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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)]
Author(s):
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;
Sir Christopher
Zeeman
Journal:
Bull. Amer. Math. Soc.
30
(1994),
178-207.
MSC (2000):
Primary 00A30;
Secondary 00A35, 00A79, 01A60
MathSciNet review:
1254073
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Additional information
References:
-
- [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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Additional Information:
DOI:
10.1090/S0273-0979-1994-00503-8
PII:
S 0273-0979(1994)00503-8
Copyright of article:
Copyright
1994,
American Mathematical Society
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