: to Michael Gage and Arnold Pizer for the creation and development of WeBWorK, one of the first web-based systems that assign and grade homework problems in mathematics and science courses.

Second award: to Jim Lewis because he created an atmosphere of commitment to teaching that established the department as a national model among mathematics departments in research universities where both teaching and research are highly valued, integrated, and rewarded.

First award: to Paul Sally, Jr. for his work with teachers and students at the precollege level, which began in the 1960s and continued unabated until the day of his death.

Seventeenth award: to David Bailey, Jonathan Borwein, Andrew Mattingly, and Glenn Wightwick forfor their article "The Computation of Previously Inaccessible Digits of π2 and Catalan's Constant," Notices of the AMS, August 2013.

Sixteenth award: to Daniel Rothman for his his paper "Earth's Carbon Cycle: A Mathematical Perspective", Bulletin of the AMS (2015). He gives the reader an understanding of the Earth's carbon cycle by applying classical ideas from applied mathematics to the data at hand.

Fifteenth award: to Jeffrey Lagarias and Chuanming Zong for their article, "Mysteries in Packing Regular Tetrahedra," which appeared in Notices of the AMS, Volume 59, No. 11, (2012), 1540-1549. The article leads the broad range of Notices readers through the 2000-year history of the subject, including its appearance in 1900 in Hilbert's 18-th problem, into its mathematical heart.

Fourteenth award: to Alex Kontorovich for his article, "From Apollonius to Zaremba: Local-global phenomena in thin orbits", which appeared in Bull. Amer. Math. Soc. 50. This article introduces a new field of number theory that has proven to be extremely fruitful, even in shedding light on some ancient problems.

Thirteenth award: to John Baez and John Huerta for their article, “The algebra of grand unified theories” (Bulletin Amer. Math. Soc., 47 (2010), no. 3, 483–552).

Twelfth award: to Persi Diaconis for his article, "The Markov chain Monte Carlo revolution" (Bulletin Amer. Math. Soc. 46 (2009), no. 2, 179–205).

Eleventh award: to David Vogan for his article, "The character table for E8" (Notices of the AMS 54 (2007), no. 9, 1122-1134).

Tenth award: to Bryna Kra for her article, "The Green-Tao Theorem on arithmetic progressions in the primes: An ergodic point of view" (Bull. Amer. Math. Soc. (N.S.) 43 (2006), no. 1, 3–23).

Ninth award: John Morgan for his article, "Recent Progress on the Poincaré Conjecture and the Classification of 3-Manifolds," Bulletin of the AMS 42 (2005), 57-78.

Eighth award: J. Brian Conrey for his article "The Riemann Hypothesis," Notices of the AMS 50 (2003) no. 3, 341-353; and to Shlomo Hoory, Nathan Linial, and Avi Wigderson for their article "Expander graphs and their applications", Bulletin of the AMS 43 (2006), no. 4, 439-561.

Seventh award: to Jeffrey Weeks for his article "The Poincare Dodecahedral Space and the Mystery of the Missing Fluctuations," Notices of the AMS 51 (2004) no. 6, 610-619.

Sixth award: to Ronald Solomon for his article “A Brief History of the Classification of the Finite Simple Groups ”, Bulletin of the AMS 38 (2001), no. 3, 315–352.

Fifth award: to Allen Knutson and Terence Tao for their stimulating article "Honeycombs and Sums of Hermitian Matrices" Notices of the AMS 48, no. 2 (2001), 175-186.

Fourth award: to Noam D. Elkies for his enlightening two-part article “Lattices, Linear Codes, and Invariants”, Notices of the AMS 47, nos. 10–11 (2000): Part I, 1238–45; Part II, 1382–91.

Third award: to Nicholas Katz and Peter Sarnak for their expository paper “Zeroes of zeta functions and symmetry ”, Bulletin of the AMS 36 1–26 (1999).

Second award: to Elliott H. Lieb and Jakob Yngvason for their article, "A Guide to Entropy and the Second Law of Thermodynamics, " Notices of the AMS 45, no. 5 (1998), 571-581.

First award: to Carl Pomerance for his paper,"A Tale of Two Sieves," Notices of the AMS 43, no. 12 (1996), 1473-1485.

Fifth award: John Friedlander and Henryk Iwaniec for their book Opera de Cribro (AMS, 2010).

Fourth award: to Cédric Villani for his book, *Optimal Transport: Old and New*. (Springer-Verlag, 2009).

Third award: to Peter Kronheimer and Tomasz Mrowka for their book Monopoles and Three-Manifolds (Cambridge University Press, 2007).

Second award: to Enrico Bombieri and Walter Gubler for their book Heights in Diophantine Geometry (Cambridge University Press, 2006).

First award: to William P. Thurston for his book Three-dimensional Geometry and Topology, edited by Silvio Levy (Princeton University Press, 1997).

Fourth award: to László Erdős and Horng-Tzer Yau for proving the universality of eigenvalue statistics of Wigner random matrices.

Third award: to Gregory W. Moore for his group of works on the structure of four-dimensional supersymmetric theories with extended supersymmetry.

Second award: to Herbert Spohn for his group of works on stochastic growth processes.

First award: to Hirosi Ooguri, Andrew Strominger, and Cumrun Vafa for their paper "Black hole attractors and the topological string", Physical Review D (3) 70 (2004), 106007.

Thirteenth award: to Francisco Santos for "A Counterexample to the Hirsch Conjecture", Annals of Mathematics, 2012.

Twelth award: to Sanjeev Arora, Satish Rao, and Umesh Vazirani for improving the approximation ratio for graph separators and related problems. ToAnders Johansson, Jeff Kahn, and Van H. Vu for determining the threshold of edge density above which a random graph can be covered by disjoint copies of a given smaller graph. To László Lovász and Balázs Szegedy for characterizing subgraph multiplicity in sequences of dense graphs.

Eleventh award: to M. Chudnovsky, N. Robertson, P. Seymour, and R. Thomas, "The strong perfect graph theorem," *Annals of Mathematics*, 164 (2006) 51-229; and to D. A. Spielman and S.-H. Teng, "Smoothed analysis of algorithms: Why the simplex algorithm usually takes polynomial time", *Journal of ACM* 51 (2004) 385-463; and to Thomas C. Hales, "A proof of the Kepler conjecture", *Annals of Mathematics* 162 (2005) 1063-1183; and to Samuel P. Ferguson, "Sphere Packings, V. Pentahedral Prisms", *Discrete and Computational Geometry* 33 (2006) 167-204.

Tenth award: to Manindra Agrawal, Neeraj Kayal and Nitin Saxena, "PRIMES is in P," *Annals of Mathematics*, Volume 160, issue 2, 2004, Pages 781--793; and to Mark Jerrum, Alistair Sinclair and Eric Vigoda, "A polynomial-time approximation algorithm for the permanent of a matrix with nonnegative entries," *J. ACM*, Volume 51, Issue 4, 2004, Pages 671--697; and to Neil Robertson and Paul D. Seymour, "Graph Minors. XX. Wagner's conjecture," *Journal of Combinatorial Theory*, Series B, Volume 92, Issue 2 , 2004, Pages 325--357.

Ninth award: to J. F. Geelen, A. M. H. Gerards and A. Kapoor, for "The Excluded Minors for GF(4)-Representable Matroids," Journal of Combinatorial Theory Series B, 79 (2000), no. 2, 247--299; and to Bertrand Guenin for "A characterization of weakly bipartite graphs," *Journal of Combinatorial Theory Series B*, 83 (2001), no. 1, 112--168; and to Satoru Iwata, Lisa Fleischer, and Satoru Fujishige for "A combinatorial strongly polynomial algorithm for minimizing submodular functions," Journal of the ACM, 48, July 2001, no. 4, 761--777; and to Alexander Schrijver for "A combinatorial algorithm minimizing submodular functions in strongly polynomial time," *Journal of Combinatorial Theory Series B*, 80 (2000), no. 2, 346--355.

Eighth award: to Michel X. Goemans and David P. Williamson for "Improved approximation algorithms for the maximum cut and satisfiability probelsm using semi-definite programming", *Journal of the Association for Computing Machinery*, 42 (1995), no. 6, pages 1115-1145; and to Michele Conforti, Gerard Cornuejols, and M. R. Rao for "Decomposition of balanced matrices", *Journal of Combinatorial Theory*, Series B, 77 (1999), no. 2, pages 292-406.

Seventh award: to Jeong Han Kim for "The Ramsey Number R(3,t) Has Order of Magnitude t2/log t," which appeared in *Random Structures and Algorithms*, volume 7, issue 3, 1995, pages 173-207.

Sixth award: to Louis Billera for "Homology of smooth splines: Generic triangulations and a conjecture of Strang", *Transactions of the AMS*, volume 310 (1988) pp. 325-340; to Gil Kalai for Upper bounds for the diameter and height of graphs of the convex polyhedra, Discrete and Computational Geometry, volume 8 (1992) pp. 363-372; and to Neil Robertson, Paul D. Seymour, and Robin Thomas for Hadwiger's conjecture for K6; free graphs, Combinatorica, volume 13 (1993) pp. 279-361.

Fifth award: to Martin Dyer, Alan Frieze, and Ravi Kannan for *A random polynomial time algorithm for approximating the volume of convex bodies*, Journal of the Association for Computing Machinery, volume 38/1 (1991) pp. 1-17; to Alfred Lehman for *The width-length inequality and degenerate projective planes*, W. Cook and P. D. Seymour (eds.), Polyhedral Combinatorics, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, volume 1, (American Mathematical Society, 1990) pp. 101-105; and to Nikolai E. Mnev for *The universality theorems on the classification problem of configuration varieties and convex polytope varieties*, O. Ya. Viro (ed.), Topology and Geometry-Rohlin Seminar, Lecture Notes in Mathematics 1346 (Springer-Verlag, Berlin, 1988) pp. 527-544.

Fourth award: to Eva Tardos for *A strongly polynomial minimum cost circulation algorithm*, Combinatorica, volume 5 (1985), pp. 247-256; and to Narendra Karmarkar for A new polynomial-time algorithm for linear programming, Combinatorica, volume 4 (1984), pp. 373-395.

Third award: to Jozsef Beck, for *Roth's estimate of the discrepancy of integer sequences is nearly sharp*, Combinatorica 1 (4),319-325, (1981); and H. W. Lenstra, Jr., for *Integer programming with a fixed number of variables*, Mathematics of Operations Research 8 (4), 538-548, (1983); and Eugene M. Luks for *Isomorphism of graphs of bounded valence can be tested in polynomial time*, Journal of Computer and System Sciences 25 (1), 42-65, (1982).

Second award: to D.B. Judin and A.S. Nemirovskii, for *Informational complexity and effective methods of solution for convex extremal problems*, Ekonomika i Matematicheskie Metody 12 (1976), 357-369, and to L. G. Khachiyan for *A polynomial algorithm in linear programming*, Akademiia Nauk SSSR. Doklady 244 (1979), 1093-1096; to G. P. Egorychev, for *The solution of van der Waerden's problem for permanents*, Akademiia Nauk SSSR. Doklady 258 (1981), 1041-1044, and D.I. Falikman, for *A proof of the van der Waerden conjecture on the permanent of a doubly stochastic matrix*, Matematicheskie Zametki 29 (1981), 931-938; and to M. Grötschel, L. Lovasz and A. Schrijver, for *The ellipsoid method and its consequences in combinatorial optimization*, Combinatorica 1 (1981), 169-197.

First award: to Richard M. Karp, for *On the computational complexity of combinatorial problems*, Networks, volume 5 (1975), pp. 45-68; to Kenneth Appel and Wolfgang Haken, for *Every planar map is four colorable*, Part I: Discharging, Illinois Journal of Mathematics, volume 21 (1977), pp. 429-490; and to Paul D. Seymour, for *The matroids with the max-flow min-cut property*, Journal of Combinatorial Theory, Series B, volume 23 (1977), pp. 189-222.

First award:

Fifth award: Caucher Birkar, Paolo Cascini, Christopher D. Hacon, and James McKernan received the 2016 AMS E. H. Moore Research Article Prize. They were honored for their article "Existence of minimal models for varieties of log general type," Journal of the AMS (2010).

Fourth award: To Michael Larsen and Richard Pink for their article “Finite subgroups of algebraic groups” (J. Amer. Math. Soc. 24 (2011), no. 4, 1105–1158).

Third award: to Sorin Popa for his article, *On the superrigidity of malleable actions with spectral gap* J. Amer. Math. Soc. 21 (2008), no. 4, 981–1000.

Second award: to Ivan Shestakov and Ualbai Umirbaev for their two ground-breaking papers, both published in the Journal of the American Mathematical Society: *The tame and the wild automorphisms of polynomial rings in three variables*, 17 (2004), no. 1, 197--227; *The tame and the wild automorphisms of polynomial rings in three variables*and *Poisson brackets and two-generated subalgebras of rings of polynomials*, 17 (2004), no. 1, 181--196.*Poisson brackets and two-generated subalgebras of rings of polynomials*

First award: to Mark Haiman for *Hilbert schemes, polygraphs, and the Macdonald positivity conjecture*, Journal of the AMS 14 (2001), 941?1006.a link

Twenty-second award: to David H. Yang for his outstanding research in algebraic geometry and geometric representation theory.

Twenty-first award: to Amol Aggarwal received for his outstanding research in combinatorics.

Twentieth award: to Levent Alpoge received for several contributions in the fields of number theory, probability, and combinatorics.

Nineteenth award: to Eric Larson for his truly exceptional record of research. He has so far authored or co-authored eight papers which have appeared in a wide spectrum of research journals.

Eighteenth award: to Fan Wei ”for her wide range of scholarly contributions".

Seventeenth award: to John Pardon for solving a problem on distortion of knots posed in 1983 by Mikhail Gromov.

Sixteenth award: to Maria Monks for her impressive work in combinatorics and number theory, which has appeared in Advances in Applied Mathematics, Proceedings of the AMS, Electronic Journal of Combinatorics, Discrete Mathematics, and Journal of Combinatorial Theory, Series A.

Fifteenth award: to Scott Duke Kominers for his outstanding and prolific record of undergraduate research spanning a broad range of topics, including number theory, computational geometry, and mathematical economics.

Fourteenth award: to Aaron Pixton for five impressive papers he has written, in addition to his Princeton senior thesis.

Thirteenth award: to Nathan Kaplan for four impressive papers in algebraic number theory.

Twelfth award: to Daniel Kane for establishing a research record that would be the envy of many professional mathematicians.

Eleventh award: to Jacob Fox for a most astounding collection of research papers by any undergraduate mathematician.

Tenth award: to Reid W. Barton for his paper "Packing densities of patterns ", Electron. J. Combin. 11 (2004), no. 1, Research Paper 80, 16 pp. Honorable Mention: To Po-Shen Loh.

Ninth award: to Melanie Wood for research on Belyi-extending maps and P -orderings. Honorable mention: To Karen Yeats.

Eighth award: to Joshua Greene for his work in combinatorics.

Seventh award: to Ciprian Manolescu for making a fundamental advance in the field by giving an elegant construction of Floer homology. Honorable mention: To Michael A. Levin.

Sixth award: to Jacob Lurie for his paper "On simply laced Lie algebras and their miniscule representations", Comment. Math. Helv. 76 (2001), no. 3, 515-575. Honorable mention: To Wai Ling Yee.

Fifth award: to Sean McLaughlin for his proof of the "Dodecahedral Conjecture," a major problem in discrete geometry related to, but distinct from, Kepler's sphere-packing problem and a conjecture that has resisted the efforts of the strongest workers in this area for nearly sixty years. Honorable mention: To Samit Dasgupta.

Fourth award: to Daniel Biss for his remarkable breadth, as well as depth. The most exciting aspect of his submission was his extension of a category which more closely binds the associations between combinatorial group theory and combinatorial topology. Honorable mention: To Aaron E. Archer.

Third award: to Jade Vinson for wide-ranging research in analysis and geometry.Honorable mention: To Vikaas Sohal.

Second award: to Manjul Bhargava for truly outstanding mathematical research in algebra. Honorable mention: To Lenhard L. Ng.

First award: to Kannan Soundararajan for truly exceptional research in analytic number theory. Honorable mention: To Kiran Kedlaya.

Fourth award: to Christoph Koutschan, Manuel Kauers, and Doron Zeilberger for their paper, "Proof of George Andrews's and David Robbins's q-TSPP conjecture," Proceedings of the National Academy of Sciences (USA) (2011).

Third award: to Alexander Razborov "for his paper, “On the minimal density of triangles in graphs” (Combinatorics, Probability and Computing 17 (2008), no. 4, 603–618), and for introducing a new powerful method, flag algebras, to solve problems in extremal combinatorics."

Second award: to Ileana Streinu of Smith College for her paper “Pseudo-triangulations, rigidity and motion planning”, Discrete Comput. Geom. 34 (2005), no. 4, 587–635.

First award: to Samuel P. Ferguson and Thomas C. Hales, for the paper "A proof of the Kepler conjecture," by Thomas C. Hales, Annals of Mathematics, 162 (2005), 1065-1185 (Section 5 of this paper is jointly authored with Ferguson).

First award: to Christiane Rousseau, Université de Montréal, in recognition of her many contributions furthering human values and the common good through mathematics.

Fourteenth award: to Laura DeMarco for her fundamental contributions to complex dynamics, potential theory, and the emerging field of arithmetic dynamics.

Thirteenth award: to Hee Oh for her fundamental contributions to the fields of dynamics on homogeneous spaces, discrete subgroups of Lie groups, and applications to number theory.

Twelfth award: to Maryam Mirzakhani for her deep contributions to the theory of moduli spaces of Riemann surfaces.

Eleventh award: to Amie Wilkinson for her remarkable contributions to the field of ergodic theory of partially hyperbolic dynamical systems.

Tenth award: to Laure Saint-Raymond for for her fundamental work on the hydrodynamic limits of the Boltzmann equation in the kinetic theory of gases.

Ninth award: to Claire Voisin for her deep contributions to algebraic geometry, and in particular for her recent solutions to two long-standing open problems: the Kodaira problem ( *On the homotopy types of compact Kähler and complex projective manifolds*, Inventiones Mathematicae, 157 (2004), no. 2, 329-343) and Green's Conjecture ( *Green's canonical syzygy conjecture for generic curves of odd genus*, Compositio Mathematica, 141 (2005), no. 5, 1163-1190; and *Green's generic syzygy conjecture for curves of even genus lying on a K3 surface*, Journal of the European Mathematical Society, 4 (2002), no. 4, 363-404).

Eighth award: to Svetlana Jitomirskaya for her pioneering work on non-perturbative quasiperiodic localization, in particular for results in her papers (1) *Metal-insulator transition for the almost Mathieu operator*, Ann. of Math. (2) 150 (1999), no. 3, 1159-1175, and (2) with J. Bourgain, *Absolutely continuous spectrum for 1D quasiperiodic operators*, Invent. Math. 148 (2002), no. 3, 453-463.

Seventh award: to Abigail Thompson for her outstanding work in 3-dimensional topology.

Sixth award: to Karen E. Smith for her outstanding work in commutative algebra, and to Sijue Wu for her work on a long-standing problem in the water wave equation.

Fifth award: to Bernadette Perrin-Riou for her number theoretical research on p-adic L-functions and Iwasawa theory.

Fourth award: to Ingrid Daubechies for her deep and beautiful analysis of wavelets and their applications.

Third award: to Sun-Yung Alice Chang for her deep contributions to the study of partial differential equations on Riemannian manifolds and in particular for her work on extremal problems in spectral geometry and the compactness of isospectral metrics within a fixed conformal class on a compact 3-manifold.

Second award: to Lai-Sang Young for her leading role in the investigation of the statistical (or ergodic) properties of dynamical systems.

First award: to Dusa McDuff for her outstanding work during the past five years on symplectic geometry.

Awarded to Jean Bourgain for the breadth of his contributions made in the advancement of mathematics.

Awarded to Martin Aigner and Günter M. Ziegler of the Freie Universität Berlin, for *Proofs from THE BOOK.*

Awarded to Sergey Fomin and Andrei Zelevinsky (posthumously) for their paper "Cluster algebras I: Foundations," published in 2002 in the Journal of the American Mathematical Society.

Awarded to James Arthur for his fundamental contributions to number theory and harmonic analysis, and in particular for his proof of the Arthur-Selberg trace formula.

Awarded to Dusa McDuff and Dietmar Salamon for their book J-holomorphic Curves and Symplectic Topology. It not only develops the topic from the basics, explaining essential notions and results in detail, but also describes many of the most spectacular results in this area.

Awarded to Leon Simon for his fundamental contributions to Geometric Analysis and in particular for his 1983 paper 'Asymptotics for a Class of Non-Linear Evolution Equations, with Applications to Geometric Problems', published in the Annals of Mathematics.

Awarded to Barry Simon for his impact on the education and research of a generation of mathematical scientists through his significant research achievements, his highly influential books, and his mentoring of graduate students and postdocs.

Awarded to David Cox, John Little and Donal O’Shea for their book Ideals, Varieties, and Algorithms, which has made algebraic geometry and computational commutative algebra accessible not just to mathematicians but to students and researchers in many fields.

Awarded to Andrew J. Majda for two papers published in the Memoirs of the AMS in 1983: “The existence of multidimensional shock fronts,” Vol 43, Number 281, and “The stability of multidimensional shock fronts,” Vol 41, Number 275.

Awarded to Victor Kac for his groundbreaking contributions to Lie Theory and its applications to Mathematics and Mathematical Physics.

Awarded to Robert Lazarsfeld for his books "Positivity in Algebraic Geometry I and II", published in 2004. These books were instant classics that have profoundly influenced and shaped research in algebraic geometry over the past decade.

Awarded to Rostislav Grigorchuk for his influential paper "Degrees of growth of finitely generated groups and the theory of invariant means," which appeared in Russian in 1984 in Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya and in English translation a year later. The paper stands as a landmark in the development of the now-burgeoning area of geometric group theory.

Awarded to Philip A. Griffiths for his contributions to our fundamental knowledge in mathematics, particularly algebraic geometry, differential geometry, and differential equations.

Awarded to Yuri Burago, Dmitri Burago, and Sergei Ivanov for their book *A Course in Metric Geometry*, in recognition of excellence in exposition and promotion of fruitful ideas in geometry.

Awarded to Luis Caffarelli, Robert Kohn, and Louis Nirenberg for their paper, "Partial regularity of suitable weak solutions of the Navier-Stokes equations." Communications Pure and Applied Math, vol 35 no 6, 771-831 (1982).

“for his pivotal role in shaping the theory of dynamical systems and for his groundbreaking contributions to ergodic theory, probability theory, statistical mechanics, and mathematical physics”

“in recognition of their book, *Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields* (Applied Mathematical Sciences, 42, Springer-Verlag, New York, 1983; reprinted with revisions and corrections, 1990).

For his book, *Classification Theory and the Number of Nonisomorphic Models* (Studies in Logic and the Foundations of Mathematics, 92, North-Holland Publishing Co., Amsterdam–New York, 1978; 2nd edition, 1990).

To Ivo M. Babuška for his many pioneering advances in the numerical solution of partial differential equations over the last half century.

To Michael Aschbacher, Richard Lyons, Steve Smith, and Ronald Solomon for their work, The classification of finite simple groups: groups of characteristic 2 type, Mathematical Surveys and Monographs, 172, American Mathematical Society, Providence, RI, 2011.

To William Thurston for his contributions to low dimensional topology, and in particular for a series of highly original papers, starting with “Hyperbolic structures on 3-manifolds. I. Deformation of acylindrical manifolds” (Ann. of Math. (2) 124 (1986), no. 2, 203–246), that revolutionized 3-manifold theory.

To John W. Milnor for standing out from the list of great mathematicians in terms of his overall achievements and his influence on mathematics in general, both through his work and through his excellent books.

To Henryk Iwaniec for his long record of excellent exposition, both in books and in classroom notes.

To Ingrid Daubechies for her paper, "Orthonormal bases of compactly supported wavelets" (*Communications on Pure and Applied Mathematics*, 41 (1988), no. 7, 909-996).

To William Fulton for playing a pivotal role in shaping the direction of algebraic geometry, forging and strengthening ties between algebraic geometry and adjacent fields, and teaching and mentoring several generations of younger mathematicians.

To David Eisenbud for his book, *Commutative Algebra: With a View Toward Algebraic Geometry* (Graduate Texts in Mathematics, 150, Springer-Verlag, New York, 1995. xvi+785 pp.)

To Robert L. Griess Jr. for his construction of the “Monster” sporadic finite simple group, which he first announced in “A construction of F1 as automorphisms of a 196,883-dimensional algebra” (Proc. Nat. Acad. Sci. U.S.A. 78 (1981), no. 2, part 1, 686–691) with details published in “The friendly giant” (Invent. Math. 69 (1982), no. 1, 1–102).

To Luis Caffarelli, one of the world's greatest mathematicians studying nonlinear partial differential equations (PDE).

To I.G. MacDonald for his book *Symmetric Functions and Hall Polynomials* (second edition, Clarendon Press, Oxford University Press, 1995).

To Richard Hamilton for his paper "Three-manifolds with positive Ricci curvature," *J. Differential Geom.* 17 (1982), 255-306.

To George Lusztig for entirely reshaping representation theory, and, in the process, changing much of mathematics.

To Neil Trudinger for his book *Elliptic Partial Differential Equations of Second Order*, written with the late David Gilbarg.

To Endre Szemerédi for his paper "On sets of integers containing no k elements in arithmetic progression", *Acta Arithmetica* XXVII (1975), 199-245.

To Henry P. McKean for his rich and magnificent mathematical career and for his work in analysis, which has a strong orientation towards probability theory.

To David Mumford for his beautiful expository accounts of a host of aspects of algebraic geometry, including *The Red Book of Varieties and Schemes* (Springer, 1988).

To Karen Uhlenbeck for her foundational contributions in analytic aspects of mathematical gauge theory. These results appeared in the two papers: "Removable singularities in Yang-Mills fields", *Communications in Mathematical Physics*, 83 (1982), 11-29 and "Connections with L:P bounds on curvature", *Communications in Mathematical Physics*, 83 (1982), 31-42.

To Frederick W. Gehring for being a leading figure in the theory of quasiconformal mappings for over fifty years; and to Dennis P. Sullivan for his fundamental contributions to many branches of mathematics.

To Lars V. Hörmander for his book, *The Analysis of Linear Partial Differential Operators*.

To Clifford S. Gardner, John M. Greene, Martin D. Kruskal, and Robert M. Miura for their paper “KortewegdeVries equation and generalizations. VI. Methods for exact solution”, *Comm. Pure Appl. Math.* 27 (1974), 97–133.

To Israel M. Gelfand for profoundly influencing many fields of research through his own work and through his interactions with other mathematicians and students.

To Branko Grünbaum for his book, *Convex Polytopes.*

To Robert P. Langlands for his paper "Problems in the theory of automorphic forms," (*Springer Lecture Notes in Math.* 170 (1970), 18-86). This is the paper that introduced what are now known as the Langlands conjectures.

To Cathleen Synge Morawetz for greatly influencing mathematics in the broad sense throughout her long and distinguished career.

To John W. Milnor in recognition of a lifetime of expository contributions ranging across a wide spectrum of disciplines including topology, symmetric bilinear forms, characteristic classes, Morse theory, game theory, algebraic K-theory, iterated rational maps…and the list goes on.

To Lawrence C. Evans and Nicolai V. Krylov for the “Evans-Krylov theorem” as first established in the papers: Lawrence C. Evans, “Classical solutions of fully nonlinear convex, second order elliptic equations”, *Communications in Pure and Applied Mathematics* 35 (1982), no. 3, 333–363; and N. V. Krylov, “Boundedly inhomogeneous elliptic and parabolic equations”, *Izvestiya Akad. Nauk* SSSR, ser. mat. 46 (1982), no. 3, 487–523; and translated in *Mathematics of the USSR, Izvestiya* 20 (1983), no. 3, 459–492.

To Ron Graham for being one of the principal architects of the rapid development worldwide of discrete mathematics in recent years; and to Victor Guillemin for playing a critical role in the development of a number of important areas in analysis and geometry.

To John B. Garnett for his book, Bounded Analytic Functions (Pure and Applied Mathematics, 96, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1981, xvi + 467 pp.)

To Ronald Jensen for his paper “The fine structure of the constructible hierarchy” (*Annals of Mathematical Logic* 4 (1972) 229–308); and to Michael Morley for his paper “Categoricity in power” (*Transactions of the AMS* 114 (1965) 514–538).

To Michael Artin for helping to weave the fabric of modern algebraic geometry, and to Elias Stein for making fundamental contributions to different branches of analysis.

To Yitzhak Katznelson for his book on harmonic analysis.

To Mark Goresky and Robert MacPherson for the papers, “Intersection homology theory”, Topology 19 (1980), no. 2, 135–62 (IH1) and “Intersection homology. II”, Invent. Math. 72 (1983), no. 1, 77–129 (IH2).

To Harry Kesten for his many and deep contributions to probability theory and its applications.

To Richard P. Stanley in recognition of the completion of his two-volume work *Enumerative Combinatorics*.

To Leslie F. Greengard and Vladimir Rokhlin for the paper "A fast algorithm for particle simulations", *J. Comput. Phys.* 73, no. 2 (1987), 325-348.

To Isadore M. Singer. Singer's series of five papers with Michael F. Atiyah on the Index Theorem for elliptic operators (which appeared in 1968-71) and his three papers with Atiyah and V.K. Patodi on the Index Theorem for manifolds with boundary (which appeared in 1975-76) are among the great classics of global analysis.

To John H. Conway in recognition of his many expository contributions in automata, the theory of games, lattices, coding theory, group theory, and quadratic forms.

To Barry Mazur for his paper "Modular curves and the Eisenstein ideal" in *Publications Mathematiques de l'Institut des Hautes Etudes Scientifiques*, no. 47 (1978), 33-186.

To Richard V. Kadison. For almost half a century, Professor Kadison has been one of the world leaders in the subject of operator algebras, and the tremendous flourishing of this subject in the last thirty years is largely due to his efforts.

To Serge Lang for his many mathematics books. Among Lang's most famous texts are *Algebra* [Addison-Wesley, Reading, MA, 1965; Second edition, 1984; Third edition, 1993, ISBN 0-201-55540-9] and *Algebraic Number Theory* [Addison-Wesley, Reading, MA, 1970; Second edition, Graduate Texts in Mathematics, 110, Springer-Verlag, New York, 1994, ISBN: 0-387-94225-4].

To Michael G. Crandall for two seminal papers: "Viscosity solutions of Hamilton-Jacobi equations" (joint with P.-L. Lions), *Trans. Amer. Math. Soc.* 277 (1983), 1-42, and "Generation of semi-groups of nonlinear transformations on general Banach spaces" (joint with T.M. Liggett), *Amer. J. Math.* 93 (1971), 265-298.

To John F. Nash for his remarkable paper: "The embedding problem for Riemannian manifolds," *Ann. of Math.* (2) 63 (1956) 20-63.

To Nathan Jacobson for his many contributions to research, teaching, exposition, and the mathematical profession. Few mathematicians have been as productive over such a long career or have had as much influence on the profession as has Professor Jacobson.

To Joseph Silverman for his books, *The Arithmetic of Elliptic Curves*, Graduate Texts in Mathematics 106, Springer-Verlag, New; York-Berlin, 1986; and *Advanced Topics in the Arithmetic of Elliptic Curves*, Graduate Texts in Mathematics 151, Springer-Verlag, New York, 1994.

To Herbert Wilf and Doron Zeilberger for their joint paper, "Rational functions certify combinatorial identities," *Journal of the American Mathematical Society*, 3 (1990) 147-158.

To Ralph S. Phillips for being one of the outstanding analysts of our time. His early work was in functional analysis: his beautiful theorem on the relation between the spectrum of a semigroup and its infinitesimal generator is striking as well as very useful in the study of PDEs. His extension theory for dissipative linear operators predated the interpolation approach to operator theory and robust control. He made major contributions to acoustical scattering theory in his joint work with Peter Lax, proving remarkable results on local energy decay and the connections between poles of the scattering matrix and the analytic properties of the resolvent. He later extended this work to a spectral theory for the automorphic Laplace operator, relying on the Radon transform on horospheres to avoid Eisenstein series. In the last fifteen years, Ralph Phillips has done brilliant work, in collaboration with others, on spectral theory for the Laplacian on symmetric spaces, on the existence and stability of cusp forms for general noncompact quotients of the hyperbolic plane, on the explicit construction of sparse optimal expander graphs, and on the structure of families of isospectral sets in two dimensions (the collection of drums that sound the same).

To Anthony W. Knapp for his book, *Representation Theory of Semisimple Groups (An overview based on examples)*, Princeton University Press, 1986, a beautifully written book which starts from scratch but takes the reader far into a highly developed subject.

To Mikhael Gromov for his paper, *Pseudo-holomorphic curves in symplectic manifolds*, Inventiones Math. 82 (1985), 307-347, which revolutionized the subject of symplectic geometry and topology and is central to much current research activity, including quantum cohomology and mirror symmetry.

To Goro Shimura for his important and extensive work on arithmetical geometry and automorphic forms; concepts introduced by him were often seminal, and fertile ground for new developments, as witnessed by the many notations in number theory that carry his name and that have long been familiar to workers in the field.

.To Bruce C. Berndt for the four volumes, *Ramanujan's Notebooks*, Parts I, II, III, and IV (Springer, 1985, 1989, 1991, and 1994).

To William Fulton for his book, Intersection Theory, Springer-Verlag, "Ergebnisse series," 1984.

To Daniel Stroock and S.R.S. Varadhan for their four papers: *Diffusion processes with continuous coefficients I and II*, Comm. Pure Appl. Math. 22 (1969), 345-400, 479-530; *On the support of diffusion processes with applications to the strong maximum principle*, Sixth Berkeley Sympos. Math. Statist. Probab., vol. III, 1970, pp. 333-360; *Diffusion processes with boundary conditions*, Comm. Pure Appl. Math. 34 (1971), 147-225; *Multidimensional diffusion processes*, Springer-Verlag, 1979.

To John T. Tate for scientific accomplishments spanning four and a half decades. He has been deeply influential in many of the important developments in algebra, algebraic geometry, and number theory during this time.

To Jean-Pierre Serre for his 1970 book *Cours d'Arithmétiqu*e, with its English translation, published in 1973 by Springer Verlag, *A Course in Arithmetic*.

To Edward Nelson for the following two papers in mathematical physics characterized by leaders of the field as extremely innovative: *A quartic interaction in two dimensions in Mathematical Theory of Elementary Particles*, MIT Press, 1966, pages 69-73; and *Construction of quantum fields from Markoff fields* in Journal of Functional Analysis, 12 (1973), 97-112. In these papers he showed for the first time how to use the powerful tools of probability theory to attack the hard analytic questions of constructive quantum field theory, controlling renormalizations with L^p estimates in the first paper, and in the second turning Euclidean quantum field theory into a subset of the theory of stochastic processes.

To Louis Nirenberg for his numerous basic contributions to linear and nonlinear partial differential equations and their application to complex analysis and differential geometry.

To Ingrid Daubechies for her book, *Ten Lectures on Wavelets* (CBMS 61, SIAM, 1992, ISBN 0-8987-1274-2).

To Louis de Branges for his proof of the Bieberbach Conjecture.

To Eugene B. Dynkin for his foundational contributions to Lie algebras and probability theory over a long period and his production of outstanding research students in both Russia and the United States, countries to whose mathematical life he has contributed so richly.

To Walter Rudin for his books *Principles of Mathematical Analysis*, McGraw-Hill (1953, 1964, and 1976); and *Real and Complex Analysis*, McGraw-Hill (1966, 1974, and1976).

To George Daniel Mostow for his paper *Strong rigidity of locally symmetric spaces*, Annals of Mathematics Studies, number 78, Princeton University Press (1973).

To Jacques Dixmier for his books *von Neumann Algebras (Algèbres de von Neumann )*, Gauthier-Villars, Paris (1957); *C*-Algebras (Les C*-Algèbres et leurs Representations )*, Gauthier-Villars, Paris (1964); and *Enveloping Algebras (Algèbres Enveloppantes)*, Gauthier-Villars, Paris (1974). [Note, since there wasn't an AMS-MAA Summer Meeting in 1992, this award was made at the January 1993 AMS-MAA Annual Meeting.]

To James Glimm for his paper, *Solution in the large for nonlinear hyperboic systems of conservation laws*, Communications on Pure and Applied Mathematics, XVIII (1965), pp. 697-715. [Note, since there wasn't an AMS-MAA Summer Meeting in 1992, this award was made at the January 1993 AMS-MAA Annual Meeting.]

To Peter D. Lax for his numerous and fundamental contributions to the theory and applications of linear and nonlinear partial differential equations and functional analysis, for his leadership in the development of computational and applied mathematics, and for his extraordinary impact as a teacher. [Note, since there wasn't an AMS-MAA Summer Meeting in 1992, this award was made at the January 1993 AMS-MAA Annual Meeting.]

To Jean-François Treves for *Pseudodifferential and Fourier Integral Operators*, Volumes 1 and 2 (Plenum Press, 1980).

To Eugenio Calabi for his fundamental work on global differential geometry, especially complex differential geometry.

To Armand Borel for his extensive contributions in geometry and topology, the theory of Lie groups, their lattices and representations and the theory of automorphic forms, the theory of algebraic groups and their representations and extensive organizational and educational efforts to develop and disseminate modern.

To R. D. Richtmyer for his book *Difference Methods for Initial-Value Problems* (Interscience, 1st Edition 1957 and 2nd Edition, with K. Morton, 1967).

To Bertram Kostant for his paper, *On the existence and irreducibility of certain series of representations*, Lie Groups and their Representations (1975), pp. 231-329.

To Raoul Bott for having been instrumental in changing the face of geometry and topology, with his incisive contributions to characteristic classes, K-theory, index theory, and many other tools of modern mathematics.

To Daniel Gorenstein for his book *Finite Simple Groups, An Introduction to their Classification* (Plenum Press, 1982); and his two survey articles *The Classification of Finite Simple Groups* and *Classifying the Finite Simple Groups*, Bulletin of the American Mathematical Society, volume 1 (1979) pp. 43-199, and volume 14 (1986) pp. 1-98, respectively.

To Alberto P. Calderón for his paper *Uniqueness in the Cauchy Problem for Partial Differential Equations*, American Journal ofMathematics, volume 80 (1958), pp. 16-36.

To Irving Kaplansky for his lasting impact on mathematics, particularly mathematics in America. By his energetic example, his enthusiastic exposition, and his overall generosity, he has made striking changes in mathematics and has inspired generations of younger mathematicians.

To Sigurdur Helgason for his books *Differential Geometry and Symmetric Spaces* (Academic Press, 1962), *Differential Geometry, Lie Groups, and Symmetric Spaces* (Academic Press, 1978); and *Groups and Geometric Analysis* (Academic Press, 1984).

To Gian-Carlo Rota for his paper *On the foundations of combinatorial theory, I. Theory of Möbius functions*, Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, volume 2 (1964), pp. 340-368.

To Deane Montgomery for his lasting impact on mathematics, particularly mathematics in America. He is one of the founders of the modern theory of transformation groups and is particularly known for his contributions to the solution of Hilbert's fifth problem.

To Martin Gardner for his many books and articles on mathematics and particularly for his column "Mathematical Games" in Scientific American.

To Herbert Federer and Wendell Fleming for their pioneering paper, *Normal and integral currents*, Annals of Mathematics, volume 72 (1960), pp. 458-520.

To Samuel Eilenberg for his fundamental contributions to topology and algebra, in particular for his classic papers on singular homology and his work on axiomatic homology theory which had a profound influence on the development of algebraic toplogy.

To Donald E. Knuth for his expository work, *The Art of Computer Programming*, 3 Volumes (1st Edition 1968, 2nd Edition 1973).

To Rudolf E. Kalman for his two fundamental papers: *A new approach to linear filtering and prediction problems*, Journal of Basic Engineering, volume 82, (1960), pp. 35-45; and *Mathematical description of linear dynamical systems*, SIAM Journal on Control and Optimization, volume 1 (1963), pp. 152-192; and for his contribution to a third paper(with R. S. Bucy), *New results in linear filtering and prediction theory*, Journal of Basic Engineering, volume 83D (1961), pp. 95-108.

To Saunders Mac Lane for his many contributions to algebra and algebraic topology, and in particular for his pioneering work in homological and categorical algebra.

To Michael Spivak for his five-volume set, *A Comprehensive Introduction to Differential Geometry* (second edition, Publish or Perish, 1979).

To Robert Steinberg for three papers on various aspects of the theory of algebraic groups: *Representations of algebraic groups*, Nagoya Mathematical Journal, volume 22 (1963), pp. 33-56; *Regular elements of semisimple algebraic groups*, Institut des Hautes Études Scientifiques, Publications Mathématiques, volume 25 (1965), pp. 49-80; and *Endomorphisms of linear algebraic groups*, Memoirs of the American Mathematical Society, volume 80 (1968).

To Hassler Whitney for his fundamental work on geometric problems, particularly in the general theory of manifolds, in the study of differentiable functions on closed sets, in geometric integration theory, and in the geometry of the tangents to a singular analytic space.

To Elias M. Stein for his book, Singular integrals and the differentiability properties of functions, Princeton University Press (1970).

To Lennart Carleson for his papers: An interpolation problem for bounded analytic functions, American Journal of Mathematics, volume 80 (1958), pp. 921-930; Interpolation by bounded analytic functions and the Corona problem, Annals of Mathematics (2), volume 76 (1962), pp. 547-559; and On convergence and growth of partial sums of Fourier series, Acta Mathematica volume 116 (1966), pp. 135-157.

To Joseph L. Doob for his fundamental work in establishing probability as a branch of mathematics and for his continuing profound influence on its development.

To Paul R. Halmos for his many graduate texts in mathematics and for his articles on how to write, talk and publish mathematics.

To Steven C. Kleene for three important papers which formed the basis for later developments in generalized recursion theory and descriptive set theory: *Arithmetical predicates and function quantifier*s, Transactions of the American Mathematical Society 79 (1955), pp. 312-340; *On the forms of the predicates in the theory of constructive ordinals* (second paper), American Journal of Mathematics 77 (1955), pp. 405-428; and *Hierarchies of number-theoretic predicates*, Bulletin of the American Mathematical Society 61 (1955), pp. 193-213.

To Shiing-Shen Chern for the cumulative influence of his total mathematical work, high level of research over a period of time, particular influence on the development of the field of differential geometry, and influence on mathematics through Ph.D. students.

To Lars V. Ahlfors for his expository work in Complex analysis (McGraw-Hill Book Company, New York, 1953), and in Lectures on quasiconformal mappings (D. Van Nostrand Co., Inc., New York, 1966) and Conformal invariants (McGraw-Hill Book Company, New York, 1973).

To Tsit-Yuen Lam for his expository work in his book *Algebraic theory of quadratic forms* (1973), and four of his papers: *K_0 and K_1-an introduction to algebraic K-theory* (1975), *Ten lectures on quadratic forms over fields* (1977), *Serre's conjecture* (1978), and *The theory of ordered fields* (1980).

To John W. Milnor for a paper of fundamental and lasting importance, *On manifolds homeomorphic to the 7-sphere*, Annals of Mathematics (2) 64 (1956), pp. 399-405.

To Fritz John for the cumulative influence of his total mathematical work, high level of research over a period of time, particular influence on the development of a field, and influence on mathematics through Ph.D. students.

To Oscar Zariski for his work in algebraic geometry, especially his fundamental contributions to the algebraic foundations of this subject.

To Eberhard Hopf for three papers of fundamental and lasting importance: *Abzweigung einer periodischen Lösung von einer stationären Lösung eines Differential systems*, Berichte über die Verhandlungen der Sächsischen Akademie der Wissenschaften zu Leipzig. Mathematisch-Naturwissenschaftliche Klasse, volume 95 (1943), pp. 3-22; *A mathematical example displaying features of turbulence*, Communications on Applied Mathematics, volume 1 (1948), pp. 303-322; and *The partial differential equation u_t + uu_x = u_{xx}*, Communications on Pure and Applied Mathematics, volume 3 (1950), pp. 201-230.

To Nelson Dunford and Jacob T. Schwartz for their expository book, *Linear operators*, Part I, *General theory*, 1958; Part II, *Spectral theory*, 1963; Part III, *Spectral operators*, 1971, Interscience Publishers, New York.

To André Weil for the total effect of his work on the general course of twentieth century mathematics, especially in the many areas in which he has made fundamental contributions.

To Harold M. Edwards for mathematical exposition in his books Riemann's zeta function, Pure and Applied Mathematics, number 58, Academic Press, New York and London, 1974; and Fermat's last theorem, Graduate Texts in Mathematics, number 50, Springer-Verlag, New York and Berlin, 1977.

To Gerhard P. Hochschild for his significant work in homological algebra and its applications.

To Antoni Zygmund for his cumulative influence on the theory of Fourier series, real variables, and related areas of analysis.

To Robin Hartshorne for his expository research article Equivalence relations on algebraic cycles and subvarieties of small codimension, Proceedings of Symposia in Pure Mathematics, volume 29, American Mathematical Society, 1975, pp. 129-164; and his book Algebraic geometry, Springer-Verlag, Berlin and New York, 1977.

To Joseph J. Kohn for his fundamental paper: Harmonic integrals on strongly convex domains. I, II, Annals of Mathematics, Series 2, volume 78 (1963), pp. 112-248 and volume 79 (1964), pp. 450-472.

To Salomon Bochner for his cumulative influence on the fields of probability theory, Fourier analysis, several complex variables, and differential geometry.

To Hans Lewy for three fundamental papers: *On the local character of the solutions of an atypical linear differential equation in three variables and a related theorem for regular functions of two complex variables*, Annals of Mathematics, Series 2, volume 64 (1956), pp. 514-522; *An example of a smooth linear partial differential equation without solution*, Annals of Mathematics, Series 2, volume 66 (1957), pp. 155-158; *On hulls of holomorphy*, Communications in Pure and Applied Mathematics, volume 13 (1960), pp. 587-591.

No awards made.

No awards made.

No awards made.

To George W. Mackey for his paper, *Ergodic theory and its significance for statistical mechanics and probability theory*, Advances in Mathematics, volume 12 (1974), pp. 178-286.

To H. Blaine Lawson for his paper, *Foliations*, Bulletin of the American Mathematical Society, volume 80 (1974), pp. 369-418.

To Lipman Bers for his paper, *Uniformization, moduli, and Kleinian groups*, Bulletin of the London Mathematical Society, volume 4 (1972), pp. 257-300.

To Martin D. Davis for his paper, *Hilbert's tenth problem is unsolvable*, American Mathematical Monthly, volume 80 (1973), pp. 233-269.

To Joseph L. Taylor for his paper, *Measure algebras*, CBMS Regional Conference Series in Mathematics, Number 16, American Mathematical Society, 1972.

To Edward B. Curtis for his paper, *Simplicial homotopy theory*, Advances in Mathematics, volume 6 (1971), pp. 107-209.

To William J. Ellison for his paper, *Waring's problem*, American Mathematical Monthly, volume 78 (1971), pp. 10-36.

To Lawrence E. Payne for his paper, *Isoperimetric inequalities and their applications*, SIAM Review, volume 9 (1967), pp. 453-488.

To Dana S. Scott for his paper, *A proof of the independence of the continuum hypothesis*, Mathematical Systems Theory, volume 1 (1967), pp. 89-111.

To James B. Carrell for his paper, written jointly with Jean A. Dieudonne, *Invariant theory, old and new*, Advances in Mathematics, volume 4 (1970), pp. 1-80.

To Jean A. Dieudonné for his paper, *Algebraic geometry, Advances in Mathematics*, volume 3 (1969), pp. 233-321, and for his paper, written jointly with James B. Carrell, Invariant theory, old and new, Advances in Mathematics, volume 4 (1970), pp. 1-80.

To Phillip A. Griffiths for his paper, *Periods of integrals on algebraic manifolds*, Bulletin of the American Mathematical Society, volume 76 (1970), pp. 228-296.

To Solomon Lefschetz for his paper, *A page of mathematical autobiography*, Bulletin of the American Mathematical Society,volume 74 (1968), pp. 854-879.

Nineteenth award: The 2016 Veblen Prize was awarded to Fernando Codá Marques and André Neves, for "their remarkable work on variational problems in differential geometry [including] the proof of the Willmore conjecture". This work resolved a longstanding question about the nature of surfaces.

Eighteenth award: The 2013 Veblen Prize was awarded to Ian Agol, for his many fundamental contributions to hyperbolic geometry, 3-manifold topology, and geometric group theory and to Daniel Wise, for his deep work establishing subgroup separability (LERF) for a wide class of groups and for introducing and developing with Frédéric Haglund the theory of special cube complexes which are of fundamental importance for the topology of three-dimensional manifolds.

Seventeenth award: to Tobias H. Colding and William P. Minicozzi II for their profound work on minimal surfaces; and to Paul Seidel for his fundamental contributions to symplectic geometry.

Sixteenth award: to Peter Kronheimer and Tomasz Mrowka for their joint contributions to both three- and four-dimensional topology through the development of deep analytical techniques and applications; and to Peter Ozsváth and Zoltán Szabó for their contributions to 3- and 4-dimensional topology through their Heegaard Floer homology theory.

Fifteenth award: to David Gabai for his work in geometric topology, in particular, the topology of 3-dimensional manifolds.

Fourteenth award: to Jeff Cheeger for his work in differential geometry, to Yakov Eliashberg for his work in symplectic and contact topology, and to Michael J. Hopkins for his work in homotopy theory.

Thirteenth award: to Richard Hamilton for his continuing study of the Ricci flow and related parabolic equations for a Riemannian metric, and to Gang Tian for his contributions to geometric analysis.

Twelfth award: to Andrew J. Casson for his work on the topology of low-dimensional manifolds, and to Clifford H. Taubes for his foundational work in Yang-Mills theory.

Eleventh award: to Michael H. Freedman for his work in differential geometry and, in particular, the solution of the four-dimensional Poincaré conjecture.

Tenth award: to Shing-Tung Yau for his work in nonlinear partial differential equations, his contributions to the topology of differentiable manifolds, and for his work on the complex Monge-Ampµere Equations on compact complex manifolds.

Ninth award: to Mikhael Gromov for his work relating topological and geometric properties of Riemannian manifolds.

Eighth award: to James Simons for his work on minimal varieties and characteristic forms.

Seventh award: to William P. Thurston for his work on foliations.

Sixth award: to Dennis P. Sullivan for his work on the Hauptvermutung summarized in the paper,*On the Hauptvermutung for manifolds*, Bulletin of the American Mathematical Society, volume 73 (1967), pp. 598-600.

Fifth award: to Robion C. Kirby for his paper, Stable homeomorphisms and the annulus conjecture, Annals of Mathematics, Series 2, volume 89 (1969), pp.575-582.

Fourth award: to Morton Brown and Barry Mazur for their work on the generalized Schoenflies theorem.

Third award: to Stephen Smale for his contributions to various aspects of differential topology.

Second award: to Raoul Bott for his papers, *The space of loops on a Lie grou*p, Michigan Mathematical Journal, volume 5 (1958), pp. 35-61, and *The stable homotopy of the classical groups*, Annals of Mathematics, Series 2, volume 70 (1959), pp. 313-337.

First award: to C. D. Papakyriakopoulos for his papers, *On Solid Tori*, Annals of Mathematics, Series 2, volume 66 (1957), pp. 1-26, and *On Dehn's lemma and the asphericity of knots*, Proceedings of the National Academy of Sciences, volume 43 (1957), pp. 169-172.

Fifth award: to Umberto Bottazzini was awarded the 2015 Whiteman Prize for his many works in the history of mathematics, notably on the rise of modern mathematics in Italy and on analysis in the 19th and early 20th centuries.

Fourth award: to Joseph Warren Dauben for his contributions to the history of Western and Chinese mathematics, and for deepening and broadening the international mathematical community’s awareness and understanding of its history and culture.

Third award: to Jeremy John Gray for his many historical works, which have not only shed great light on the history of modern mathematics but also have given an example of the ways in which historical scholarship can contribute to the understanding of mathematics and its philosophy.

Second award: to Harold M. Edwards to pay tribute to his many publications over several decades that have fostered a greater understanding and appreciation of the history of mathematics, especially the theory of algebraic numbers.

First award: to Thomas Hawkins to recognize an outstanding historian of mathematics whose current research and numerous publications display the highest standards of mathematical and historical sophistication.

Thirteenth award: to Constantine M. Dafermos for his foundational work in partial differential equations and continuum physics.

Twelfth award: to Andrew Majda “his groundbreaking work in theoretical fluid mechanics and its application to problems in atmospheric science and oceanography.”

Eleventh award: to David L. Donoho for introducing novel fundamental and powerful mathematical tools in signal processing and image analysis.

Tenth award: to Craig Tracy and Harold Widom for their deep and original work on Random Matrix Theory, a subject which has remarkable applications across the scientific spectrum, from the scattering of neutrons off large nuclei to the behavior of the zeros of the Riemann zeta-function.

Ninth award: to James A. Sethian for his seminal work on the computer representation of the motion of curves, surfaces, interfaces, and wave fronts, and for his brilliant applications of mathematical and computational ideas to problems in science and engineering.

Eighth award: to Alexandre J. Chorin in recognition of his seminal work in computational fluid dynamics, statistical mechanics, and turbulence; and to Arthur T. Winfree in recognition of his profound impact on the field of biological rhythms, otherwise known as coupled nonlinear oscillators.

Seventh award: to Hermann Flaschka for deep and original contributions to our understanding of completely integrable systems; and to Ciprian Foias, for basic contributions to operator theory, analysis, and dynamics and their applications.

Sixth award: to Michael Aizenman for his outstanding contribution of original and non-perturbative mathematical methods in statistical mechanics by means of which he was able to solve several long open important problems concerning critical phenomena, phase transitions, and quantum field theory; and to Jerrold E. Marsden for his outstanding contributions to the study of differential equations in mechanics: he proved the existence of chaos in specific classical differential equations; his work on the momentum map, from abstract foundations to detailed applications, has had great impact.

Fifth award: to Clifford S. Gardner for his contributions to applied mathematics in the areas of supersonic aerodynamics, plasma physics and hydromagnetics, and especially for his contributions to the truly remarkable development of inverse scattering theory for the solution of nonlinear partial differential equations.

Fourth award: to Gerald B. Whitham for his broad contributions to the understanding of fluid dynamical phenomena and his innovative contributions to the methodology through which that understanding can be constructed.

Third award: to Tosio Kato for his distinguished work in the perturbation theory of quantum mechanics.

Second award: to Peter D. Lax for his broad contributions to applied mathematics, in particular, for his work on numerical and theoretical aspects of partial differential equations and on scattering theory.

First award: to Richard E. Bellman for his pioneering work in the area of dynamic programming, and for his related work on control, stability, and differential-delay equations.

Forty-second award

Forty-first award

Fortieth award to Xinwen Zhu

Thirty-ninth award: to Karin Melnick

Thirty-eighth award: to Andrew S. Toms

Thirty-seventh award: to Joel Bellaiche

Thirty-sixth award: to Antonio Montalban

Thirty-fifth award: to Christopher Hoffman

Thirty-fourth award: to Martin Kassabov

Thirty-third award: to Christopher Hacon and to Bryna Kra

Thirty-second award: to Yuan-Pin Lee and Mihnea Popa

Thirty-first award: to Jinho Baik and to Nitu Kitchloo

Thirtieth award: to Henry H. Kim and to John E. Meier

Twenty-ninth award: to Albert C. Fannjiang and to Wee Teck Gan and to Ravi Kumar Ramakrishna

Twenty-eighth award: to Ivan Dimitrov, Ravi Vakil, Jiahong Wu, Meijun Zhu

Twenty-seventh award: to Siqi Fu, Christopher Herald, Wei-Dong Ruan, Vasily Strela

Twenty-sixth award: to Charles W. Rezk, Bin Wang, Changyou Wang, and Tonghai Yang

Twenty-fifth award: to Mark Andrea A. de Cataldo, Stavros Garoufalidis, Sándor Kovács, and Yanguang Li

Twenty-fourth award: to Ovidiu Costin,Fred Diamon, Gang Liu, Zhongwei, and Stephanie Frank Singer

Twenty-third award: to Yi Hu,Robert McCann, Alexander Voronov, and Jiaping Wang

Twenty-second award: to Rafael de la Llave, William Gordon McCallum, and Kent Edward Orr

Twenty-first award: to Patricia E. Bauman and David E. Marker

Twentieth award: to Jacques Hurtubise, Andre Scedrov, and David Webb

Nineteenth award: to Krzysztof Burdzy, William Menasco, and David Morrison

Eighteenth award: to Daniel Bump and Kari Vilonen

Seventeenth award: to Michael Anderson, Carolyn Gordon, and Steven Mitchell

Sixteenth award: to Isaac Y. Efrat, John M. Lee, and Ralf J. Spatzier

Fifteenth award: to Steven R. Bell, Don M. Blasius, and David Gabai

Fourteenth award: to Richard Hain and Bill Jacob

Thirteenth award: to Dinakar Ramakrishnan

Twelfth award: to R. Michael Beals

Eleventh award: to Richard Timothy Durrett

Tenth award: to Russell David Lyons

Ninth award: to Nicholas J. Kuhn

Eighth award: to Lawrence Man-Hou Ein and Mark William

Seventh award: to Robert K. Lazarsfeld, Thomas H. Parker, and Robert Sachs

Sixth award: to Scott W. Brown, Jeffrey E. Hoffstein, Jeffry N. Kahn, James E. McClure, Rick L. Smith, and Mark Steinberger

Fifth award: to Alan Dankner, David Harbater, Howard Hiller, Steven P. Kerckhoff, and Robert C. McOwen

Fourth award: to Steven Kalikow, Charles Patton, Duong-Hong Phong, and David Vogan

Third award: to Fredric D. Ancel and Joseph A. Sgro

Second award: to Terence J. Gaffney, Paul Nèvai, and George M. Reed

First award: to Fred G. Abramson and James Li-Ming Wang

Twenty-sixth award: The Award for Expository and Popular Books to Siobhan Roberts for for her engaging biographies of eminent mathematicians and articles about mathematics that are appreciated by the general public and scientific audiences alike and the Award for Public Outreach to Arthur Benjamin for his ability and commitment to share the joy of mathematics, and excites and engages audiences at all levels.

Twenty-fifth award: The Award for Expository and Popular Books to Simon Singh for his numerous books and productions which bring mathematics vividly to life and the Award for Public Outreach to the Museum of Mathematics for enhancing public understanding and perception of mathematics through dynamic exhibits and programs.

Twenty-fourth award: to Nate Silver for his award-winning FiveThirtyEight.com website, his New York Times best-seller The Signal and the Noise: Why Most Predictions Fail—But Some Don’t (2012), and a host of other ways in which he has helped the public to better understand the world through sound and innovative use of statistics and extraordinarily lucid explanations of his work.

Twenty-third award: to Danica McKellar because her books, blog, and public appearances have encouraged countless middle and high school students, especially girls, to be more interested in mathematics.

Twenty-second award: to John Allen Paulos "because his books, columns, reviews, speeches, and editorials have for more than twenty-five years brought mathematically informed ideas, information, opinion, and humor to a broad nonspecialist audience."

Twenty-first award: to Dana Mackenzie for a remarkably broad and deep body of writing for experts and nonexperts alike.

Twentieth award: to Nicolas Falacci and Cheryl Heuton for their positive portrayal of the power and fun of mathematics through their hit TV series, *Numb3rs*.

Nineteenth award: to Marcus du Sautoy for complementing his love of mathematical discovery with a passion for communicating mathematics to a broad public.

Eighteenth award: to George Csicsery for communicating the beauty and fascination of mathematics and the passion of those who pursue it.

Seventeenth award: to Carl Bialik for increasing the public's understanding of mathematical concepts.

Sixteenth award: to Steven H. Strogatz for making a consistent effort to reach out to a wider audience.

Fifteenth award: to Roger Penrose for the discovery of Penrose tilings, which have captured the public’s imagination, and for an extraordinary series of books that brought the subject of consciousness to the public in mathematical terms.

Fourteenth award: to Barry Cipra for writing about mathematics of every kind—from the most abstract to the most applied—for nearly twenty years. His lucid explanations of complicated ideas at the frontiers of research have appeared in dozens of articles in newspapers, magazines, and books.

no award given

Thirteenth award: to Robert Osserman for being an erudite spokesman for mathematics, communicating its charm and excitement to thousands of people from all walks of life.

Twelfth award: to Helaman Ferguson and Claire Ferguson for dazzling the mathematical community and a far wider public with exquisite sculptures embodying mathematical ideas, along with artful and accessible essays and lectures elucidating the mathematical concepts.

Eleventh award: to Keith J. Devlin for his many contributions to public understanding of mathematics through great numbers of radio and television appearances; public talks; books; and articles in magazines, newsletters, newspapers, journals, and online.

Tenth award: to Sylvia Nasar for *A Beautiful Mind*, her biography of John Forbes Nash, Jr.

Ninth award: to Ian Stewart for communicating the excitement of science and mathematics to millions of people around the world for more than twenty years and to John Lynch and Simon Singh for their exceptional contributions to public understanding of mathematics through their documentary on Andrew Wiles and the Fermat Conjecture, entitled "Fermat's Last Theorem" (shown on NOVA as "The Proof").

Eighth award: to Constance Reid for writing about mathematics with grace, knowledge, skill and clarity.

Seventh award: to Philip J. Davis for being a prolific communicator of mathematics to the general public.

Sixth award: to Gina Kolata for consistently giving outstanding coverage to many of the most exciting breakthroughs in mathematics and computer science over the past twenty years.

Fifth award: to Martin Gardner, for authoring numerous books and articles about mathematics, including his long-running *Scientific American* column, "Mathematical Games," and his books, *Fads and Fallacies in the Name of Science* and *Mathematical Carnival*.

Fourth award: to Joel Schneider for "Square One TV."

Third award: to Ivars Peterson for exceptional skill in communicating mathematics to the general public over the last decade.

Second award: to Hugh Whitemore for contributions to communicating mathematics to the public in his play, "Breaking the Code," which chronicles the brilliant but troubled life of the British mathematician Alan Turing.

First award: to James Gleick for sustained and outstanding contributions in communicating mathematics to the general public.

Fifteenth awards.

Fourteenth awards.

Thirteenth awards.

Twelfth awards.

Eleventh awards.

Tenth award.

Ninth awards.

Eighth awards.

Seventh awards.

Sixth awards.

Fifth awards.

Fourth awards.

Third awards.

Second awards.

First awards.

Twelfth award: the Department of Mathematics at the University of Illinois at Urbana-Champaign.

Eleventh award: the Department of Mathematics at California State University at Northridge.

Tenth award: to Iowa State University

Ninth award: to Williams College

Eighth award: to University of Texas at Arlington.

Seventh award: to Bryn Mawr College

Sixth award: to University of Arizona

Fifth award: to North Carolina State University

Fourth award: to University of Nebraska Lincoln

Third award: to University of Iowa

Second award: to University of California, Los Angeles

First award: to Harvey Mudd College

Ninth award: Best photograph, painting, or print was awarded to Doug Dunham and John Shier for "Fractal Monarchs," a 30 x 40 cm digital print. Best textile, sculpture, or other medium was awarded to Jiangmei Wu for "Torus", made of Hi-tec Kozo Paper and 45 x 45 x 20 cm. Honorable Mention was awarded to Mary Klotz for " AAABBB, two juxtapositions: Dots & Blossoms, Windmills & Pinwheels". This work made of hand dyed silk ribbon is 66 x 46 x 3 cm.

Eighth award: Best photograph, painting, or print was awarded to Karl Kattchee for for "45 Poppies," a 18 x 31 cm digital print. Best textile, sculpture, or other medium was awarded to George Hart for Sword Dancing". The work is made of wood (dyed) and cable ties and measures 32 x 45 x 45 cm. Honorable Mention was awarded to Robert Orndorff for "OSU Triptych No. 2". The paper and acrylic triptych is 20 x 46 cm.

Seventh award: Best photograph, painting, or print was awarded to Kerry Mitchell for "Penrose Pursuit 2," a 16" high x 20" wide digital print onto an aluminum panel. Best textile, sculpture, or other medium was awarded to Susan Goldstine for "Map Coloring Jewelry Set". The set includes glass beads, gold-filled beads, thread, and ear wires. Honorable Mention was awarded to Aaron Pfitzenmaier for "15 Irregular Hexahedra," made of paper, 10.5" x 10.5" x 10.

Sixth award: "Enigmatic Plan of Inclusion I and II," by Conan Chadbourne was awarded Best photograph, painting, or print. "Three-Fold Development," by Robert Fathauer was awarded Best textile, sculpture, or other medium. "Blue Torus," by Faye E. Goldman received Honorable Mention.

Fifth award: Vladimir Bulatov was awarded best photograph, painting, or print for his work "Bended Circle Limit III," a 24 x 24 inch digital print. Kevin Lee for was awarded best textile, sculpture, or other medium for his inlaid wooden box, "Inlaid Wooden Boxes of Makoto Nakamura's Tessellations," 4 x 4 x 4 inches, made of cherry, maple, walnut, oak, butternut, and mahogany. Susan Goldstine received honorable mention for "Tessellation Evolution," her beaded necklace, 18 inches x 15 inches, made of glass beads, gold-plated glass beads, onyx beads, gold-plated clasp, and thread.

Fourth award: First place to Sylvie Donmoyer for "Still Life with Magic Square" ; second place award to Thomas Hull, Robert Lang, and Ray Schamp for "Pleated Multi-sliced Cone,"; and third place award to Carlo H. Séquin for "Lawson's Minimum-Energy Klein Bottle."

Third award: First place award to to Margaret Kepner for "Magic Square 25 Study" ; second place award to Carlo H. Séquin for "Torus Knot"(5,3); and third place award to Anne Burns for "Circles on Orthogonal Circles."

Second award: First place award to Robert Bosch for "Embrace"; second place award to Harry Benke for "The Vase"; and third place award to Richard Werner for "Meditations on f(x,y) = x2/2 + xy/2 - y4/8."

First award: First place award to Goran Konjevod, for his origami work, "Wave (32), 2006"; second place award to Carlo Séquin, for his sculpture, "Figure-8 Knot, 2007"; and third place award to Robert Fathauer, for "Twice Iterated Knot No. 1, 2008.

Twelfth award: The National Alliance for Doctoral Studies in the Mathematical Sciences, known as the Math Alliance, was chosen to receive the 2017 AMS Mathematics Programs that Make a Difference Award for its programs over the last 10 years promoting participation by groups underrepresented in doctoral programs in the mathematical sciences.

Eleventh award: The Mathematics Department at Morehouse Collegea has been chosen to receive the 2016 AMS Mathematics Programs that Make a Difference Award for its significant efforts to encourage students from underrepresented groups to continue in the study of mathematics and statistics.

Tenth award: The Center for Undergraduate Research in Mathematics (CURM) at Brigham Young University and the Pacific Coast Undergraduate Mathematics Conference (PCUMC) have been chosen to receive the 2015 AMS Mathematics Programs that Make a Difference Award for their “significant efforts to encourage students from underrepresented groups to continue in the study of mathematics.”

Ninth award: The AMS recognizes the Carleton College Summer Mathematics Program for Women and the Rice University Summer Institute of Statistics. Both programs have made significant, successful efforts to encourage either underrepresented minorities and/or women to continue in the study of mathematics.

Eighth award: The AMS recognizes the Nebraska Conference for Undergraduate Women in Mathematics (NCUWM) is honored for its remarkable contribution to the national effort to produce more women PhDs in the mathematical sciences.

Seventh award: The AMS recognizes the Mathematical Sciences Research Institute (MSRI) for its efforts to encourage students from underreppresented groups to continue in the study of mathematics.

Sixth award: to Department of Mathematics at North Carolina State University and the Center for Women in Mathematics and the Center's Post-baccalaureate Program at Smith College. See citations and descriptions of programs.

Fifth award: to Department of Computational and Applied Mathematics (CAAM) at Rice University and the Summer Program in Quantitative Sciences at the Harvard School of Public Health. See citations and descriptions of programs.

Fourth award: to Department of Mathematics at the University of Mississippi and the Department of Statistics at North Carolina State University. See citations and descriptions of programs.

Third award: to Summer Undergraduate Mathematical Science Research Institute (SUMSRI), Miami University (Ohio) and Mathematics Summer Program in Research and Learning (Math SPIRAL), University of Maryland, College Park. See citations and descriptions of programs.

Second award: to Enhancing Diversity in Graduate Education (EDGE), Bryn Mawr College and Spelman College; and Mathematical Theoretical Biology Institute (MTBI), Arizona State University. See citations and descriptions of programs.

First award: to Summer Institute in Mathematics for Undergraduates (SIMU), Universidad de Puerto Rico, Humacao; and Graduate Program, Department of Mathematics, University of Iowa. See citations and descriptions of programs.

Fifteenth award: to Aloysius "Loek" Helminck for "his dynamic and public-spirited leadership of the Department of Mathematics at North Carolina State University, and for his work, both in his department and at the national level, to increase the diversity of the mathematical research community."

Fourteenth award: to Philip Kutzko for his leadership of a national effort to increase the number of doctoral degrees in the mathematical sciences earned by students from underrepresented groups.

Thirteenth award: to William McCallum for his energetic and effective efforts in promoting improvements to mathematics education.

Twelfth award: to Carlos Castillo-Chavez for having a major impact with his efforts and activities in improving the representation in the broad mathematical sciences of the nation's traditionally underrepresented and economically disadvantaged students.

Eleventh award: to Herbert Clemens for his superb research in complex algebraic geometry, his continuing efforts in education, and his seminal role in the founding and continuation of the Park City/IAS Mathematics Institute.

Tenth award: to Roger Howe for his multifaceted contributions to mathematics and to mathematics education.

Ninth award: to Richard A. Tapia for inspiring and teaching thousands of people (from elementary school students to senior citizens) to study and appreciate the mathematical sciences.

Eighth award: to Margaret H. Wright for notable contributions to the federal government and the scientific community, and for encouraging women and minority students.

Seventh award: to Paul J. Sally, Jr. for the quality of his research, for his service to the [American Mathematical] Society as Trustee, but more importantly for his many efforts in improvement of mathematics education for the nation's youth and especially for members of minority and underrepresented groups and for his longitudinal mentoring of students, in particular the mathematics majors at Chicago.

Sixth award: to Kenneth C. Millett for his work devoted to underrepresented minority students in the mathematical sciences. Professor Millett founded the University of California, Santa Barbara Achievement Program and directed the mathematics component of the Summer Academic Research Internship and the Summer Institute in Mathematics and Science at UCSB.

Fifth award: no award made

Fourth award: to Donald J. Lewis for his many contributions to mathematical education, mathematics policy, and mathematical research and administration during a career that has spanned several decades.

Third award: to Isadore M. Singer in recognition of his outstanding contributions to his profession, to science more broadly, and to the public good by bringing the best of mathematics and his own insights to bear on the activities of the National Academy of Sciences; on committees of the National Research Council, including the two so-called David Committees on the health of the mathematical sciences, and the Committee on Science, Engineering, and Public Policy; on the President's Science Advisory Council; on decisions of Congress, through testimony concerning the support of mathematics and mathematical research; and on a host of critical situations over many years in which his wisdom and intervention helped gain a hearing for the problems of his community and the contributions it makes to the nation.

Second award: to Harvey B. Keynes for his multifaceted efforts to revitalize mathematics education, especially for young people.

First award: to Kenneth M. Hoffman for his outstanding leadership in establishing channels of communication between the mathematical community and makers of public policy as well as the general public.

Third award: to Liang-Shin Hahn and Arnold E. Ross. Liang-Shin Hahn for carrying forward and developing the New Mexico High School Mathematics Contest and for exposition and popularization of mathematics attractive to and suitable for potential candidates for the contest and others with similar intellectual interests. Arnold E. Ross for inspiring generations of young people through the summer mathematics programs he created and has continued to run for nearly 40 years.

Second award: to Marcia P. Sward for her contributions toward establishing and directing the Mathematical Sciences Education Board from its inception in the fall of 1985 until August 1989.

First award: to Andre Z. Manitius for the contributions he made to the mathematical community while employed in the Division of Mathematical Sciences at the National Science Foundation.

Twenty-sixth award: Terence Coelho - Rutgers University, New Brunswick; Renee Adonteng - Virginia Commonwealth University; Breana Kechelle Leach - University of Tennessee at Chattanooga; Seth Erik Emblem - Texas Christian University; Madison C. DuPont - University of North Texas; Andrew D. Coleman - Colorado State University at Pueblo; Edwin Garcia - San Francisco State University

Twenty-fifth award: Kiyon Hahm - Johns Hopkins University, Stephen Wayne Brazil - New Mexico University,Josephine Atsuko Sechrist - Oregon State University, Alexandra Platt - University of Delaware,Kristen Marie Amman - University of Michigan, Ann Arbor, Emily Wardenburg - University of Northern Iowa, Sara Catherine Fee - University of Tulsa.

Twenty-fourth award: Kathleen Marie Chamberlain - Old Dominion University; Daniel Bickley - Miami University, Oxford; Sariah Dawn Reese - Oral Roberts University; Horacio Alexandre Sanchez Cardenas - California State University Fullerton; Matthew Stuart Farrell - Cornell University; Prabhat Kumar - West Chester University of Pennsylvania; Taylor Huettenmueller - Emporia State University.

Twenty-third award: to John Douglas Helbig Jr. - Kean University; Chaoren Lin - SUNY at Binghamton; Paul George Ponmattam - Vanderbilt University; Ruth Mariko Fujino - Winthrop University; Paige Ferguson - University of North Dakota; Michael W. Brown - University of New Mexico; Shalaine L. Buck - University of New Mexico; Michael VanDyke - Idaho State University.

Twenty-second award: to Tyler Raven Billingsley - Purdue University Calumet; Benjamin Levi Heebner - Pennsylvania State University; Matthew Phillip Larson - Hendrix College; Emily Mavaddat - University of Denver; Anakaren Santana - University of California, Berkeley; Abigail Margaret Skelton - Lebanon Valley College; and Ryan T. Uding - University of Missouri-St. Louis.

Twenty-first award: to David Samuel Allen - Colorado State University; Xavier Eduardo Garcia - University of Minnesota Twin Cities; Jeffrey Hart - California State University San Marcos; Amina S. Mendez - Ohio Wesleyan University; Amanda Nicole Rodriguez - Texas A&M University Corpus Christi; Tyler Wippel - Central Michigan University; Maocai Wu - Brooklyn College-CUNY.

Twentieth award: to Vianey Carolina Leos Barajas - California State University, Bakersfield; Langston W. Joiner - University of Cincinnati; Michelle Chu - Emory University; Perla Salazar - Kansas State University; Dana C. Haymon - University of Oklahoma; James S. Wratten Jr. - Rochester Institute of Technology; Bebi Z. G. Rajendra - York College.

Ninteenth award: to Alison Lynette Ashe - University of Vermont; Kendall Olivia Brown - Truman State University; Zehui Chen - Smith College; Jonathan Jordan Edwards - Kenyon College; David Hassan - University of California, Santa Barbara; Ana-Cristina Cerda Jimenez - California State University, Fresno; Mantatisi S. Walker - Jackson State University.

Eighteenth award: to Aaron Peterson - Luther College, Faith L. Buell - Wright State University, Phillip David Lorren - Georgia Southern University, Daksha Shakya - Ithaca College, Joseph Zancocchio - College of Staten Island (CUNY), Amanda J. Mueller - University of Wisconsin - Milwaukee, Hans Parshall - Humboldt State University.

Seventeenth award: to Susan Christine Massey - University of Washington, Amy Streifel - Lewis and Clark College, Rosemary Holguin - SUNY at New Paltz, Emily Jean Ognacevic - Saint Louis University, Betsy Kay Barr - University of Tennessee Knoxville, Kayla Rose Boyle - University of Northern Iowa.

Sixteenth award: to Lorena Pulido and Jennifer Renee Winter - California State University, San Bernardino, Sean Michael Eagan - University of Missouri, Rolla, Khadijah Shadeed - University of Central Missouri, Elizabeth Rini - Boston College, Elizabeth R. Morra - Eckerd College, John Roosevelt Quinn - University of California, San Diego, Adam Joseph Lizzi - Swarthmore College.

Fifteenth award: to Carissa Joy Strawn - Abilene Christian University, Jennifer A. Roberge - Amherst College, Yukiko Kozakai - Arizona State University, Melanie Marie Meyer - University of Missouri, Kansas City, Christian Sykes - University of North Carolina at Greensboro, Christopher Piecuch - University of Rhode Island, Sophia Leibman and Gabor Revesz - Ohio State University.

Fourteenth award: to Laura Wolfram - Beloit College, Prince Chidyagwai, Ekaterina Jager, and Blerta Shtylla - Lafayette College, Antonio Veloz - Michigan State University, Daniel Pomerleano - University of Pennsylvania, Kathryn Carr and Cass Bath - Portland State University, Olivia Gistand - Santa Clara University.

Thirteenth award: to Thida S. Aye - Bryn Mawr College, Andrew Richard Tackmann - Minnesota State University at Mankato, Maria Christin Llewellyn - University of Maryland at Baltimore County, Rahbar Virk - Colorado College, Sarah Deiwert and Angela Martinho- California State University, Hayward, Timothy P. Lewis - Lehigh University, Bishal Thapa - State University of New York at Potsdam.

Twelfth award: to Marcus A. Arreguin - Stephen F. Austin State University, Challis Kinnucan - Bates College, Julie Brinton - Brigham Young University, Suzanne L. Robertson - The College of William and Mary, Kevin L. Smith - Furman University, Aimee J. Groudas - University of Hartford, Peter Kirkpatrick - University of Southern California, Kevin R. Pond- University of Texas at Dallas.

Eleventh award: to Alexander Ivanov Sotirov - Columbia University, Gregory Nevil Leuchiali Maxwell - Florida Atlantic University, Ann Smith - Henderson State University, Andrea C. Forney - John Carroll University, Sinead Pollom - Seattle University, Virginia Roberts - University of Texas at Austin, Paul T. Watkins - University of Utah, Yakov Kronrod and Megan Lally - Worcester Polytechnic Institute.

Tenth award: to Yen Hai Le - California State University at Long Beach, Alexander Statnikov - Case Western Reserve University, Matthew Bartholomew - Clarkson University, Alyssa Burns - University of Houston.

Ninth award: to Hulya Cebeciouglu - City University of New York, Jeremy Copeland - Reed College, Danielle Lyles - University of Texas at San Antonio, Marcia Jean Mercer - Western Kentucky University. See also theApril 2000 issue of the Notices of the AMS.

Eighth award: to Kelly Cornish - Stevens Institute of Technology, Kevin A. Wilson - Georgia State University, Matthew A. Halverson - Iowa State University, Dumitru C. Tutuianu - University of Nevada at Las Vegas. [no Notices article.]

Seventh award: to Martin Akguc - Georgetown University, Laura Steiner, Claudia Catalan, and Elizabeth Madrigal - Loyola Marymount University, Emily Press - New York University, Laura Wasser - Southern Illinois University at Carbondale.

Sixth award: to Christie M. Safin - Murray State University, Andreea Nicoara - Stanford University, Allison Pacelli - Union College, Lorna Renee Sanders - Western Illinois University.

Fifth award: to Mark Robert Moseley - University of Arizona, Donna J. Shepherd - Arkansas State University, Clayton T. Hester - Mississippi State University, James R. Jarrell III - Montclair State College.

Fourth award: to William Hudson and Margaret Norris - Boise State University, Guanghong Xu - Illinois Institute of Technology, Coleen Clemetson - Temple University, Mikhail G. Konikov - University of Maryland at College Park.

Third award: to Michelle L. Lanir - University of California at Los Angeles, Jodi C. Wright - State University of New York at Geneseo, Rebecca K. Moore - Eastern New Mexico University, Mikhail Krichman - University of Virginia.

Second award: to Julianne Stile - Allegheny College, Cassandra Burns - Memphis State University, James Anthony Nunez - University of California at Irvine , Juan Ramon Romero-Oliveras - University of Puerto Rico.

First award: to Robert Lane Bassett, Linie Yunwen Chang, and Kara Lee Lavender - Duke University, Thomas A. Shimkus - University of Scranton, Melissa Cockerill, Deborah Fagan, and Sherry Heis - Montana State University, Pamela Jo Chaney - Howard Payne University.

To Charles L. Epstein, University of Pennsylvania, and François Trèves, Rutgers University. Epstein is honored for his fundamental contributions to the theory of embeddability and stability of 3-dimensional Cauchy-Riemann (CR) structures. Trèves is honored for his many fundamental contributions to several complex variables and partial differential equations.

To Eric Bedford of Stony Brook University and Jean-Pierre Demailly of University of Grenoble-Alpes. Bedford is honored his many fundamental contributions to Several Complex Variables, Pluripotential Theory and Complex Dynamics. Demailly has long been recognized as a dominant figure in several complex variables and complex geometry.

To Takeo Ohsawa of Nagoya University and Sławomir Kołodziej of Jagiellonian University Ohsawa’s work has led to important advances in a wide variety of areas, including local structure of plurisubharmonic functions, invariance of plurigenera, multiplier ideal sheaves, and estimates for the Bergman kernel. Kołodziej is recognized for his seminal contributions to the complex Monge-Ampère equation and pluripotential theory, including necessary and sufficient conditions for the existence of bounded solutions, stability, and other sharp estimates.

To Xiaojun Huang and Steve Zelditch because they are leaders in geometric analysis, a focus of contemporary mathematical research. Their penetrating insights have solved long-standing problems and transformed subsequent work in the field.

To David S. Jerison (MIT) and John M. Lee (University of Washington) for their pioneering works on the CR Yamabe problem, which lead to finding canonical metrics in a given conformal class, for strictly pseudo-convex manifolds.

To Gennadi Henkin

To Ngaiming Mok and Duong H. Phong

To Alexander Nagel and Stephen Wainger

To Kengo Hirachi

To Elias M. Stein

To Joseph J. Kohn

To M. Salah Baouendi and Linda Preiss Rothschild

To László Lempert and Sidney Webster

To Masatake Kuranishi

To John P. D'Angelo

To David E. Barrett and Michael Christ

To Harold P. Boas and Emil J. Straube

To John Erik Fornaess

To Yum-Tong Siu

To Charles Fefferman

To Steven Bell and Ewa Ligocka

To David Catlin

Fifth Prize

Fourth Prize

Third Prize

Second Prize

First Prize

The Milestone Prize: to Woodrow W. Bledsoe

The Current Prize: to Robert S. Boyer and J Strother Moore

The Milestone Prize: to J. Alan Robinson

The Milestone Prize: to Hao Wang

The Current Prize: to Lawrence Wos and Steven Winker