Bulletin of the American Mathematical Society

Author(s): Peter D. Lax
Journal: Bull. Amer. Math. Soc. 45 (2008), 135-152.
MSC (2000): Primary 35-XX, 76-XX, 46-XX
Posted: October 30, 2007
Retrieve article in: PDF

1.: Birkhoff, G. D., What is the ergodic theorem? Amer. Math. Monthly 49 (1942), 222-226. MR 0006619 (4:15b)
2.: Boltzmann, L., Wissenschaftliche Abhandlungen, Chelsea Pub. Co., New York, 1968. MR 0237281 (38:5571)
3.: Christodoulou, D., and Klainerman, S., The Global Nonlinear Stability of the Minkowski Space, Princeton University Press, Princeton, NJ, 1993. MR 1316662 (95k:83006)
4.: de Branges, L., A proof of the Bieberbach conjecture, Acta Math. 154 (1985), 137-152. MR 772434 (86h:30026)
5.: Dyson, F., Statistical theory of the energy levels of complex systems, I, II, III, J. Math. Physics 3 (1962), 140-175.
6.: Dyson, F., Missed opportunities, Bull. Amer. Math. Soc. 78 (1972), 635-652. MR 0522147 (58:25442)
7.: Gibbs, J. W., The Collected Works of J. Willard Gibbs, Longman's, Green and Co., 1931.
8.: Glimm, J., Solutions in the large for nonlinear hyperbolic systems of equations, CPAM 18 (1965), 697-715. MR 0194770 (33:2976)
9.: Gottlieb, D., and Shu, C.-W., On the Gibbs phenomenon and its resolution, SIAM Review 39 (1997), 644-668. MR 1491051 (98m:42002)
10.: Hewitt, E., and Hewitt, R. E., The Gibbs-Wilbraham phenomenon: an episode in Fourier analysis, Archive for History of Exact Sciences 21 (1979), 129-160. MR 0555102 (81g:01015)
11.: Hilbert, D., Begründung der kinetischen Gastheorie, Math. Ann. 72 (1912), 562-577. MR 1511713
12.: Hou, S., and Liu, X.-D., Solutions of multi-dimensional hyperbolic systems of conservation laws by square entropy condition satisfying discontinuous Galerkin method, J. Sci. Computing 31 (2007), 127-151.MR 2304273
13.: Koestler, A., and Butterfield, H., The Sleepwalkers, Peregrine Books, 1959.
14.: Leray, J., Sur le mouvement d'un fluide visqueux emplissant l'espace, Acta Math. 63 (1934), 193-248. MR 1555394
15.: Liu, X. D., and Lax, P. D., Solution of two-dimensional Riemann problems of gas dynamics by positive schemes, SIAM J. Sci. Comp. 19 (1998), 319-340 (electronic). MR 1618863
16.: Loewner, C., Untersuchungen über schlichte konforme Abbildungen des Einheitskreises, I. Math. Ann. 89 (1923), 103-121. MR 1512136
17.: Maxwell, J. C., A dynamical theory of the electromagnetic field, Royal Soc. Trans. 155 (1865), The Scientific Papers of James Clerk Maxwell, Scottish Acad. Press, 1982, 526-597. MR 0778034 (87i:01032)
18.: McCoy, B. M., Introductory Remarks to Szegö's Paper ``On Certain Hermitean Forms Associated with the Fourier Series of a Positive Function'', in Gabor Szegö Collected Papers, R. Askey, ed., Vol. 1, 47-51, Birkhäuser, 1982.
19.: Neugebauer, O., Notes on Kepler, CPAM 14 (1961), 593-597. MR 0131339 (24:A1191)
20.: Odlyzko, A., On the distribution of the spacing between the zeros of the $\zeta$ function, Math. Comp. 48 (1989), 273-308.
21.: Onsager, L., Statistical hydrodynamics, Nuovo Cimento 6, Suppl. 261 (1949). MR 0036116 (12:60f)
22.: Riemann, B., Über die Fortpflanzung ebener Luftwellen von endlicher Schwingingsweite, 188-207, Collected Papers, Springer Verlag, 1990.
23.: Schrödinger, E., Collected Papers on Wave Mechanics, Blackie and Son, Ltd., London, 1928. MR 0750301 (85k:01057)
24.: Schultz-Rinne, C. W., Collins, J. P., and Glaz, H. M., Numerical solution of the Riemann problem for two-dimensional gas dynamics, SIAM J. Sci. Comp. 14 (1993), 1394-1414. MR 1241592 (94j:76062)
25.: Schwartz, J., The pernicious influence of mathematics on science, in Logic, Methodology and Philosophy of Science, Nagel, Suppes and Tarski, eds., Stanford University Press, 1962. MR 0166069 (29:3347)
26.: Szegö, G., On certain Hermitean forms associated with Fourier series of a positive function, Comm. Sem. Math. Univ. Lund, Tome Supplementaire, Festshrift Marcel Riesz, Lund (1952), 228-238; also Gabor Szegö Collected Papers, E. Askey, ed., Vol. 3, 270-280, Birkhäuser, 1982. MR 0051961 (14:553d), MR 0674484 (84d:01082c)
27.: von Neumann, J., Proof of the Quasi-ergodic Hypothesis, NAS Proc. 186 (1932), 70-82; see also Vol. I, Collected Works, Pergamon Press, 1961. MR 0157871 (28:1100)
28.: -, Mathematische Begründung der Quantenmechanic, Goett. Nach. 1927, 1-57; see also Vol. I, Collected Works, Pergamon Press, 1961. MR 0157871 (28:1100)
29.: -, with Burke, A. W., and Goldstine, H. H., Preliminary Discussion of the Logical Design of an Electronic Computing Instrument, Vol. V, Collected Works, Pergamon Press, 1963. MR 0157875 (28:1104)
30.: Werner, W., Random planar curves and Schramm-Loewner evolutions, Lectures on Probability Theory and Statistics, 107-195, in Lecture Notes in Math. 1840, Springer Verlag, 2004. MR 2079672 (2005m:60020)
31.: Wigner, E., On the statistical distribution of the width and spacing of nuclear resonance levels, Proc. Cambridge Phil. Soc. 47 (1951), 790-798.
32.: Wigner, E., Random Matrices in Physics, SIAM Review 9 (1967), 1-23.
33.: Wilbraham, H., On certain periodic functions, Cambridge Dublin Math. J. 3 (1848), 198-204.
34.: Witten, E., Magic, Mystery and Matrix, 343-352, in Mathematics: Frontiers and Perspectives, Arnold, Atiyah et al., eds., Amer. Math. Soc., Providence, RI, 2000. MR 1756796

Retrieve articles in Bulletin of the American Mathematical Society with MSC (2000): 35-XX, 76-XX, 46-XX

Peter D. Lax
Affiliation: Courant Institute, New York University, 251 Mercer Street, New York, New York 10012-1110

DOI: 10.1090/S0273-0979-07-01182-2
PII: S 0273-0979(07)01182-2
Received by editor(s): May 7, 2007
Posted: October 30, 2007
Additional Notes: This article is based on the author's Gibbs Lecture at the Joint Mathematics Meetings in New Orleans in 2007.
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-9485(e) ISSN 0273-0979(p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues: 1891 - Present Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2009, American Mathematical Society Privacy Statement		Search the AMS