David Mumford

Archive for Reprints, Notes, Talks, and Blog

Professor Emeritus
Brown and Harvard Universities

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Works on the History of Mathematics

The History of Mathematics is usually taught from a very Western-centric point of view. Without a doubt the Greek contributions were huge, but once you open your mind to the fact that mathematical truth can and has been discovered by many routes other than Euclid-style proofs (think of calculus in the 17th-18th century), you find a much richer picture in which Mesopotamia, India and China all developed deep mathematical ideas, sometimes before, sometimes after similar ideas appeared in the West.

I have been studying Indian math in particular, which is astonishing in both its similarities and differences from the West (see my review of Plofker's recent book Mathematics in India).

The background is my wife's photo of the Arabian desert, to evoke Mesopotamia, the place of the first great explosion of math.

  • Course notes from a 2006 Brown survey course in "math for non-math majors" that followed its historical development in the West: Click here (the notes only cover the first 2/3rds of the course as I ran out of steam).
  • Art, Mathematics and the Zeitgeist: parallels between the two most international disciplines, Lecture at the Festival of Mathematics, Rome, March 15, 2008. pdf of talk.
  • Henri's Crystal Ball (with Phil Davis), Notices of the AMS, 55, 2008, pp. 458-466. Link to notices OR Digital reprint
  • Review of Mathematics in India by Kim Plofker, Notices of the AMS, 2010, pp. 385-390. Link to notices OR Digital reprint
  • What's so Baffling about Negative Numbers -- a Cross-Cultural Comparison, in Studies in the History of Indian Mathematics, C. S. Seshadri editor, Hindustan Book Agency (distr. in US by AMS), 2010.Digital reprint
  • The Invention of Algebra as Reification, talk at a meeting on "Mathematics in Ancient Times", Calicut, India, 2010. Powerpoint of Talk
  • Intuition and Rigor and Enriques's Quest, Notices of the AMS, 58, 2011, pp. 250-260. Link to notices OR Digital reprint
  • "Yu laid out the lands": georeferencing the Chinese Yujitu [Map of the Tracks of Yu] of 1136 (with Alexander Akin), Cartography and Geographic Information Science Journal, 2012.Digital reprint
  • My introduction to functors and schemes, in Alexandre Grothendieck: A Mathematical Portrait, edited by Leila Schneps. Digital manuscript
  • "Assessing the accuracy of ancient eclipse predictions", in Mathematics of Takebe Katahiro and History of Math in East Asia, Advanced Studies in Pure Mathematics, Math. Soc. of Japan, 29, 2018, Proof sheets

I also include here my appreciations of friends' and colleague's work, one for the Field's medal and others who have passed away:

  • Oscar Zariski: 1899-1986, in the Notices of the American Math. Society, 33, 1986, pp.891-894. With help from Michael Artin, I recently put together a more complete obituary for the National Academy of Science: pdf file
  • An Instinct for the Key Idea (with John Tate), Science, 1979,202, pp.737-739.
    Scanned reprint
  • The work of C. P. Ramanujam in algebraic geometry, in C. P. Ramanujam, a Tribute , T.I.F.R. 1978, pp.8-10. Scanned reprint
  • In Memoriam: Professor George R. Kempf 1944-2002, Amer. Journal of Mathematics, vol. 124, pp.ii-iii, 2002. Digital reprint
  • George Mackey, Proceedings of the American Philosophical Society, 152 pp.559-563, 2008. Digital reprint
  • Andrew Gleason, Proceedings of the American Philosophical Society, 154 pp.471-476, 2010. Scanned reprint
  • Glimpses of Benoit Mandelbrot, Notices of the Amer. Math. Soc., 59, p. 1057; The influence of Benoit Mandelbrot, Notices of the Amer. Math. Soc., 59, pp. 1212-1213; Originally I wrote this as one tribute: here is the Digital manuscript
  • Remembering Raoul Bott, Notices of the Amer. Math. Soc., 60, pp. 401-402. Here is the full obituary: Digital reprint