Michael Spivak

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Michael David Spivak
Spivak Michael.jpg
Michael Spivak, Berkeley 1974.
Born (1940-05-25) May 25, 1940 (age 80)
Alma materPrinceton University
Known forThe Hitchhiker's Guide to Calculus
Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus
A Comprehensive Introduction to Differential Geometry
Scientific career
Differential geometry
ThesisOn Spaces Satisfying Poincaré Duality (1964)
Doctoral advisorJohn Milnor

Michael David Spivak (born May 25, 1940)[1] is an American mathematician specializing in differential geometry, an expositor of mathematics, and the founder of Publish-or-Perish Press. Spivak is the author of the five-volume A Comprehensive Introduction to Differential Geometry.


Spivak was born in Queens, New York. He received an A.B. from Harvard University in 1960,[1] while in 1964 he received a Ph.D. from Princeton University under the supervision of John Milnor, with thesis On Spaces Satisfying Poincaré Duality.[2] In 1985 Spivak received the Leroy P. Steele Prize.

Spivak has lectured on elementary physics.[3] Spivak's most recent book, Physics for Mathematicians: Mechanics I, which contains the material that these lectures stemmed from and more, was published on December 6, 2010.[4] Spivak is also the designer of the MathTime Professional 2 fonts (which are widely used in academic publishing)[5] and the creator of Science International.[6]

Spivak coined Spivak pronouns, a set of English gender-neutral pronouns.[7] He is unrelated to mathematician David Spivak.


Among Spivak's pedagogical works, his five-volume magnum opus A Comprehensive Introduction to Differential Geometry (Publish or Perish Inc., 1970; 2nd ed., 1979; 3rd ed., 1999, revised 2005) is among his most influential and celebrated. The distinctive pedagogical aim of the work, as stated in its preface, was to elucidate for graduate students the often obscure relationship between classical differential geometry—geometrically intuitive but imprecise—and its modern counterpart, replete with precise but unintuitive algebraic definitions. On several occasions, most prominently in Volume 2, Spivak "translates" the classical language that Gauss or Riemann would be familiar with to the abstract language that a modern differential geometer might use. The Leroy P. Steele Prize was awarded to Spivak in 1985 for his authorship of the work.

Spivak has also authored several well-known undergraduate textbooks. Among them, his text Calculus (W. A. Benjamin Inc., 1967; Publish or Perish, 4th ed., 2008) takes a rigorous and theoretical approach to introductory calculus and includes proofs of many theorems taken on faith in most other introductory textbooks.[8] Spivak acknowledges in the preface that others might consider this textbook to be an introduction to mathematical analysis rather than a calculus book. Another of his well-known textbooks is Calculus on Manifolds (W. A. Benjamin Inc., 1965; Addison-Wesley, revised edition, 1968), a concise (146 pp.) but rigorous and modern treatment of multivariable calculus accessible to advanced undergraduates.[9]

Spivak has also written The Joy of TeX: A Gourmet Guide to Typesetting With the AMS-TeX Macro Package and The Hitchhiker's Guide to Calculus. The book Morse Theory, by John Milnor, was based on lecture notes by Spivak and Robert Wells (as mentioned on the cover page of the booklet).[10]


  • Spivak, Michael (1967). "Spaces satisfying Poincaré duality". Topology. 6 (1): 77–101. doi:10.1016/0040-9383(67)90016-X. MR 0214071.
  • Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus, (1965, revised 1968)
  • Calculus, (1967, 4th ed. 2008)
  • A Comprehensive Introduction to Differential Geometry,[11][12] (1970, revised 3rd ed. 2005)
  • The Joy of TeX: A Gourmet Guide to Typesetting with the AMS-TeX Macro package, (1990)
  • A Hitchhiker's Guide to the Calculus,[13] (1995)
  • Spivak, Michael (2010). Physics for mathematicians—mechanics I. Houston, TX: Publish or Perish. ISBN 978-0-914098-32-4. MR 2761185.

See also[edit]


  1. ^ a b Biographical sketch in Notices of the AMS, Vol. 32, 1985, p. 576.
  2. ^ Michael Spivak at the Mathematics Genealogy Project
  3. ^ Videos Archived 2012-09-03 at Archive.today of Spivak's 2004 Pathway Lectures at Keio University and the text for Elementary mechanics from a mathematician's viewpoint.
  4. ^ Spivak, Michael (2010). Physics for Mathematicians, Mechanics I. ISBN 978-0914098324.
  5. ^ "MathTime Professional 2 Fonts". pctex.com. Retrieved October 15, 2013.
  6. ^ "Snippets of science from a goon". New Scientist. Vol. 98 no. 1352. Reed Business Information. April 7, 1983.
  7. ^ McCurdy, Christen. "Are Gender-Neutral Pronouns Actually Doomed?". Pacific Standard. Retrieved February 26, 2014.
  8. ^ When Spivak was writing his Calculus book, the current "popular" book was by Thomas. Spivak joked about naming his book, "Thomas's Calculus" [by Michael Spivak,] so that students who asked to buy Thomas's Calculus would end up with Spivak's book.
  9. ^ When Spivak receives the galley proofs of Calculus on Manifolds, the manuscript was proofread out loud (for $2/hour) by one of his roommates, J. Kowit, who has an autographed copy that reads "For Joel, who read every word, left parenthesis, and subscript. - Mike." One of the references in the index reads, "Lac locus." This relates to a period of time during which Spivak worked with a friend in the Biology Department of Brandeis, dealing with the lac operon, a set of genes whose study won the Nobel Prize for Jacob and Monod. These genes are named i, o, z, and y, and these letters can be found in the equations on page 106 - a very inside joke.
  10. ^ It is rumored that in each of Spivak's books there are hidden references to yellow pigs, an idea Spivak apparently came up with at a bar while drinking with David C. Kelly.
  11. ^ Guillemin, Victor (1973). "Review: A comprehensive introduction to differential geometry, Vols. 1 & 2, by M. Spivak". Bull. Amer. Math. Soc. 79 (2): 303–306. doi:10.1090/s0002-9904-1973-13149-0.
  12. ^ Alexander, Stephanie (1978). "Review: A comprehensive introduction to differential geometry, Vols. 3, 4, & 5, by M. Spivak". Bull. Amer. Math. Soc. 84 (1): 27–32. doi:10.1090/s0002-9904-1978-14399-7.
  13. ^ Fernando Q. Gouvêa (2 February 1996). "Review: A Hitchhiker's Guide to the Calculus by Michael Spivak". MAA Reviews.

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