Michael David Spivak (25 May 19401 October 2020)Biographical sketch in
Notices of the AMS
', Vol. 32, 1985, p. 576. was an American

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

specializing in

differential geometry Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multili ...

, an expositor of

mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

, and the founder of Publish-or-Perish Press. Spivak was the author of the five-volume ''A Comprehensive Introduction to Differential Geometry''.

Biography

Spivak was born in

Queens Queens is a borough of New York City, coextensive with Queens County, in the U.S. state of New York. Located on Long Island, it is the largest New York City borough by area. It is bordered by the borough of Brooklyn at the western tip of Long ...

New York New York most commonly refers to: * New York City, the most populous city in the United States, located in the state of New York * New York (state), a state in the northeastern United States New York may also refer to: Film and television * '' ...

. He received an

A.B. Bachelor of arts (BA or AB; from the Latin ', ', or ') is a bachelor's degree awarded for an undergraduate program in the arts, or, in some cases, other disciplines. A Bachelor of Arts degree course is generally completed in three or four yea ...

from

Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher le ...

in 1960, while in 1964 he received a

Ph.D. A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is a ...

from

Princeton University Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...

under the supervision of

John Milnor John Willard Milnor (born February 20, 1931) is an American mathematician known for his work in differential topology, algebraic K-theory and low-dimensional holomorphic dynamical systems. Milnor is a distinguished professor at Stony Brook Uni ...

, with thesis ''On Spaces Satisfying Poincaré Duality''. In 1985 Spivak received the

Leroy P. Steele Prize The Leroy P. Steele Prizes are awarded every year by the American Mathematical Society, for distinguished research work and writing in the field of mathematics. Since 1993, there has been a formal division into three categories. The prizes have b ...

. Spivak lectured on elementary physics. Spivak's book, ''Physics for Mathematicians: Mechanics I'' (published December 6, 2010), contains the material that these lectures stemmed from and more. Spivak was also the designer of the

MathTime MathTime (sometimes MathTıme) is a Times-style mathematical typeface for TeX, created by Michael Spivak. MathTime has been widely adopted by academic publishers such as by Elsevier, American Physical Society, and Springer.Springer-Verlag �Leit ...

Professional 2 fonts (which are widely used in academic publishing) and the creator of ''

Science International ''Science International'', later retitled ''What Will They Think of Next!'', is a Canadian television series produced by the Global Television Network from 1976 to 1979. Each episode featured approximately 20 short segments on scientific devel ...

''.

Writing

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

was awarded to Spivak in 1985 for his authorship of the work. Spivak also authored several well-known undergraduate textbooks. Among them, his textbook ''Calculus'' (W. A. Benjamin Inc., 1967; Publish or Perish, 4th ed., 2008) takes a rigorous and theoretical approach to introductory

calculus Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithm ...

and includes proofs of many theorems taken on faith in most other introductory textbooks.When Spivak was writing his Calculus book, the current "popular" book was by Thomas. Spivak joked about naming his book, "Thomas's Calculus"

y Michael Spivak, Y, or y, is the twenty-fifth and penultimate letter of the Latin alphabet, used in the modern English alphabet, the alphabets of other western European languages and others worldwide. According to some authorities, it is the sixth (or seventh ...

so that students who asked to buy Thomas's Calculus would end up with Spivak's book. Spivak acknowledged in the preface of the second edition that the work is arguably an introduction to mathematical analysis rather than a calculus textbook. Another of his well-known textbooks is '' Calculus on Manifolds'' (W. A. Benjamin Inc., 1965; Addison-Wesley, revised edition, 1968), a concise (146 pages) but rigorous and modern treatment of multivariable calculus accessible to advanced undergraduates.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 The ''lactose'' operon (''lac'' operon) is an operon required for the transport and metabolism of lactose in ''E. coli'' and many other enteric bacteria. Although glucose is the preferred carbon source for most bacteria, the ''lac'' operon allows ...

, 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. Spivak also wrote ''The Joy of TeX: A Gourmet Guide to Typesetting With the

AMS-TeX AMS-LaTeX is a collection of LaTeX document classes and packages developed for the American Mathematical Society (AMS). Its additions to LaTeX include the typesetting of multi-line and other mathematical statements, document classes, and fonts co ...

Macro Package'' and ''The Hitchhiker's Guide to Calculus''. The book ''

Morse Theory In mathematics, specifically in differential topology, Morse theory enables one to analyze the topology of a manifold by studying differentiable functions on that manifold. According to the basic insights of Marston Morse, a typical differentiabl ...

'', by

, was based on lecture notes by Spivak and Robert Wells (as mentioned on the cover page of the booklet).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.

Spivak pronouns

Spivak used a set of English

gender-neutral pronouns A third-person pronoun is a pronoun that refers to an entity other than the speaker or listener. Some languages with gender-specific pronouns have them as part of a grammatical gender system, a system of agreement where most or all nouns have a va ...

in his book ''The Joy of TeX'', which are often referred to as Spivak pronouns. (Spivak stated that he did not originate these pronouns.)

Bibliography

* * '' 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'', (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'', (1995) *

Notes

References

External links

Publish or Perish, Inc.
company owned by Spivak

Michael Spivak @ Everything2.com
*
Michael D. Spivak, 1940-2020
obituary in TUGboat by Barbara Beeton {{DEFAULTSORT:Spivak, Michael 1940 births 2020 deaths American textbook writers American male non-fiction writers 20th-century American mathematicians Differential geometers Mathematical analysts Princeton University alumni People from Queens, New York Mathematicians from New York (state) Topologists Harvard University alumni