Mathematics and Humanities: From the History of Relations
https://doi.org/10.22405/2226-8383-2025-26-3-307-334
Abstract
The work is devoted to the history of the relationship between mathematics and its applications in the humanities, in this case with economic sciences, linguistics, literary criticism, history. It is generally recognized that the role of mathematics in the humanities, where man
is invariably present with his emotions, preferences, moods and other manifestations of the human spirit, can be useful in the computational and statistical aspects. The main question is how productive can the role of mathematics be, can we expect fundamentally new results from
mathematical methods? Consideration of the impact of mathematics on various humanities convinces us of a positive answer to this question. The extent of the application of mathematics is extremely broad: from the accuracy and clarity of the conceptual apparatus, the penetration of the "mathematical spirit"to solving problems according to the standards of rigor and logical precision adopted in mathematics itself, from quantitative methods to qualitative models.
About the Authors
Anna Vyacheslavovna Boeva
Stary Oskol Technological Institute named after A. A. Ugarov (branch) of the National Research Technological University “MISiS”
Russian Federation
Russian Federation
candidate of pedagogical sciences
Zinara Zievna Mukhina
Stary Oskol Technological Institute named after. A. A. Ugarov (branch) of the National Research Technological University “MISiS”
Russian Federation
Russian Federation
doctor of historical sciences
Ravil Rafkatovich Mukhin
Stary Oskol Technological Institute named after A. A. Ugarov (branch) of the National Research Technological University “MISiS”
Russian Federation
Russian Federation
doctor of physical and mathematical sciences
References
1. Thomson, W. 1891, Lecture on “Electrical Units of Measurement”, Sir William Thomson. Popular Lectures and Adresses. L.: Macmillan and co., pp. 8–143.
2. Prigogine, I., Stengers, I. “Order out of Chaos”, Toronto-NY-L.: Bantom Books, 1984. 348 p.
3. Debreu G. 1991 “The Mathematization of Economic Theory”, Amer. Econom. Rev., Vol. 81. № 1. pp. 1–7.
4. Mukhin, R.R., Chernikova, A.A. 2014, “On the history of econophysics, nonlinear and evolutionary economics”, News of universities. Applied nonlinear dynamics, Vol. 22, № 3, pp. 3-25 (in Russian).
5. Bachelier, L. 1900, “Th´eorie de la sp´eculation. Doctoral dissertation”, Ann. Ecole Norm. Sup., Vol. 17, pp. 21-86.
6. Jarrow, R., Protter, P. 2004, “A short history of stochastic integration and mathematical finance. The early years, 1880 – 1970”, Lecture notes Inst. Math. Statistics, Vol. 45, pp. 75-91.
7. Mandelbrot B., Hudson, R. 2004, “The (mis)Behavior of Markets”, NY: Basic Books, 326 p.
8. Lasker, E. 1907, “Kampf”, NY: Verlag Lasker’s Publishing Co., 80 P.
9. Zermelo, E. 1913, “ ¨Uber eine Anwendung der Mengenlehre auf die Theorie des Schachspiels”, Proc. Fifth Congress Math. Camb.: Camb. Univ. Press, pp. 501-504.
10. Borel, E. 1921, “La th´eorie du jeu et les equations, integrals a noyau symetrique gauche”, Comt. Rend., Vol. 173, pp. 1304-1308.
11. Borel, E. 1924, “Sur les jeu ou interviennent l’hasard et l’habilite des joueurs”, ´ El´ements de la Th´eorie des Probabilit´es. Paris: J. Hermann, pp. 204-224.
12. Borel, E. 1927, “Sur les syst`emes de formes lin´eaires `a d´eterminant sym´etrique gauche et la th´eorie g´en´erale du jeu”, Compt. Rend., Vol. 184, pp. 52–54.
13. Neuman, J. von. 1928, “Zur Theorie der Gesellschaftspiele”, Math. Annal., Vol. 100, pp. 295–320.
14. Neumann, J. von, Morgenstern, O., 1944, “Theory of Games and Economic Behaviour”, Princeton: Princeton Univ. Press, 625 p.
15. Neuman J. von. 1945, “A model of general economic equilibrium”, The Rev. Econom. Studies, Vol. 13, No 1. pp. 1-–9.
16. Weintraub, E.R. 1977, “General Equilibrium Theory”, Modern Economic Thought. Philadelphia: Univ. of Pennsylvania Press, 1977. pp. 107–131.
17. Nash, J.F., Jr. 1950, “Equilibrium points in N-person games”, Proc. National Acad. Sci. USA., 1950. Vol. 36. No 1. pp. 48–49.
18. Nash, J.F., Jr. 1951, “Non-cooperative games”, Ann. Math. Second ser., Vol. 54, № 2, pp. 286–295.
19. Braudel, F. 1958, “Histoire et science sociale: La Long Dur´ee”, Ann. E.S.C., № 4, pp. 725–753.
20. Goodwin, R.M. 1951, “The nonlinear accelerator and the persistence of business cycles”, Econometrica, Vol. 19, № 1, pp. 1–17.
21. Andronov, A.A., Khaikin, S.E. 1949, “Theory of oscillations”, Princeton, NJ: Princeton Univ. Press, 1949. 377 p.
22. Cartwtighte, M., Littlewood, J.E. 1945, “On non-linear differential equation of the second order: −𝑘(1 − 𝑦2) + 𝑦 = 𝑏𝜆𝑘𝑐𝑜𝑠(𝜆𝑡 + 𝛼), 𝑘𝑙𝑎𝑟𝑔𝑒”, London Math. Soc., Vol. 20, Part 3, pp. 180–189.
23. Wiener, N. 1948, “Cybernetics: Or Control and Communication in the Animal and the Machine”, Camb. Mass.: MIT Press, 212 p. Available at: https://en.wikipedia.org/wiki/Norbert_Wiener.
24. Levi-Strauss, C. 1963, “Structural Anthropology”, NY: Basic Books, XVI + 410 p.
25. Kolmogorov, A.N. “Three approaches to the definition of the notion of amount of information”, Select. Works of A. N. Kolmogorov. Vol. III. Information Theory and the Theory of Algorithms, Springer-Science+Business Media, B.V., pp. 184–193.
26. Kolmogorov, A.N. “To the logical foundations of the theory of information and probability theory”, Select. Works of A. N. Kolmogorov. Vol. III. Information Theory and the Theory of Algorithms, Springer-Science+Business Media, B.V., pp. 203–207.
27. Shapir, M.I. 2005, “You have no number and measure. On the possibilities and limits of “exact methods” in the humanities”, Questions of linguistics, № 1. pp. 43-62 (in Russian).
28. Gladkiy, A.V. 2007 “On exact and mathematical methods in linguistics and other humanities”, Questions of linguistics, № 5. pp. 22–38 (in Russian).
29. Lebedev, V. 1996, “ “True” history”, Questions of Philosophy, № . 11, pp. 137–142 (in Russian).
30. Uspensky, V.A. 2002, “Review of the dissertation of Andrey Anatolyevich Zaliznyak”, Works on NON-mathematics. Moscow: OGI, pp. 369–383 (in Russian).
31. Lotman, Yu.M. Culture and Explosion // Yu.M. Lotman. Semiosphere. SPb.: "Art-SPB 2010. pp. 11–148 (in Russian).
32. Lotman Yu.M. 2010, “Inside the Thinking Worlds”, Yu. M. Lotman. Semiosphere. SPb.: “Art-SPB”, pp. 150–390 (in Russian).
33. Kling, O.A. 2009, “Andrey Bely: The idea of synthesis of “exact knowledge” and humanities”, Bull. Moscow State Univ., Ser. 9, Philology, № 6. pp. 29–35 (in Russian).
34. Levi-Strauss, C. 1956, “Les Mathematique de l’homme”, Esprit, Vol. 10, Nouvelle Ser. 243, pp. 525–528.
35. Khrolenko, A.T. 2013, “Fundamentals of modern philology”, Moscow: FLINTA, 344 p. (in Russian).
36. Saussure, F. 2011, “de. Course in general linguistics”, NY: Columbia University Press, 2011.
37. Gladkiy, A.V., Melchuk I.A. 1969, “Elements of Mathematical Linguistics”, Moscow: Nauka, 192 p. (in Russian).
38. Klein, L.S. 1998, “Anatomy of the Iliad”, St. Petersburg: Publishing House of St. Petersburg University, 560 p. (in Russian).
39. Zaliznyak, A.A. 2004, “The Tale of Igor’s Campaign”: a linguist’s view”, Moscow: Languages of Slavic Culture, 2004. 352 p. (in Russian).
40. Thom, R. 1970, “Topologie et linguistique”, Essays on topology and related topics. Memoirs dedies a George de Rham. Berlin: Springer Verlag, 1970. pp. 226–248.
41. Polubichenko, L.V. 2012, “Philological topology: stages of development and scientific problems”, Bull. of Moscow Univ., Ser. 19, № 2, pp. 39–50. (in Russian).
42. Polubichenko, L.V. 2017, “Topological paradigm of humanitarian knowledge: myth or reality?”, Bull. of Moscow Univ., Ser. 19, № 4, pp. 102–117. (in Russian).
43. Surganova, T.V. 2010, “Topology of poetry and prose by Rudyard Kipling”, Abstract of Cand. Philological Sciences Dissertation. Moscow, 2010. 26 p. (in Russian).
44. Surganova, T.V. 2009, “Topological vision of artistic discourse: ‘The case of Kipling” ”, Bull. of Moscow Univ., Series 19, № 2, pp. 104–111 (in Russian).
45. Polubichenko, L.V. 2016, “On the issue of the sphere of fixation of quotations”, Bull. of Moscow Univ., Series 19, № 1, pp. 42–51 (in Russian).
46. Sadikova, V.A. 2015, “On the issue of language topology”, Bull. of Tver Univ. Ser. “Philology”, № . 4, pp. 44–49 (in Russian).
47. Richardson, J., Kroeber, A.L. 1940, “Three centuries of women’s dress fashion. A quantitative analysis”, Antropol. Rev., Vol. 5, № 2, pp. 111–154.
48. Robert, Vogel. 2001, “Nobel laureates of the twentieth century”, Economy. M.: ROSSPEN, pp. 255–260 (in Russian).
49. Douglas, North. 2001, “Nobel laureates of the twentieth century”, Economics. Moscow: ROSSPEN, pp. 248–254 (in Russian).
50. Gurevich, A.Ya. 1996, “History of the end of the twentieth century in search of a method”, Odyssey. Moscow: Nauka, pp. 4–8 (in Russian).
51. Fogel, R.W. 1964, “Railroads and American Economic Growth: Essays in Economic History”, Baltimor: Johns Hopkins Press, XV + 296 p.
52. Fogel, R.W., Engerman, S.L. 1971, “The Reinterpretation of American Economic History”, NY: Harper and Row, 494 p.
53. North, D.C. 1961, “The economic growth of the United States 1790-1860”, NY: Prentice Hall, 304 p.
54. North, D.C. 1968, “Sources of Productivity in Ocean Shipping”, J. Polit. Economy, Vol. 76, pp. 953–970.
55. North, D.C., Davis, L.E. 1971, “Institutional Change and Economic Growth”, J. Economic History, Vol. 34, No 1, pp. 1–7.
56. Kovalchenko, I.D. 1987, “Methods of historical research”, Moscow: Nauka, 440 p. (in Russian).
57. Kovalchenko, I.D. 1991, “Stolypin agrarian reform. Myths and reality”, History of the USSR, № 2, pp. 52–77 (in Russian).
58. Milov, L.V. 2001, “Great Russian Plowman and the Peculiarities of the Russian Historical Process”, Moscow: ROSSPEN, 576 p. (in Russian).
59. Mozheiko, M.A. 2012, “The idea of nonlinearity and the phenomenon of neodetheminism: a methodological turn in modern science”, Sociology, № . 2, pp. 39–53 (in Russian).
60. Prigogine, I. 1980, “From Being to Becoming: Time and Complexity in the Physical Sciencies”, San Francisco: W. H. Freeman and Co., xix + 272 pp.
61. Haken, G. 1980, “Synergetics”, Berlin-Heidelberg-NY: Springer-Verlag, 355 p.
62. Kiel, D., Elliott, E.W. 1996, “Chaos Theory in the Social Sciences. Ann Arbor”, Univ. of Michigan Press, 1996. 349 p. Available at: https://openlibrary.org/publishers/University_of_Michigan_Press
63. Szillard, L. 1929, “ ¨Uber die Entropieverminderung in einem thermodynamischen System bei eingriffen intelligenter Wesen”, Zeits. Physik, Bd. 53, pp. 840–856.
64. Trotsky, L. 1986, “Diaries and Letters”, NY: HERMITAGE, 224 p. (in Russian).
65. Borodkin, L.I. 2019, “Challenges of instability: concepts of synergetics in the study of the historical development of Russia”, Ural historical bull., № . 2 (63), pp. 127–136 (in Russian).
66. Gurevich, A.Ya. 1969, “On historical regularity”, Philosophical problems of historical science. Moscow: Nauka, pp. 51–79 (in Russian).
67. Andreev, A.Yu., Borodkin, L.I. 2003, “Nonlinear model of the strike movement: analysis of self-organization effects”, Circle of ideas: electronic resources of historical informatics / Proc. of the Conf. of the Association “History and Computer”. Ed. L.I. Borodkin, V.N. Vladimirov. Moscow-Barnaul, pp. 434–489 (in Russian).
68. Borodkin, L.I. 2016, “Modeling of historical processes”, St. Petersburg: Aleteya, 304 p. (in Russian).
69. Markov, A.A. 1913, “An example of statistical research on the text “Eugene Onegin”, illustrating the connection of tests in the cycle”, Bulletin of the Imperial Academy of Sciences, 6-th series, Vol. 7, Iss. 3, pp. 153—162 (in Russian).
Review
For citations:
Boeva A.V., Mukhina Z.Z., Mukhin R.R. Mathematics and Humanities: From the History of Relations. Chebyshevskii Sbornik. 2025;26(3):307-334. (In Russ.) https://doi.org/10.22405/2226-8383-2025-26-3-307-334
Views:
34
Email this article 