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Norbert Wiener Bibliography Maker

  • 1. Norbert Wiener, On the rearrangement of the positive integers in a series of ordinal numbers greater than that of any given fundamental sequence of omegas, Messenger of Math, 3 (1913), No. 511.
  • 2. Norbert Wiener, The highest good, J. Phil. Psych. and Sci. Method 9 (1914), 512-520.
  • 3. Norbert Wiener, Relativism, J. Phil. Psych. and Sci. Method 9 (1914), 561-577.
  • 4. Norbert Wiener, A simplification of the logic of relations, Proc. Cambridge Philos. Soc. 27 (1914), 387-390.
  • 5. Norbert Wiener, A contribution to the theory of relative position, Proc. Cambridge Philos. Soc. 27 (1914), 441-449.
  • 6. Norbert Wiener, Studies in synthetic logic, Proc. Cambridge Philos. Soc. 18 (1915), 24-28.
  • 7. Norbert Wiener, The shortest line dividing an area in a given ratio, J. Phil. Psych. and Sci. Method (1915), 567-574.
  • 8. Norbert Wiener, Certain formal invariance in Boolean algebras, Trans. Amer. Math. Soc. 18 (1917), 65-72.

    Mathematical Reviews (MathSciNet): MR1501062
    Digital Object Identifier: doi:10.1090/S0002-9947-1917-1501062-4

  • 9. Norbert Wiener, Bilinear operations generating all operations rational in a domain, Ann. of Math. 21 (1920), 157-165.

    Mathematical Reviews (MathSciNet): MR1503613
    Digital Object Identifier: doi:10.2307/2007254

  • 10. Norbert Wiener, A set of postulates for fields, Trans. Amer. Math. Soc. 21 (1920), 237-246.

    Mathematical Reviews (MathSciNet): MR1501142
    Digital Object Identifier: doi:10.1090/S0002-9947-1920-1501142-3

  • 11. Norbert Wiener, Certain iterative characteristics of bilinear operations, Bull. Amer. Math. Soc. 27 (1920), 6-10.

    Mathematical Reviews (MathSciNet): MR1560347
    Digital Object Identifier: doi:10.1090/S0002-9904-1920-03347-1
    Project Euclid: euclid.bams/1183425416

  • 12. Norbert Wiener, The mean of a functional of arbitrary elements, Ann. of Math. (2) 22 (1920), 66-72.

    Mathematical Reviews (MathSciNet): MR1502573
    Digital Object Identifier: doi:10.2307/1967855

  • 13. Norbert Wiener, On the theory of sets of points in terms of continuous transformations, G. R. Strasbourg Math. Congress, 1920.
  • 14. Norbert Wiener, Certain iterative properties of bilinear operations, G. R. Strasbourg Math. Congress, 1920.
  • 15. Norbert Wiener, A new theory of measurement: A study in the logic of mathematics, Proc. London Math. Soc. 19 (1921), 181-205.
  • 16. Norbert Wiener, A new vector in integral equations (with F. L. Hitchcock), J. Math, and Phys. 1 (1921), 20 pp.

    Mathematical Reviews (MathSciNet): MR2271720

  • 17. Norbert Wiener, The average of an analytical functional, Proc. Nat. Acad. Sci. U.S.A. 7 (1921), 253-260.
  • 18. Norbert Wiener, The average of an analytical functional and the Brownian movement, Proc. Nat. Acad. Sci. U.S.A. 7 (1921), 294-298.
  • 19. Norbert Wiener, The isomorphisms of complex algebra, Bull. Amer. Math. Soc. 27 (1921), 443-445.

    Mathematical Reviews (MathSciNet): MR1460269

  • 20. Norbert Wiener, The relation of space and geometry to experience, Monist. 32 (1922), 12-60; 200-247; 364-394.
  • 21. Norbert Wiener, The group of the linear continuum, Proc. London Math. Soc. 20 (1922), 329-346.
  • 22. Norbert Wiener, A new type of integral expansion, J. Math, and Phys. 1 (1922), 167-176.
  • 23. Norbert Wiener, Limit in terms of continuous transformation, Bull. Soc. Math. France (1922), 119-134.

    Mathematical Reviews (MathSciNet): MR1504813

  • 24. Norbert Wiener, Certain notions in potential theory, J. Math, and Phys. 3 (1924), 24-51.
  • 25. Norbert Wiener, The equivalence of expansions in terms of orthogonal functions (with J. L. Walsh), J. Math, and Phys. 1 (1922), 103-122.
  • 26. Norbert Wiener, On the nature of mathematical thinking, Austral. J. Psych, and Phil. 1 (1923), 268-272.
  • 27. Norbert Wiener, Note on a paper of M. Banach, Fund. Math. 4 (1923), 136-143.
  • 28. Norbert Wiener, Nets and the Dirichlet problem (with H. B. Phillips), J. Math, and Phys. 2 (1923), 105-124.
  • 29. Norbert Wiener, Differential space, J. Math, and Phys. 2 (1923), 131-174.
  • 30. Norbert Wiener, Note on a new type of summability, Amer. J. Math. 45 (1923), 83-86.

    Mathematical Reviews (MathSciNet): MR1506492
    Digital Object Identifier: doi:10.2307/2370489

  • 31. Norbert Wiener, Discontinuous boundary conditions and the Dirichlet problem, Trans. Amer. Math. Soc. 25 (1923), 307-314.

    Mathematical Reviews (MathSciNet): MR1501246
    Digital Object Identifier: doi:10.1090/S0002-9947-1923-1501246-8

  • 32. Norbert Wiener, Note on the series ∑(+1∕n), Bull. Acad. Polon. Ser. A (1923), 87-90.
  • 33. Norbert Wiener, In memory of Joseph Lipka, J. Math. and Phys. 3 (1924), 63-65.

    Mathematical Reviews (MathSciNet): MR1460272

  • 34. Norbert Wiener, The quadratic variation of a function and its Fourier coefficients, J. Math. and Phys. 3 (1924), 72-94.
  • 35. Norbert Wiener, The Dirichlet problem, J. Math. and Phys. 3 (1924), 127-147.

    Mathematical Reviews (MathSciNet): MR1460272

  • 36. Norbert Wiener, Une condition nécessaire et suffisante de possibilité pour le problème de Dirichlet, C. R. Acad. Sci. Paris 178 (1924), 1050-1053.
  • 37. Norbert Wiener, The average value of a functional, Proc. London Math. Soc. 22 (1924), 454-467.

    Mathematical Reviews (MathSciNet): MR1460273
    Zentralblatt MATH: 0879.01051

  • 38. Norbert Wiener, Un problème de probabilités dénombrables, Bull. Soc. Math. France 11 (1924), 3-4.
  • 39. Norbert Wiener, Note on a paper of O. Perron, J. Math. and Phys. 4 (1925), 21-32.
  • 40. Norbert Wiener, The solution of a difference equation by trigonometrical integrals, J. Math. and Phys. 4 (1925), 153-163.
  • 41. Norbert Wiener, A contribution to the theory of interpolation, Ann. of Math. (2) 26 (1925), 212-116.

    Mathematical Reviews (MathSciNet): MR1502691
    Digital Object Identifier: doi:10.2307/1967899

  • 42. Norbert Wiener, Note on quasi-analytic functions, J. Math. and Phys. 4 (1925), 193-199.

    Mathematical Reviews (MathSciNet): MR1319275
    Zentralblatt MATH: 1042.01522

  • 43. Norbert Wiener, On the representation of functions by trigonometrical integrals, Math. Z. 24 (1925), 576-616.
  • 44. Norbert Wiener, Verallgemeinerte Trigonometrische Entwicklungen, Gott. Nachrichten (1925), 151-158.
  • 45. Norbert Wiener, A new formulation of the laws of quantization for periodic and aperiodic phenomena (with M. Born), J. Math, and Phys. 5 (1926), 84-98.
  • 46. Norbert Wiener, Eine neue Formulierung der Quantengesetze fur Periodische und nicht Periodische Borganze, Z. Physik 36 (1926), 174-187.
  • 47. Norbert Wiener, The harmonic analysis of irregular motion, J. Math. and Phys. 5 (1926), 99-121.
  • 48. Norbert Wiener, The harmonic analysis of irregular motion (Second Paper), J. Math. and Phys. 5 (1926), 158-189.
  • 49. Norbert Wiener, The operational calculus, Math. Ann. 95 (1926), 557-584.

    Mathematical Reviews (MathSciNet): MR1512294
    Digital Object Identifier: doi:10.1007/BF01206627

  • 50. Norbert Wiener, Analytical approximations to topological transformations (with P. Franklin), Trans. Amer. Math. Soc. 28 (1926), 762-785.

    Mathematical Reviews (MathSciNet): MR1501373
    Digital Object Identifier: doi:10.1090/S0002-9947-1926-1501373-8

  • 51. Norbert Wiener, On the closure of certain assemblages of trigonometrical functions, Proc. Nat. Acad. Sci. 13 (1927), 27-29.
  • 52. Norbert Wiener, Laplacians and continuous linear functionals, Acta Sci. Math. (Szeged) 3 (1927), 7-16.
  • 53. Norbert Wiener, The spectrum of an array and its application to the study of the translation properties of a simple class of arithmetical functions, J. Math. and Phys. 6 (1927), 145-157.
  • 54. Norbert Wiener, Quantum theory and gravitational relativity (with D. J. Struik), Nature 119 (1927), 853-854.
  • 55. Norbert Wiener, A relativistic theory of quanta (with D. J. Struik), J. Math. and Phys. 7 (1927), 1-23.
  • 56. Norbert Wiener, Sur la théorie relativiste des quanta (with D. J. Struik), C. R. Acad. Sci. Paris 185 (1927), 42-44.
  • 57. Norbert Wiener, On a new definition of almost periodic functions, Ann. of Math. (2) 28 (1927), 365-367.

    Mathematical Reviews (MathSciNet): MR1502789
    Digital Object Identifier: doi:10.2307/1968381

  • 58. Norbert Wiener, On a theorem of Bochner and Hardy, J. London Math. Soc. 2 (1927), 118-123.
  • 59. Norbert Wiener, Sur la théorie relativiste des quanta, C. R. Acad. Sci. Paris 185 (1927), 184-185.
  • 60. Norbert Wiener, Une généralisation des fonctionelles a variation bornée, C. R. Acad. Sci. Paris 185 (1927), 65-67.

    Mathematical Reviews (MathSciNet): MR32983

  • 61. Norbert Wiener, Une méthode nouvelle pour la démonstration des théorèms de Tauber, C. R. Acad. Sci. Paris 184 (1927), 793-795.
  • 62. Norbert Wiener, The fifth dimension in relativistic quantum theory (with D. J. Struik), Proc. Nat. Acad. Sci. 14 (1928), 262-268.
  • 63. Norbert Wiener, The spectrum of an arbitrary function, Proc. London Math. Soc. 27 (1928), 287-496.
  • 64. Norbert Wiener, Coherency matrices and quantum theory, J. Math. and Phys. 1 (1928), 109-125.
  • 65. Norbert Wiener, A new method of Tauberian theorems, J. Math. and Phys. 7 (1928), 161-184.
  • 66. Norbert Wiener, Harmonic analysis and the quantum theory, J. Franklin Inst. 207 (1929), 525-534.
  • 67. Norbert Wiener, Hermitian polynomials and Fourier analysis, J. Math. and Phys. 8 (1929), 70-73.
  • 68. Norbert Wiener, Harmonic analysis and group theory, J. Math. and Phys. 8 (1929), 148-154.
  • 69. Norbert Wiener, On the spherically symmetrical statistical field in Einstein's unified theory of electricity and gravitation, Proc. Nat. Acad. Sci. 15 (1929), 353-356.
  • 70. Norbert Wiener, On the spherically symmetrical statistical field in Einstein's unified theory: A correction (with M. S. Vallarta), Proc. Nat. Acad. Sci. 15 (1929), 802-804.
  • 71. Norbert Wiener, A type of Tauberian theorem applying to Fourier series, Proc. London Math. Soc 30 (1929), 1-8.
  • 72. Norbert Wiener, Fourier analysis and asymptotic series, Operational circuit analysis by V. Bush, Wiley, New York, 1929; Appendix, pp. 366-379.
  • 73. Norbert Wiener, Generalized harmonic analysis, Acta Math. 55 (1930), 117-258.

    Mathematical Reviews (MathSciNet): MR1555316
    Digital Object Identifier: doi:10.1007/BF02546511

  • 74. Norbert Wiener, Tauberian theorems, Ann. of Math. 33 (1932), 1-100.

    Zentralblatt MATH: 0004.05905
    Mathematical Reviews (MathSciNet): MR1503035
    Digital Object Identifier: doi:10.2307/1968102

  • 75. Norbert Wiener, A note on tauberian theorems, Ann. of Math. 33 (1932), 787.

    Zentralblatt MATH: 0005.25003
    Mathematical Reviews (MathSciNet): MR1503094

  • 76. Norbert Wiener, A new deduction of the Gaussian distribution, J. Math. and Phys. 10 (1931), 284-288.

    Zentralblatt MATH: 0004.06603

  • 77. Norbert Wiener, Characters of infinite Abelian groups (with R. E. A. C. Paley), Int'l. Math. Congr., Zürich, 1932.
  • 78. Norbert Wiener, Über eine Klasse Singulärer Integralgleichungen (with E. Hopf), S.-B. Preuss. Akad. Wiss. (1932), 696.

    Zentralblatt MATH: 0003.30701

  • 79. Norbert Wiener, Review: Harald Bohr. Fastperiodische Funktionen, Math. Gaz. 17 (1933), No. 54.
  • 80. Norbert Wiener, Review: A. S. Besicovitch. Almost periodic functions, Math. Gaz. 16 (1932), No. 220.
  • 81. Norbert Wiener, The Fourier integral and certain of its applications, Cambridge Univ. Press, New York, 1933; reprint, Dover, New York, 1959; Math. Rev. 20 (1959), rev. no. 6634.

    Zentralblatt MATH: 0006.05401
    Mathematical Reviews (MathSciNet): MR100201

  • 82. Norbert Wiener, Notes on the theory and application of Fourier transforms (with R. E. A. C. Paley) I, II, Trans. Amer. Math. Soc. 35 (1933), 348-355; III, IV, V, VI, VII, ibid. 35 (1933), 761-791.

    Zentralblatt MATH: 0008.15203

  • 83. Norbert Wiener, A one-sided Tauberian theorem, Math. Z. 36 (1933), 787-789.

    Zentralblatt MATH: 0007.00906
    Mathematical Reviews (MathSciNet): MR1545370
    Digital Object Identifier: doi:10.1007/BF01188648

  • 84. Norbert Wiener, R. E. A. C. Paley—In memoriam, Bull. Amer. Math. Soc. 39 (1933), 476.

    Mathematical Reviews (MathSciNet): MR1562651
    Digital Object Identifier: doi:10.1090/S0002-9904-1933-05637-9

  • 85. Norbert Wiener, Characters of Abelian groups (with R. E. A. C. Paley), Proc. Nat. Acad. Sci. 19 (1933), 253-257.

    Zentralblatt MATH: 0006.15001

  • 86. Norbert Wiener, Review: E. C. Titchmarsh, The Fourier integral and certain of its applications, Math. Gaz. 17 (1933), 129; Science 132 (1933), 731.
  • 87. Norbert Wiener, Notes on random functions (with R. E. A. C. Paley and A. Z. Zygmund), Math. Z. 37 (1933), 647-668.

    Zentralblatt MATH: 0007.35402
    Mathematical Reviews (MathSciNet): MR1545426
    Digital Object Identifier: doi:10.1007/BF01474606

  • 88. Norbert Wiener, The total variation of g(xh)—f(x) (with R. C. Young), Trans. Amer. Math. Soc. 35 (1933), 327-340.

    Zentralblatt MATH: 0006.19401
    Mathematical Reviews (MathSciNet): MR1501686

  • 89. Norbert Wiener, Leibnitz and Haldane, Philos. Sci. 1 (1934), No. 4.
  • 90. Norbert Wiener, Notes on the Kron theory of tensors in electrical machinery, Abstract, J. Electr. Eng. China 7, 3-4.
  • 91. Norbert Wiener, A class of gap theorems, Ann. Scuola Norm. Sup. Pisa, E (1934-1936), 1-6.

    Zentralblatt MATH: 0010.02803

  • 92. Norbert Wiener, Fourier transforms in the complex domain (with R. E. A. C. Paley), Amer. Math. Soc. Colloq. Publ., Vol. 19, Amer. Math. Soc. Providence, R. I., 1934.

    Zentralblatt MATH: 0011.01601

  • 93. Norbert Wiener, Random functions, J. Math. and Phys. 14 (1934), No. 1.
  • 94. Norbert Wiener, The closure of Bessel functions. Abstract 66, Bull. Amer. Math. Soc. 41 (1935), 35.
  • 95. Norbert Wiener, Fabry's gap theorem, Sci. Repts. of Nat'l. Tsing Hua Univ., Ser. A, 3 (1935), 239-245.

    Zentralblatt MATH: 0013.17102

  • 96. Norbert Wiener, A theorem of Carleman, Sci. Repts. of Nat'l. Tsing Hua Univ., Ser. A, 3 (1935), 291-298.

    Zentralblatt MATH: 0014.39906

  • 97. Norbert Wiener, Math. in American secondary schools, J. Math. Assoc. Japan for Secondary Education, Tokyo, 1935.
  • 98. Norbert Wiener, The role of the observer, Philos. Sci. 3 (1936), 307-319.
  • 99. Norbert Wiener, Sur les séries de Fourier lacunaires. Théorème direct (with Szolem Mandelbrojt), C. R. Acad. Sci. Paris 203 (1936), 34-36.

    Zentralblatt MATH: 0014.30402

  • 100. Norbert Wiener, Séries de Fourier lacunaires. Théorème inverses, with Szolem Mandelbrojt, C. R. Acad. Sci. Paris 203 (1936), 233-234.

    Zentralblatt MATH: 0014.30403

  • 101. Norbert Wiener, Gap theorems, C. R. de Congr. Int'l. des Math., 1936.

    Zentralblatt MATH: 0019.03402

  • 102. Norbert Wiener, A Tauberian gap theorem of Hardy and Littlewood, J. Chinese Math. Soc. 1 (1936), 15.

    Zentralblatt MATH: 0015.20901

  • 103. Norbert Wiener, Taylor's series of entire functions of smooth growth (with W. T. Martin), Duke Math. J. 3 (1937), 213-223.

    Zentralblatt MATH: 0016.40604
    Mathematical Reviews (MathSciNet): MR1545980
    Digital Object Identifier: doi:10.1215/S0012-7094-37-00314-4
    Project Euclid: euclid.dmj/1077490036

  • 104. Norbert Wiener, Random Waring's theorems. Abstract (with N. Levinson), Science 85 (1937), 439.
  • 105. Norbert Wiener, On absolutely convergent Fourier-Stieltjes transforms (with H. R. Pitt), Duke Math. J. 4 (1938), No. 2.

    Zentralblatt MATH: 0019.16803
    Mathematical Reviews (MathSciNet): MR1546064
    Digital Object Identifier: doi:10.1215/S0012-7094-38-00435-1
    Project Euclid: euclid.dmj/1077490649

  • 106. Norbert Wiener, Fourier-Stieltjes transforms and singular infinite convolutions (with Aurel Wintner), Amer. J. Math. 60 (1938), No. 3.

    Zentralblatt MATH: 0019.16901
    Mathematical Reviews (MathSciNet): MR1507332
    Digital Object Identifier: doi:10.2307/2371591

  • 107. Norbert Wiener, Remarks on the classical inversion formula for the Laplace integral (with D. V. Widder), Bull. Amer. Math. Soc. 44 (1938), 573.

    Mathematical Reviews (MathSciNet): MR1563795
    Digital Object Identifier: doi:10.1090/S0002-9904-1938-06812-7
    Project Euclid: euclid.bams/1183500627

  • 108. Norbert Wiener, The homogeneous chaos, Amer. J. Math. 60 (1938), 897-936.

    Zentralblatt MATH: 0019.35406
    Mathematical Reviews (MathSciNet): MR1507356
    Digital Object Identifier: doi:10.2307/2371268

  • 109. Norbert Wiener, The decline of cookbook engineering, Tech. Rev. 41 (1938), 23.
  • 110. Norbert Wiener, Review: L. Hogben, Science for the citizen, Tech. Rev. 41 (1938), 66-67.
  • 111. Norbert Wiener, The historical background of harmonic analysis, Amer. Math. Soc. Semicentennial Publications Vol. II, Semicentennial Addresses, Amer. Math. Soc., Providence, R. I., 1938.
  • 112. Norbert Wiener, Review: Roger Burlingame, March of the iron men, Tech. Rev. 41 (1939), 115.
  • 113. Norbert Wiener, Convergence properties of analytic functions of Fourier-Stieltjes transforms (with R. H. Cameron), Trans. Amer. Math. Soc. 46 (1939), 97-109; Math. Rev. 1 (1940), 13; 400.

    Zentralblatt MATH: 0021.32202
    Mathematical Reviews (MathSciNet): MR72

  • 114. Norbert Wiener, Generalization of Ikehara's theorem (with J. R. Pitt), J. Math. and Phys. 17 (1939), No. 4.

    Zentralblatt MATH: 0023.04802

  • 115. Norbert Wiener, On singular distribution (with Aurel Wintner), J. Math. and Phys. 17 (1939), No. 4.

    Zentralblatt MATH: 0022.35501

  • 116. Norbert Wiener, A new method in statistical mechanics (with B. McMillan), Abstract 133, Bull. Amer. Math. Soc. 45 (1939), 234; Science 90 (1939), November 3.
  • 117. Norbert Wiener, The ergodic theorem, Duke Math. J. 5 (1939), 1-18.

    Zentralblatt MATH: 0021.23501
    Mathematical Reviews (MathSciNet): MR1546100
    Digital Object Identifier: doi:10.1215/S0012-7094-39-00501-6
    Project Euclid: euclid.dmj/1077491072

  • 118. Norbert Wiener, The use of statistical theory in the study of turbulence, Nature 144 (1939), 728.

    Zentralblatt MATH: 0022.42103

  • 119. Norbert Wiener, A canonical series for symmetric functions in statistical mechanics. Abstract 133, Bull. Amer. Math. Soc. 46 (1940), 57.
  • 120. Norbert Wiener, Review: M. Fukamiya, On dominated ergodic theorems in Lp (p≥1), Math. Rev. 1 (1940), 148.
  • 121. Norbert Wiener, Review: M. Fukamiya, The Lipschitz condition of random functions, Math. Rev. 1 (1940), 149.
  • 122. Norbert Wiener, Review: Th. De Donder, L'énergétique déduite de la mécanique statistique générale, Math. Rev. 1 (1940), 192.
  • 123. Norbert Wiener, Harmonic analysis and ergodic theory (with Aurel Wintner), Amer. J. Math. 63 (1941), 415-426; Math. Rev. 2 (1941), 319.

    Zentralblatt MATH: 0025.06504
    Mathematical Reviews (MathSciNet): MR4098
    Digital Object Identifier: doi:10.2307/2371534

  • 124. Norbert Wiener, On the ergodic dynamics of almost periodic systems (with Aurel Wintner), Amer. J. Math. 63 (1941), 794-824.

    Zentralblatt MATH: 0026.13102
    Mathematical Reviews (MathSciNet): MR6618
    Digital Object Identifier: doi:10.2307/2371623

  • 125. Norbert Wiener, On the oscillation of the derivatives of a periodic function (with George Pólya), Trans. Amer. Math. Soc. 52 (1942), 249-256.

    Zentralblatt MATH: 0060.19504
    Mathematical Reviews (MathSciNet): MR7169

  • 126. Norbert Wiener, Ergodic dynamics of almost periodic systems (with Aurel Wintner), Math. Rev. 4 (1943), 15 (same as reference 124 above).

    Zentralblatt MATH: 0026.13102

  • 127. Norbert Wiener, Behavior, purpose, and teleology (with Arturo Rosenblueth and J. Bigelow), Philos. Sci. 10 (1943), 18-24.
  • 128. Norbert Wiener, The discrete chaos (with Aurel Wintner), Amer. J. Math. 65, 279-298; Math. Rev. 4 (1943), 220.

    Zentralblatt MATH: 0063.08250
    Mathematical Reviews (MathSciNet): MR7949
    Digital Object Identifier: doi:10.2307/2371816

  • 129. Norbert Wiener, The role of models in science (with Arturo Rosenblueth), Philos. Sci. 12 (1945), 316-322.
  • 130. Norbert Wiener, La teoria de la extrapolacion estadistica, Bol. Soc. Mat. Mexicana 2 (1945), 37-42; Math. Rev. 7 (1946), 461.

    Zentralblatt MATH: 0060.29201
    Mathematical Reviews (MathSciNet): MR15724

  • 131. Norbert Wiener, The mathematical formulation of the problem of conduction of impulses in a network of connected excitable elements, specifically in cardiac muscle (with Arturo Rosenblueth), Arch. Inst. Cardiol. Méxicana 16 (1946), 205-265; Bol. Soc. Mat. Mexicana 2 (1945), 37-42; Math. Rev. 9 (1948), 604.

    Zentralblatt MATH: 0063.08249
    Mathematical Reviews (MathSciNet): MR15724

  • 132. Norbert Wiener, Theory of statistical extrapolation, Math. Rev. 7 (1946), 416 (same as reference 130 above).

    Mathematical Reviews (MathSciNet): MR15724

  • 133. Norbert Wiener, A generalization of the Wiener-Hopf integral equation (with Albert E. Heins), Proc. Nat. Acad. Sci. U.S.A. 32 (1946), 98-101; Math. Rev. 8 (1947), 29.

    Zentralblatt MATH: 0063.01983
    Mathematical Reviews (MathSciNet): MR16521
    Digital Object Identifier: doi:10.1073/pnas.32.4.98

  • 134. Norbert Wiener, Sur les fonctions indéfiniment dérivables sur une demi-droite (with Szolem Mandelbrojt), C. R. Acad. Sci. Paris 225 (1947), 978-980; Math. Rev. 9 (1948), 230.

    Zentralblatt MATH: 0030.11703
    Mathematical Reviews (MathSciNet): MR22586

  • 135. Norbert Wiener, A scientist rebels, Atlantic Monthly 179 (1947), 46.
  • 136. Norbert Wiener, Teleological mechanisms (with L. K. Frank, G. E. Hutchinson, W. K. Livingston, and W. S. McCulloch), Ann. New York Acad. Sci. 50 (1948), 187-278.

    Mathematical Reviews (MathSciNet): MR26285
    Digital Object Identifier: doi:10.1111/j.1749-6632.1948.tb39853.x

  • 137. Norbert Wiener, Review: L. Infeld, Whom the Gods love: The story of Evariste Galois, Scripta Math. 14 (1948), 273-274.
  • 138. Norbert Wiener, Cybernetics, or control and communication in the animal and the machine, Actualités Sci. Ind., no. 1053; Hermann et Cie., Paris; The MIT Press, Cambridge, Mass. and Wiley, New York, 1948; Math. Rev. 9 (1948), 598.

    Zentralblatt MATH: 0098.11705
    Mathematical Reviews (MathSciNet): MR25096

  • 139. Norbert Wiener, A rebellious scientist after two years, Bull. Atomic Scientists 4 (1948), 338.
  • 140. Norbert Wiener, Time, communication and the nervous system, Ann. New York Acad. Sci. 50 (1948), 197-220; Math. Rev. 10 (1949), 133.

    Mathematical Reviews (MathSciNet): MR26285
    Digital Object Identifier: doi:10.1111/j.1749-6632.1948.tb39853.x

  • 141. Norbert Wiener, Cybernetics, Scientific American 179 (1948), 14-18.
  • 142. Norbert Wiener, An account of the spike potential of axons (with Arturo Rosenblueth, W. Pitts, and J. Garcia Ramos), J. Comp. Physiol. (1948), December.
  • 143. Norbert Wiener, Sur la théorie de la prévision statistique et du filtrage des ondes, Analyse Harmonique, Colloques Internationaux du CNRS, No.15, pp. 67-74. Centre National de la Recherche Scientifique, Paris, 1949; Math. Rev. 11 (1950), 376.

    Zentralblatt MATH: 0039.34703
    Mathematical Reviews (MathSciNet): MR32983

  • 144. Norbert Wiener, Extrapolation, interpolation, and smoothing of stationary time series. With engineering applications, The MIT Press, Cambridge, Mass.; Wiley, New York; Chapman & Hall, London, 1949; Math. Rev. 11 (1950), 118.

    Zentralblatt MATH: 0036.09705
    Mathematical Reviews (MathSciNet): MR31213

  • 145. Norbert Wiener, New concept of communication engineering, Electronics 22 (1949), 74-77.
  • 146. Norbert Wiener, Obituary: Godfrey Harold Hardy (1877-1947), Bull. Amer. Math. Soc. 55 (1949), 72-77; Math. Rev. 10 (1949), 420.

    Zentralblatt MATH: 0031.09906
    Mathematical Reviews (MathSciNet): MR28232
    Digital Object Identifier: doi:10.1090/S0002-9904-1949-09165-6
    Project Euclid: euclid.bams/1183513380

  • 147. Norbert Wiener, Sound communication with the deaf, Philos. Sci. 16 (1949), No. 3.
  • 148. Norbert Wiener, Some problems in sensory prosthesis (with L. Levine), Science 110 (1949), November 11.
  • 149. Norbert Wiener, The thinking machine, Time 55 (1950), January 23.
  • 150. Norbert Wiener, Some prime-number consequences of the Ikehara theorem (with Leonard Geiler), Acta Sci. Math. (Szeged) 12, Leopoldo Fejer et Frederico Riesz LXX annos natis dedicatus, Pars B, 25-28 (1950); Math. Rev. 11 (1950), 644; ibid 12 (1951), 1002.

    Zentralblatt MATH: 0038.18302
    Mathematical Reviews (MathSciNet): MR34801

  • 151. Norbert Wiener, The human use of human beings, Houghton Mifflin, Boston, 1950 (paperback edition (Anchor) by Doubleday, 1954).
  • 152. Norbert Wiener, Cybernetics, Bull. Amer. Acad. Arts and Sci. 3 (1950), No. 7.
  • 153. Norbert Wiener, Some maxims for biologists and psychologists, Dialectica 4 (September 1950), 3.
  • 154. Norbert Wiener, Purposeful and non-purposeful behavior (with Arturo Rosenblueth), Philos. Sci. (1950), October.
  • 155. Norbert Wiener, Speech, language, and learning, J. Acoust. Soc. Amer. 22 (1950), 696-697.
  • 156. Norbert Wiener, Comprehensive view of prediction theory, Proceedings of the International Congress of Mathematicians, Cambridge, Mass., 1950, Vol. 2, pp. 308-321; Amer. Math. Soc. Providence, R. I, 1952, Expository lecture; Math. Rev. 13 (1952), 477.

    Zentralblatt MATH: 0049.09509
    Mathematical Reviews (MathSciNet): MR44777

  • 157. Norbert Wiener, Entropy and information, Proc. Sympos. Appl. Math., Vol. 2, Amer. Math. Soc. Providence, R. I., 1950; p. 89; Math. Rev. 11 (1950), 305.

    Zentralblatt MATH: 0035.26101
    Mathematical Reviews (MathSciNet): MR32544

  • 158. Norbert Wiener, Problems of sensory prosthesis, Bull. Amer. Math. Soc. 57 (1951), 27-35.

    Mathematical Reviews (MathSciNet): MR1565264
    Digital Object Identifier: doi:10.1090/S0002-9904-1951-09433-1
    Project Euclid: euclid.bams/1183515799

  • 159. Norbert Wiener, Homeostasis in the individual and society, J. Franklin Inst. 251 (1951), No. 1.

    Mathematical Reviews (MathSciNet): MR130700

  • 160. Norbert Wiener, The brain (ss), Tech. Eng. News (1952), April; reprinted in paperback anthology, Crossroads in Time, ed. Groff Conklin, Doubleday, New York, 1953.
  • 161. Norbert Wiener, Les machines à calculer et la forme (Gestalt), Les machines à calculer et la pensée humaine, Colloques Internationaux du Centre National de la Recherche Scientifique, Paris, 1953; pp. 461-463; Math. Rev. 16 (1955), 529.

    Mathematical Reviews (MathSciNet): MR66110

  • 162. Norbert Wiener, A new form for the statistical postulate of quantum mechanics (with Armand Siegel), Phys. Rev. 91 (1953), 1551-1560; Math. Rev. 15 (1954), 273.

    Zentralblatt MATH: 0052.22009
    Mathematical Reviews (MathSciNet): MR57763
    Digital Object Identifier: doi:10.1103/PhysRev.91.1551

  • 163. Norbert Wiener, Distributions quantiques dans l'espace différentiel pour les fonctions d'ondes dépendant du spin, C. R. Acad. Sci. Paris 237 (1953), 1640-1642; Math. Rev. 15 (1954), 490.

    Zentralblatt MATH: 0052.22101
    Mathematical Reviews (MathSciNet): MR59197

  • 164. Norbert Wiener, Miracle of the broom closet (ss), Tech. Eng. News 33 (1952), No. 7; reprinted in the Magazine of Fantasy and Science Fiction, ed. Anthony Boucher, February, 1954.
  • 165. Norbert Wiener, Ex-prodigy: my childhood and youth, Simon and Schuster, New York, 1953; The MIT Press, Cambridge, Mass. 1965 (also paperback edition by MIT Press); Math. Rev. 15 (1954), 277.

    Mathematical Reviews (MathSciNet): MR57817

  • 166. Norbert Wiener, The concept of homeostasis in medicine, Transactions and Studies of the College of Physicians of Philadelphia (4) 20 (1953), No. 3.
  • 167. Norbert Wiener, The differential space theory of quantum mechanics (with Armand Siegel), Phys. Rev. 91 (1953), 1551.

    Zentralblatt MATH: 0052.22009

  • 168. Norbert Wiener, Optics and the theory of stochastic processes, J. Opt. Soc. Amer. 43 (1953); 225-228; Math. Rev. 17 (1956), 33.[note[

    Mathematical Reviews (MathSciNet): MR70767
    Digital Object Identifier: doi:10.1364/JOSA.43.000225

  • 169. Norbert Wiener, The future of automatic machinery, Mechanical Engineering (1953), 130-132, February.
  • 170. Norbert Wiener, Nonlinear prediction and dynamics, Proc. Third Berkeley Symposium on Mathematical Statistics and Probability, University of California Press, 1954; Math. Rev. 18 (1957), 949.

    Mathematical Reviews (MathSciNet): MR84928

  • 171. Norbert Wiener, The differential space theory of quantum systems (with Armand Siegel), Nuovo Cimento (10) 2 (1955), 982-1003, No. 4, Suppl.

    Zentralblatt MATH: 0068.22301
    Mathematical Reviews (MathSciNet): MR94161
    Digital Object Identifier: doi:10.1007/BF02744277

  • 172. Norbert Wiener, On the factorization of matrices, Comment. Math. Helv. 29 (1955), 97-111; Math. Rev. 16 (1955), 921.

    Zentralblatt MATH: 0064.06301
    Mathematical Reviews (MathSciNet): MR68663
    Digital Object Identifier: doi:10.1007/BF02564273

  • 173. Norbert Wiener, Thermodynamics of the message, Neurochemistry, ed. K. E. C. Elliott, Thomas, Springfield, 1955.
  • 174. Norbert Wiener, Time and organization, Second Fawley Foundation Lecture, University of Southampton, 1955.
  • 175. Norbert Wiener, The "Theory of measurement" in differential space quantum theory (with Armand Siegel), Phys. Rev. 101 (1956), 429-432.

    Mathematical Reviews (MathSciNet): MR94162
    Digital Object Identifier: doi:10.1103/PhysRev.101.429

  • 176. Norbert Wiener, The theory of prediction, Modern mathematics for the engineer, ed. E. F. Beckenbach, McGraw-Hill, New York, 1956.
  • 177. Norbert Wiener, I am a mathematician. The later life of a prodigy, Doubleday, Garden City, New York, 1956 (paperback edition by The MIT Press); Math. Rev. 17 (1956), 1037.

    Zentralblatt MATH: 0071.00415
    Mathematical Reviews (MathSciNet): MR77455

  • 178. Norbert Wiener, Brain waves and the interferometer, J. Phys. Soc. Japan 18 (1956), No. 8.
  • 179. Norbert Wiener, Moral reflections of a mathematician, Bull. Atomic Scientists 12 (1956), 53-57; reprinted from I am a mathematician.
  • 180. Norbert Wiener, Rhythms in physiology with particular reference to encephalography. Proceedings of the Rudolf Virchow Medical Society in the City of New York, Vol. 16, 1957; pp. 109-124.
  • 181. Norbert Wiener, The definition and ergodic properties of the stochastic adjoint of a unitary transformation (with E. J. Akutowicz), Rend. Circ. Mat. Palermo (2) 6 (1957), 205-217, Addendum, 349; Math. Rev. 20 (1959), rev. no. 4328.[note[

    Zentralblatt MATH: 0082.11503
    Mathematical Reviews (MathSciNet): MR97863
    Digital Object Identifier: doi:10.1007/BF02843846

  • 182. Norbert Wiener, Notes on Pólya's and Turan's hypotheses concerning Liouville's factor, Rend, Circ. Mat. Palermo (2) 6 (1957), 240-248; Math. Rev. 20 (1959), rev. no. 5759.

    Zentralblatt MATH: 0082.29101
    Mathematical Reviews (MathSciNet): MR99319
    Digital Object Identifier: doi:10.1007/BF02843849

  • 183. Norbert Wiener, The role of the mathematician in a materialistic culture (A scientist's dilemma in a materialistic world), Columbia Engineering Quarterly, Proceedings of the Second Combined Plan Conference, Arden House, October 6-9, 1957; pp. 22-24.
  • 184. Norbert Wiener, On the non-vanishing of Euler products (with Aurel Wintner), Amer. J. Math. 79 (1957), 801-808.

    Zentralblatt MATH: 0089.28603
    Mathematical Reviews (MathSciNet): MR1507477
    Digital Object Identifier: doi:10.2307/2372436

  • 185. Norbert Wiener, The prediction theory of multivariate stochastic processes. I. The regularity condition (with P. Masani), Acta Math. 98 (1957), 111-150; Math. Rev. 20 (1959), rev. no. 4323.

    Zentralblatt MATH: 0080.13002
    Mathematical Reviews (MathSciNet): MR97856
    Digital Object Identifier: doi:10.1007/BF02404472

  • 186. Norbert Wiener, The prediction theory of multivariate stochastic processes. II. The linear predictor (with P. Masani), Acta Math. 99 (1958), 93-137; Math. Rev. 20 (1959), rev. no. 4325.

    Zentralblatt MATH: 0080.13002
    Mathematical Reviews (MathSciNet): MR97859
    Digital Object Identifier: doi:10.1007/BF02392423

  • 187. Norbert Wiener, Logique, probabilité et méthode des sciences physiques, La Methodes dans les Sciences Modernes, Editions Science et Industrie, ed. François Le Lionnais, Paris, 1958; pp. 111-112.
  • 188. Norbert Wiener, My connection with cybernetics. Its origin and its future, Cybernetica (1958), 1-14.

    Zentralblatt MATH: 0867.01048
    Mathematical Reviews (MathSciNet): MR1328045

  • 189. Norbert Wiener, Random time, Nature 181 (1958), 561-562.

    Zentralblatt MATH: 0078.43101

  • 190. Norbert Wiener, Time and the science of organization, Scientia (1958), September.
  • 191. Norbert Wiener, Nonlinear problems in random theory, The MIT Press, Cambridge, Mass., and Wiley, New York 1958; Math. Rev. 20 (1959), rev. no. 7337.

    Zentralblatt MATH: 0121.12302
    Mathematical Reviews (MathSciNet): MR100912

  • 192. Norbert Wiener, Sur la prévision linéaire des processus stochastiques vectoriels à densité spectrale bornée. I (with P. Masani), C. R. Acad. Sci. Paris 246 (1958), 1492-1495; Math. Rev. 20 (1959), rev. no. 4324a.

    Zentralblatt MATH: 0080.34902
    Mathematical Reviews (MathSciNet): MR97857

  • 193. Norbert Wiener, Sur la prévision linéaire des processus stochastiques vectoriels à densité spectrale bornée. II (with P. Masani), C. R. Acad. Sci. Paris 246 (1958), 1655-1656; Math. Rev. 20 (1959), rev. no. 4324b.

    Zentralblatt MATH: 0083.13902
    Mathematical Reviews (MathSciNet): MR97858

  • 194. Norbert Wiener, A factorization of positive Hermitian matrices (with E. J. Akutowicz), J. Math. Mech. 8 (1959), 111-120.

    Zentralblatt MATH: 0082.28103
    Mathematical Reviews (MathSciNet): MR103388

  • 195. Norbert Wiener, The tempter, Random House, New York, 1959.
  • 196. Norbert Wiener, Non-linear prediction (in "Probability and statistics") (with P. Masani), The Harald Cramer Volume, ed. U. Grenander, Stockholm, 1959.

    Zentralblatt MATH: 0201.51605

  • 197. Norbert Wiener, On bivariate stationary processes and the factorization of matrix-valued functions (with P. Masani), Theory of Probability and its Applications (Moscow) 4 (1959), 322-331; (English transl., pp. 300-308).

    Zentralblatt MATH: 0089.34003
    Mathematical Reviews (MathSciNet): MR114250

  • 198. Norbert Wiener, Preface to "Cybernetics of natural systems" by D. Stanley-Jones, Pergamon Press, London, 1960.
  • 199. Norbert Wiener, "The grand privilege", Saturday Review (1960), March 5.
  • 200. Norbert Wiener, Some moral and technical consequences of automation, Science 131 (1960).
  • 201. Norbert Wiener, Kybernetik, Contribution to Das Soziologische Wörterbuch, F. Enke Verlag, Stuttgart, 1960.
  • 202. Norbert Wiener, Ueber Informationstheorie, Naturwissenschaften 7 (1961), 174-176.

    Zentralblatt MATH: 0113.12002
    Mathematical Reviews (MathSciNet): MR127444
    Digital Object Identifier: doi:10.1007/BF00597467

  • 203. Norbert Wiener, Science and society, Voprosy Filosofii (1961), No. 7.
  • 204. Norbert Wiener, Cybernetics, Second edition, The MIT Press and Wiley, New York, 1961, (also paperback edition by MIT Press).

    Mathematical Reviews (MathSciNet): MR127995

  • 205. Norbert Wiener, L'homme et la machine, Proc. Colloques Philosophiques Internationaux de Royaumont, July, 1962; Le concept d'information dans la science contemporaine, Gauthier-Villars, Paris, 1965, pp. 99-132.
  • 206. Norbert Wiener, Contribution to Proc. of the International Symposium on the Application of Automatic Control in Prosthetics Design, August 27-31, 1962, Opatija, Yugoslavia; p. 132.
  • 207. Norbert Wiener, The mathematics of self-organizing systems, Recent developments in information and decision processes, Macmillan, New York, 1962.
  • 208. Norbert Wiener, Introduction to neurocybernetics and Epilogue (With J. P. Schade), Progress in brain research, Vol. 2 (Nerve, Brain and Memory Models), Elsevier Publishing Co., Amsterdam, 1963, pp. 1-7, 264-268.
  • 209. Norbert Wiener, Random theory in classical phase space and quantum mechanics (with Giacomo della Riccia), Proc. Internat. Conference on Functional Analysis, Massachusetts Institute of Technology, Cambridge, Mass., June 9-13, 1963; Analysis in function space, pp. 3-14, The MIT Press, Cambridge, Mass. 1964.

    Mathematical Reviews (MathSciNet): MR186250

  • 210. Norbert Wiener, On the oscillations of nonlinear systems, Proc. Symposium on Stochastic Models in Medicine and Biology, Mathematics Research Center, U. S. Army, June 12-14, 1963.

    Zentralblatt MATH: 0202.56603

  • 211. Norbert Wiener, God and Golem, Inc.: A comment on certain points where cybernetics impinges on religion, The MIT Press, Cambridge, Mass., 1964.
  • 212. Norbert Wiener, Dynamical systems in physics and biology, Contribution to series "Fundamental Science in 1984", The New Scientist, London, 1964.

    Mathematical Reviews (MathSciNet): MR127995

  • 213. Norbert Wiener, Reprinting of [143] as Time series, Wiley paperbacks, 1964 (paperback edition by The MIT Press).
  • 214. Norbert Wiener, Selected papers of Norbert Wiener: Expository papers by Y. W. Lee, Norman Levinson, and W. T. Martin, The MIT Press, Cambridge, Mass., 1964.

    Mathematical Reviews (MathSciNet): MR182520

  • Norbert Wiener, (born Nov. 26, 1894, Columbia, Mo., U.S.—died March 18, 1964, Stockholm, Swed.), American mathematician who established the science of cybernetics. He attained international renown by formulating some of the most important contributions to mathematics in the 20th century.

    Wiener, a child prodigy whose education was controlled by his father, a professor of Slavonic languages and literature at Harvard University, graduated in mathematics from Tufts College (now Tufts University, Medford, Massachusetts) in 1909 at the age of 14. He spent a year at Harvard as a graduate student in zoology but left after he found that he was inept at laboratory work. At his father’s suggestion, he began to study philosophy, and he completed a Ph.D. at Harvard in 1913 with a dissertation on mathematical logic.

    On a grant from Harvard, Wiener went first to England, to study mathematical logic at the University of Cambridge under Bertrand Russell, and then to the University of Göttingen in Germany, to study with David Hilbert. On the advice of Russell, he also began a serious study of general mathematics, in which he was strongly influenced by Russell, by the English pure mathematician Godfrey Hardy, and to a lesser extent by Hilbert. He published his first paper in the mathematical journal Messenger of Mathematics in 1913 at Cambridge.

    When World War I broke out, he tried to enlist but was rejected because of poor eyesight. For five years he tried a variety of occupations. He was a teacher at the University of Maine, a writer for an encyclopaedia, an apprentice engineer, a journalist of sorts, and a mathematician at the Aberdeen (Maryland) Proving Grounds. Finally, in 1919, he was hired as an instructor by the mathematics department at the Massachusetts Institute of Technology (MIT), a department with no real tradition of scholarship or research at that time. It turned out, however, to have been the right move for Wiener, for he had entered upon an extremely productive period, just as MIT itself was beginning to develop into a great centre of learning in science and technology. Wiener remained on the MIT faculty until his retirement.

    During the 1920s Wiener did highly innovative and fundamental work on what are now called stochastic processes and, in particular, on the theory of Brownian motion and on generalized harmonic analysis, as well as significant work on other problems of mathematical analysis. In 1933 Wiener was elected to the National Academy of Sciences but soon resigned, repelled by some of the aspects of institutionalized science that he encountered there.

    During World War II Wiener worked on the problem of aiming gunfire at a moving target. The ideas that evolved led to Extrapolation, Interpolation, and Smoothing of Stationary Time Series (1949), which first appeared as a classified report and established Wiener as a codiscoverer, with the Russian mathematician Andrey Kolmogorov, of the theory on the prediction of stationary time series. It introduced certain statistical methods into control and communications engineering and exerted great influence in these areas. This work also led him to formulate the concept of cybernetics.

    In 1948 his book Cybernetics; or, Control and Communication in the Animal and the Machine was published. For a scientific book it was extremely popular, and Wiener became known in a much broader scientific community. Cybernetics is interdisciplinary in nature; based on common relationships between humans and machines, it is used today in control theory, automation theory, and computer programs to reduce many time-consuming computations and decision-making processes formerly done by human beings. Wiener worked at cybernetics, philosophized about it, and propagandized for it the rest of his life, all the while keeping up his research in other areas of mathematics.

    After the war Wiener continued to contribute new ideas to widely divergent subjects, including mathematical prediction theory and quantum theory, providing the latter a possible solution to a difficulty that had been debated by the physicists Niels Bohr and Albert Einstein. Applying his theoretical description of Brownian motion to quantum phenomena, he showed how quantum theory, to the extent that it is based on probability, is consistent with other branches of science. In 1963 Wiener was awarded the National Medal of Science; he was presented with the medal a few weeks before his death the following year.

    Wiener wrote many other works. He discussed the implications of mathematics for public and private affairs in The Human Use of Human Beings (rev. ed., 1954) and God and Golem, Inc.: A Comment on Certain Points Where Cybernetics Impinges on Religion (1964). Wiener also completed two volumes of autobiography, Ex-Prodigy (1953) and I Am a Mathematician (1956).