Bulletin of the American Mathematical Society

Missed opportunities

Freeman J. Dyson
Source: Bull. Amer. Math. Soc. Volume 78, Number 5 (1972), 635-652.
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Permanent link to this document: http://projecteuclid.org/euclid.bams/1183533964
Mathematical Reviews number (MathSciNet): MR0522147
Zentralblatt MATH identifier: 0271.01005

References

1. D. Hilbert, Mathematische Probleme, Lecture to the Second Internat. Congress of Math. (Paris, 1900), Arch. Math. und Phys. (3) 1 (1901), 44-63; 213-237; English transl., Bull. Amer. Math. Soc. 8 (1902), 437-479.
2. H. Minkowski, Raum und Zeit, Lecture to the 80th Assembly of Natural Scientists (Köln, 1908), Phys. Z. 10 (1909), 104-111. English transl., The principle of Relativity, Aberdeen Univ. Press, Aberdeen, 1923.
3. I. G. MacDonald, Affine root systems and Dedekind's η-function, Invent. Math. 15 (1972), 91-143. See also R. V. Moody, Euclidean Lie algebras, Canad. J. Math. 21 (1969), 1432-1454. MR 41 # 287.
Zentralblatt MATH: 0244.17005
Mathematical Reviews (MathSciNet): MR357528
Digital Object Identifier: doi:10.1007/BF01418931
4. G. H. Hardy, Ramanujan, Cambridge Univ. Press, Cambridge; Macmillan, New York, 1940, Chap. 10, p. 161. MR 3, 71.
Zentralblatt MATH: 0027.19608
Mathematical Reviews (MathSciNet): MR4860
5. S. Ramanujan, On certain arithmetical functions, Trans. Cambridge Philos. Soc. 22 (1916), 159-184.
6. L. J. Mordell, On Mr. Ramanujan's empirical expansions of modular functions, Proc. Cambridge Philos. Soc. 19 (1917), 117-124.
7. E. Hecke, Über Modulfunktionen und die Dirichletschen Reihen mit Eulerscher Produktentwicklung, Math. Ann. 114 (1937), 1-28; 316-351.
Mathematical Reviews (MathSciNet): MR1513142
Digital Object Identifier: doi:10.1007/BF01594180
8. M. Newman, An identity for the coefficients of certain modular forms, J. London Math. Soc. 30 (1955), 488-493. MR 17, 15; A. O. L. Atkin, Ramanujan congruences for p-k (n), Canad J. Math. 20 (1968), 67-78; corrigendum, ibid. 21 (1969), 256. MR 38 # 2098.
Zentralblatt MATH: 0064.28203
Mathematical Reviews (MathSciNet): MR70658
Digital Object Identifier: doi:10.1112/jlms/s1-30.4.488
9. R. C. Gunning, Lectures on modular forms, Ann. of Math. Studies, no. 48, Princeton Univ. Press, Princeton, N.J., 1962. MR 24 #A2664; A. Ogg, Modular forms and Dirichlet series, Benjamin, New York, 1969. MR 42 # 1648.
Zentralblatt MATH: 0178.42901
Mathematical Reviews (MathSciNet): MR132828
10. L. Winquist, An elementary proof of p(11m + 6) ≡ 0 (mod 11), J. Combinatorial Theory 6 (1969), 56-59. MR 38 #4434. Winquist sent this proof to me in January 1968.
Zentralblatt MATH: 0241.05006
Mathematical Reviews (MathSciNet): MR236136
Digital Object Identifier: doi:10.1016/S0021-9800(69)80105-5
11. C.G.J. Jacobi, Fundamenta nova theoriae functionum ellipticarum, Königsberg, 1829, 66, Eq. (5).
12. F. Klein and R. Fricke, Vorlesungen über die Theorie der elliptischen Modulfunktionen. Vol. 2, Teubner, Leipzig, 1892, p. 373.
15. J. Clerk Maxwell, A dynamical theory of the electromagnetic field, Philos. Trans. Roy. Soc. (London) 155 (1865), 459-512.
16. J. Clerk Maxwell, Presidential Address to Section A (Mathematical and Physical Sciences) of the British Association, Liverpool, 1870. Nature 2 (1870), 419-422.
17. I. Newton, Mathematical principles of natural philosophy, translated into English by Andrew Motte in 1729, edited by F. Cajori, Univ. of California Press, Berkeley, Calif., 1946, p. 397.
Zentralblatt MATH: 0127.00501
Mathematical Reviews (MathSciNet): MR175748
18. Henry J.S. Smith, Presidential Address to Section A (Mathematical and Physical Sciences) of the British Association, Bradford, 1873. Nature 8 (1873), 448-452.
19. J. Clerk Maxwell, A treatise on electricity and magnetism, Oxford Univ. Press, Oxford, 1873.
Zentralblatt MATH: 1049.01021
20. Michael Pupin,From immigrant to inventor, 1924.
21. H. Bacry and J.-M. Lévy-Leblond, Possible kinematics, J. Mathematical Phys. 9 (1968), 1605-1614. MR 38 # 6821. To save time I have slightly misstated their conclusion; each of the groups D, P′ and N can occur in two alternative forms, so that the number of possibilities is strictly speaking 11 rather than 8.
Zentralblatt MATH: 0162.58606
Mathematical Reviews (MathSciNet): MR238545
Digital Object Identifier: doi:10.1063/1.1664490
22. J.-M. Lévy-Leblond, Une nouvelle limite non-relativiste du groupe de Poincaré, Ann. Inst. H. Poincaré Sect. A 3 (1965), 1-12. MR 33 # 1125.
Zentralblatt MATH: 0143.22601
Mathematical Reviews (MathSciNet): MR192900
23. L. Carroll, Through the looking-glass, and what Alice found there, Macmillan, London, 1871.
24. J. Willard Gibbs, On multiple algebra, Vice-Presidential Address to the Section of Mathematics and Astronomy of the American Association for the Advancement of Science, Proc. Amer. Assoc. Adv. Sci. 35 (1886), 37-66.
25. W. R. Hamilton, On quaternions; or on a new system of imaginaries in algebra, Philos. Mag. 25 (1844), 10-13.
26. H. Grassmann, Die lineale Ausdehnungslehre, ein neuer Zweig der Mathematik, Otto Wigand, Leipzig, 1844.
27. See R. Brauer and H. Weyl, Spinors in n dimensions, Amer. J. Math. 57 (1935), 425-449.
Mathematical Reviews (MathSciNet): MR1507084
Digital Object Identifier: doi:10.2307/2371218
28. A. Einstein, Die Grundlage der allgemeinen Relativitätstheorie, Ann. Phys. 49 (1916), 769-822.
29. R. Haag and D. Kastler, An algebraic approach to quantum field theory, J. Mathematical Phys. 5 (1964), 848-861. MR 29 # 3144.
Zentralblatt MATH: 0139.46003
Mathematical Reviews (MathSciNet): MR165864
Digital Object Identifier: doi:10.1063/1.1704187
30. J. Dixmier, Les C*-algèbres et leurs représentations, Cahiers Scientifiques, fasc. 29, Gauthier-Villars, Paris, 1964. MR 30 # 1404.
Zentralblatt MATH: 0174.18601
Mathematical Reviews (MathSciNet): MR171173
31. R. P. Feynman, Mathematical formulation of the quantum theory of electromagnetic interaction, Phys. Rev. (2) 80 (1950), 440-457. MR 12, 889; R. P. Feynman, Space-time approach to non-relativistic quantum mechanics, Rev. Modern Phys. 20 (1948), 367-387. MR 10, 224.
Zentralblatt MATH: 0040.28002
Mathematical Reviews (MathSciNet): MR41726
Digital Object Identifier: doi:10.1103/PhysRev.80.440
32. R. E. Peierls, The commutation laws of relativistic field theory, Proc. Roy. Soc. London Ser. A 214 (1952), 143-157. MR 14, 520.
Zentralblatt MATH: 0048.44606
Mathematical Reviews (MathSciNet): MR51725
Digital Object Identifier: doi:10.1098/rspa.1952.0158
33. I. M. Gel'fand and A. M. Jaglom, Integration in functional spaces and its applications in quantum physics, Uspehi Mat. Nauk 11 (1956), no. 1 (67), 77-114; English transl., J. Mathematical Phys. 1 (1960), 48-69. MR 22 # 3455, and its bibliography is complete up to 1956. Substantial progress in justifying the use of Feynman sums in a nonrelativistic context has been made more recently; see E. Nelson, Feynman integrals and the Schrödinger equation, J. Mathematical Phys. 5 (1964), 332-343. MR 28 # 4397, and C. M. DeWitt, Feynman's path integral, definition without limiting procedure, Univ. of Texas, Austin, Tex., 1972 (preprint).
Zentralblatt MATH: 0071.22409
Mathematical Reviews (MathSciNet): MR112604
Digital Object Identifier: doi:10.1063/1.1703636
34. J. von Neumann, Über ein ökonomisches Gleichungssystem und eine Veralgemeinerung des Brouwerschen Fixpunktsatzes, Ergebnisse eines mathematischen Seminars, edited by K. Menger, Wien, 1938; English transl., Rev. Economic Studies 13 (1945), 1-9.
35. E. W. Brown, Resonance in the solar system, Bull. Amer. Math. Soc. 34 (1928), 265-289.
Mathematical Reviews (MathSciNet): MR1561551
Digital Object Identifier: doi:10.1090/S0002-9904-1928-04554-8
Project Euclid: euclid.bams/1183492726
36. C. J. Cohen and E. C. Hubbard, Libration of the close approaches of Pluto to Neptune, Astronom. J. 70 (1965), 10-13.
Mathematical Reviews (MathSciNet): MR135582
Digital Object Identifier: doi:10.1086/108597
37. J. Hadamard, The psychology of invention in the mathematical field, Princeton Univ. Press, Princeton, N.J., 1945, Chap. 4. MR 6, 198.
Zentralblatt MATH: 0063.01843
Mathematical Reviews (MathSciNet): MR11665

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