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I am looking at all mathematicians. Who are the mathematicians who are interested in the history of mathematics? I found that among modern mathematicians whose information is relatively easy to obtain, Andre Weil and Jean Pierre Serre exist. Are there any other mathematicians interested in the history of mathematics?

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  • $\begingroup$ Perhaps Jeremy Avigad (andrew.cmu.edu/user/avigad/papers.html)? $\endgroup$ Commented Jun 7 at 18:21
  • $\begingroup$ Thank you to everyone who wrote comments and answers to this question. $\endgroup$ Commented Jun 8 at 4:01
  • $\begingroup$ The question asked for "modern mathematicians", but the majority of the individuals mentioned have been dead for many years (nearly 100 years in the case of Felix Klein). These people are history, and quite ancient history at that! $\endgroup$ Commented Jun 8 at 6:35
  • $\begingroup$ @DavidLoeffler I would take that term to refer to the modern era. $\endgroup$ Commented Jun 8 at 15:48
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    $\begingroup$ I was going to write an answer mentioning current mathematicians such as John Stillwell, David Bressoud, Jeremy Gray and Fernando Gouvêa, but after reading some comments, I then wasn't sure anymore that's what you're after. Would you mind editing the question for clarity? $\endgroup$
    – J W
    Commented Jun 10 at 6:56

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Jean Dieudonné (examples):

  • Dieudonné, Jean (1989). A history of algebraic and differential topology, 1900-1960. Birkhäuser.
  • Dieudonné, Jean (1981). History of functional analysis. North-Holland Pub. Co.
  • Dieudonné, Jean. "The historical development of algebraic geometry." The American Mathematical Monthly 79.8 (1972): 827-866.

Felix Klein:

  • Klein, Felix (1926):. Vorlesungen über die Entwicklung der Mathematik im 19. Jahrhundert. Springer.

Saunders Mac Lane (example):

  • Mac Lane, Saunders. "Topology becomes algebraic with Vietoris and Noether." Journal of Pure and Applied Algebra 39 (1986): 305-307.

P.S. There are many examples in response to a similar question on SE:MO.

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To those already mentioned I can add:

  • Felix Klein (Development of Mathematics in The 19th Century)
  • Wilhelm Blaschke (book on Greek geometry)
  • Vladimir Arnold (his book on Huygens, Newton, Barrow and Hooke)
  • Robin Hartshorne (his book on Euclid's geometry)
  • S. Chandrasekhar (commentary to Newton's Principia)
  • B. L. van der Waerden (Science awakening)
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Norbert Schappacher is an example of a contemporary mathematician who has made significant contributions both to original research mathematics, and to mathematical history. His Wikipedia page here gives some biographical details.

(I can't resist quoting a sentence from his short biography of Gotthold Eisenstein:

Hilbert ... strove in his grandiose systematic treatment of algebraic number theory, the Zahlbericht of 1897, to replace what he called Kummer's calculations in the arithmetic of cyclotomic fields by "Riemann's conceptual method." He was thus proud to show that he could do completely without Kummer's logarithmic derivatives of units, i.e., without a technique that has since come to be a key tool of contemporary arithmetic through the work of Artin, Hasse, Iwasawa, Shafarevich, Coates and Wiles. [emphasis added]

I think this is an interesting example of how experience of modern research can give a new perspective on the history of much earlier eras.)

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  • $\begingroup$ Great quote! Hahaha! :) It does seem to turn out that self-declared "purists" are often misguided. But/and, we do have the extreme case of A. Grothendieck. :) $\endgroup$ Commented Jun 8 at 19:26
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Bourbaki, of course, with Eleménts d'histoire des mathématiques.

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Harold Jacques Dutka (1919 - 2002), with whom I had the pleasure to collaborate

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An older work (in German) I sometimes consult for pointers to historical sources is:

Moritz Cantor, Vorlesungen über Geschichte der Mathematik, Leipzig: Teubner (Vol. 1, 1880; Vol. 2, 1892; Vol. 3, 1898; Vol. 4, 1908)

The standard reference on the history of continued fractions is by a contemporary French mathematician who is also [co-]author of several other works on the history of specific mathematical subject areas, including the following books:

Claude Brezinski, History of Continued Fractions and Padé Approximants, Springer 1991
Claude Brezinski and Luc Wuytack, Numerical Analysis: Historical Developments in the 20th Century, Elsevier 2001
Claude Brezinski and Dominique Tournès, André-Louis Cholesky: Mathematician, Topographer and Army Officer, Birkhäuser 2014
Claude Brezinski and Michela Redivo-Zaglia, Extrapolation and Rational Approximation: The Works of the Main Contributors, Springer 2020
Claude Brezinski, Gérard Meurant, and Michela Redivo-Zaglia, A Journey through the History of Numerical Linear Algebra, SIAM 2022

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Unlike mathematicians like Weil, van der Waerden, and Freudenthal, who took issue with received historians with regard to relatively ancient history (see for example this article: Katz, M. "Mathematical conquerors, Unguru polarity, and the task of history." Journal of Humanistic Mathematics 10 (2020), no. 1, 475-515. https://doi.org/10.5642/jhummath.202001.27, https://arxiv.org/abs/2002.00249), Abraham Robinson challenged the received interpretation of what could be called the "modern" period of mathematics, namely the 17-19 centuries. Challenging the received view that the Cantor-Dedekind-Weierstrass paradigm in analysis replaced unrigorous contradictory infinitesimals thus saving analysis from the abyss of imprecision, Robinson showed that infinitesimals as used by Leibniz, Euler, and Cauchy can be placed on a modern footing acceptable to today's mathematicians. Robinson was intensely interested in Leibniz specifically and studied him in primary documents. Some of the results of his investigations were presented in chapter X of his 1966 book

Robinson, Abraham Non-standard analysis. North-Holland Publishing, Amsterdam, 1966.

Robinson's proposed historical paradigm has inspired much recent work; see for example this webpage.

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Ernst Hairer, Gerhard Wanner; maybe Syvert Paul Nørsett, Christian Lubich — various combinations have been co-authors of a few books. I'm not sure which of them are most interested in the history of mathematics. The books themselves often contain historical references. I especially like the facsimiles of original works. None of them may be historians per se, but some or all of them are interested in the history of mathematics. A notable book is this one:

  • Hairer and Wanner, Analysis by its History, Springer

Also:

  • Hairer, Lubich, and Wanner, Geometric Numerical Integration, Springer 2004.

  • Hairer, Nørsett and Wanner, Solving Ordinary Differential Equations I & II, Springer, 1993.


Another applied mathematician: Herman Goldstine. He wrote several papers on the history of mathematics and computing and a book:

  • Goldstine, A History of Numerical Analysis from the 16th through the 19th Century, Springer, 1977.
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There's a less serious study of the history of pesudomathematics in Mathematical Cranks by Underwood Dudley. This was published by the Mathematical Association of America in 1992. It consists of 57 essays on various aspects of pesudomathematics, including:

  • Squaring the circle
  • Angle trisection
  • Fermat's Last Theorem
  • Non-Euclidean geometry and the parallel postulate
  • The golden ratio
  • Perfect numbers
  • The four colour theorem,
  • Advocacy for duodecimal and other non-standard number systems,
  • Cantor's diagonal argument for the uncountability of the real numbers
  • Doubling the cube
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Morris Kline (1908-1992):

Mathematics in Western Culture, Oxford University Press,1953

Mathematical Thought from Ancient to Modern Times, Oxford University Press, 1972

Mathematics: The Loss of Certainty, Oxford University Press, 1980

Mathematics and the Search for Knowledge, Oxford University Press, 1985

Oh, and check out his other books. Even his calculus textbook was a good read!

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