history of mathematics



In the nLab we appear to currently be interested mainly in the development of ideas of category theory, topology, higher category theory, sheaf theory, homological algebra, foundations of mathematics and the general concept of space, as well as interactions between physics, mathematics and philosophy. Hence we will concentrate here on references with similar emphasis and list only a few works for the general history of mathematics (wikipedia has a nice reference list there).

Spaces, categories, topology, sheaves, topoi, cohomology, …

  • Mathieu Bélanger. Grothendieck et les topos : rupture et continuité dans les modes d’analyse du concept d’espace topologique, thesis, Université de Montréal 2010 pdf
  • Pierre Cartier, A mad day’s work: from Grothendieck to Connes and Kontsevich The evolution of concepts of space and symmetry, Bull. Amer. Math. Soc. 38 (2001), 389-408, pdf
  • Ralf Krömer, Tool and object: A history and philosophy of category theory, Birkhäuser 2007
  • John Bell, The development of categorical logic (pdf)
  • Jean-Pierre Marquis, Gonzalo E. Reyes, The history of categorical logic 1963–1977, 111 pp. pdf

General history of mathematics

  • C. B. Boyer, A history of mathematics, 2nd ed. rev. by Uta C. Merzbach. New York: Wiley, 1989
  • Felix Klein, The development of mathematics in 19th century
  • Julian Lowell Coolidge, A history of geometrical methods, 1940, Dover Phoenix Editions, Oxford University Press 1940.
  • J. Gray, The real and the complex: a history of analysis in the 19th century, Springer Undergraduate Mathematics Series
  • Dirk Jan Struik, A concise history of mathematics
  • Umberto Bottazzini, Il flauto di Hilbert: Storia della matematica, UTET Università, 473pp.; The higher calculus: A history of real and complex analysis from Euler to Weierstrass, Springer 1986

Wiki, collection and encyclopaedia articles

Researchers and institutes for history of mathematics

  • hsm at Jussieu

nnLab entries with historical information

Other literature

  • G.A. Miller, Felix Klein and the history of modern mathematics, PNAS 13, 1927, 611-613

The relation of the techniques of the pioneers of infinitesimal calculus and the modern nonstandard analysis is discussed in

  • Piotr Blaszczyk, Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz, Semen S. Kutateladze, David Sherry, Toward a history of mathematics focused on procedures, arxiv/1609.04531

A collection of articles on XX-century mathematics is in

Last revised on June 8, 2018 at 18:17:44. See the history of this page for a list of all contributions to it.