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Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

 
 

 

Responses to: A. Jaffe and F. Quinn, ``Theoretical mathematics: toward a cultural synthesis of mathematics and theoretical physics'' [Bull. Amer. Math. Soc. (N.S.) 29 (1993), no. 1, 1-13; MR1202292 (94h:00007)]


Authors: Michael Atiyah, Armand Borel, G. J. Chaitin, Daniel Friedan, James Glimm, Jeremy J. Gray, Morris W. Hirsch, Saunders Mac Lane, Benoit B. Mandelbrot, David Ruelle, Albert Schwarz, Karen Uhlenbeck, René Thom, Edward Witten and Sir Christopher Zeeman
Journal: Bull. Amer. Math. Soc. 30 (1994), 178-207
MSC (2000): Primary 00A30; Secondary 00A35, 00A79, 01A60
DOI: https://doi.org/10.1090/S0273-0979-1994-00503-8
MathSciNet review: 1254073
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  • [1] A. Jaffe and F. Quinn, Theoretical Mathematics: Toward a cultural synthesis of mathematics and theoretical physics, Bull. Amer. Math. Soc. 29 (1993), 1-13. MR 1202292 (94h:00007)
  • [2] G. J. Chaitin, Algorithmic information theory, revised third printing, Cambridge Univ. Press, Cambridge, 1990. MR 917482 (89g:68022)
  • [3] G. J. Chaitin, Information, randomness & incompleteness--papers on algorithmic information theory, second edition, World Scientific, Singapore, 1990. MR 1153671 (92m:01094)
  • [4] G. J. Chaitin, Information-theoretic incompleteness, World Scientific, Singapore, 1992. MR 1189794 (94e:68001)
  • [5] G. J. Chaitin, Exhibiting randomness in arithmetic using Mathematica and C, IBM Research Report RC-18946, June 1993.
  • [6] G. J. Chaitin, Randomness in arithmetic and the decline and fall of reductionism in pure mathematics, Bull. European Assoc. for Theoret. Comput. Sci., no. 50 (July 1993).
  • [7] G. J. Chaitin, The limits of mathematics--Course outline and software, IBM Research Report RC-19324, December 1993.
  • [8] G. J. Chaitin, Randomness and complexity in pure mathematics, Internat. J. Bifur. Chaos 4 (1994) (to appear). MR 1276801 (95b:00005)
  • [K] Appel and W. Haken, Every planar map is four colorable. Part I: Discharging, Illinois J. Math. 21 (1977), 421-490; Part II: Reducibility, ibid, 491-567. MR 0543793 (58:27598b)
  • [K] Appel and W. Haken, The four color proof suffices, Mathematical Intelligencer 8 (1986), 10-20. MR 823216 (87b:05055)
  • [S] Smale, The fundamental theorem of algebra and complexity theory, Bull. Amer. Math. Soc. 4 (1981), 1-36. MR 590817 (83i:65044)
  • [P] Heegard, Sur l'analysis situs, Bull. Soc. Math. France 44 (1916), 161-142. [Translation of: Forstudier til en topologisk teori för de algebraiske Sammenhang, dissertation, Copenhagen, Det Nordiske Forlag Ernst Bojesen, 1898.]
  • [H] Poincaré, Sur les nombres de Betti, Comptes Rendus Acad. Sci. (Paris) 128 (1899), 629-630. [Reprinted in Œuvres 6.]
  • [H] Poincaré, Complément à l'analysis situs, Rendiconti Circolo Matematico Palermo 13 (1899), 285-343. [Reprinted in Œuvres 6.]
  • [H] Poincaré, Deuxième complément à l'analysis situs, Proc. London. Math. Soc. 32 (1900), 277-308. [Reprinted in Œuvres 6.]
  • [H] Poincaré, Cinquième complément à l'analysis situs, Rendiconti Circolo Matematico Palermo 18 (1904), 45-110. [Reprinted in Œuvres 6.]
  • [1] A. Jaffe, F. Quinn, Theoretical Mathematics: Toward a cultural synthesis of mathematics and theoretical physics, Bull. Amer. Math. Soc. 29 (1993), 1-13. MR 1202292 (94h:00007)
  • [2] J. Adams, Infinite loop spaces, Princeton, 1978. MR 505692 (80d:55001)
  • [3] A. Schwarz, The partition function of degenerate quadratic functional and Ray-Singer invariants, Lett. Math. Phys. 2 (1978), 247-252. MR 0676337 (58:32690)
  • [4] A. Schwarz, New topological invariants arising in the theory of quantized fields, Baku International Topological Conference, Abstracts (Part 2) Baku, 1987.
  • [5] E. Witten, Quantum field theory and Jones polynomial, Comm. Math. Phys. 121 (1989), 351-399. MR 990772 (90h:57009)
  • [1] A. Jaffe and F. Quinn, Theoretical Mathematics: Toward a cultural synthesis of mathematics and theoretial physics, Bull. Amer. Math. Soc. 29 (1993), 1-13. MR 1202292 (94h:00007)
  • [2] B. Malgrange, Ideals of differentiable functions, Oxford Univ. Press, Oxford, 1966. MR 0212575 (35:3446)
  • [3] S. Smale, Review of E.C. Zeeman: Catastrophe theory, selected papers 1972-1977, Bull. Amer. Math. Soc. 84 (1978), 1360-1368. MR 1567101
  • [4] R. Thom, Les singularités des applications différentiables, Ann. Inst. Fourier 6 (1956), 43-87. MR 0087149 (19:310a)
  • [5] R.S. Zahler and H. Sussmann, Claims and accomplishments of applied catastrophe theory, Nature 269 (1977), 759-763.
  • [6] Correspondence on catastrophe theory, Nature 270 (1977), 381-384 and 658.
  • [7] E. C. Zeeman, Catastrophe theory, selected papers 1972-1977, Addison Wesley, Reading, MA, 1977. MR 0474383 (57:14025)
  • [8] E. C. Zeeman, Controversy in science: On the ideas of Daniel Bernoulli and René Thom, The 1992/3 Johann Bernoulli Lecture, Gröningen (to appear in Nieuw Archief van de Wiskunde). MR 1251489 (94k:01019)

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DOI: https://doi.org/10.1090/S0273-0979-1994-00503-8
Article copyright: © Copyright 1994 American Mathematical Society

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