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

A couple of months into the course, I was trolling the aisles of my favorite bookstore, and saw there a copy of the book. I think it was the first edition. It was definitely in soft covers, perhaps an edition for sale in third world markets. I remembered the name, bought the book, took it home, and set to reading it.

Michael David Spivak [1] (May 25, 1940–October 1, 2020) [2] [3] was an American mathematician specializing in differential geometry, an expositor of mathematics, and the founder of Publish-or-Perish Press. Spivak was the author of the five-volume A Comprehensive Introduction to Differential Geometry. Solid state physics Quantum theory Chemical bonds SCIENCE Physics Condensed Matter Física do estado sólido Mecânica quântica Prof. Michael D. Spivak Pathway Lectures". September 3, 2012. Archived from the original on September 3, 2012.

His five-volume 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 works. 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. 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. Archived from the original on April 17, 2021 . Retrieved April 28, 2021.But the core of the text is still the same. If you want a calculus textbook that does everything honestly but gently enough so that good first-year students can follow it, this is the one. Spivak, Michael (2010). Physics for Mathematicians, Mechanics I. Publish or Perish. ISBN 978-0914098324. It was love at first sight. OK, I'll admit that I wasn't doing all— or even most — ofthe problems. (There are lots of very hard problems; instructors will be glad that there is an answer book.) But Spivak's account of what Calculus is all about, his careful but precise account of the theoretical underpinnings of the material, his chapter on the "hard theorems" (the ones that require an understanding of the completeness of the reals), his pictures, even his asides... this was calculus as an intellectual adventure, deep,compelling, and beautiful. I read the whole book, making my way far beyond what we had covered inclass by that point. I even read, with some small level of understanding, the sections on complex analysis and the explanation of Dedekind cuts.