Reuben Hersh (December 9, 1927 – January 3, 2020) 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 ...

and

academic An academy (Attic Greek: Ἀκαδήμεια; Koine Greek Ἀκαδημία) is an institution of secondary education, secondary or tertiary education, tertiary higher education, higher learning (and generally also research or honorary membershi ...

, best known for his writings on the nature, practice, and social impact of mathematics. Although he was generally known as Reuben Hersh, late in life he sometimes used the name Reuben Laznovsky in recognition of his father's ancestral family name. His work challenges and complements mainstream

philosophy of mathematics The philosophy of mathematics is the branch of philosophy that studies the assumptions, foundations, and implications of mathematics. It aims to understand the nature and methods of mathematics, and find out the place of mathematics in people's ...

Education

After receiving a B.A. in

English literature English literature is literature written in the English language from United Kingdom, its crown dependencies, the Republic of Ireland, the United States, and the countries of the former British Empire. ''The Encyclopaedia Britannica'' defines E ...

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 1946, Hersh spent a decade writing for ''

Scientific American ''Scientific American'', informally abbreviated ''SciAm'' or sometimes ''SA'', is an American popular science magazine. Many famous scientists, including Albert Einstein and Nikola Tesla, have contributed articles to it. In print since 1845, it i ...

'' and working as a machinist. After losing his right thumb when working with a band saw, he decided to study mathematics at the

Courant Institute of Mathematical Sciences The Courant Institute of Mathematical Sciences (commonly known as Courant or CIMS) is the mathematics research school of New York University (NYU), and is among the most prestigious mathematics schools and mathematical sciences research cente ...

. In 1962, he was awarded a Ph.D. in mathematics from

New York University New York University (NYU) is a private research university in New York City. Chartered in 1831 by the New York State Legislature, NYU was founded by a group of New Yorkers led by then-Secretary of the Treasury Albert Gallatin. In 1832, the ...

; his advisor was P.D. Lax. He was affiliated with the

University of New Mexico The University of New Mexico (UNM; es, Universidad de Nuevo México) is a public research university in Albuquerque, New Mexico. Founded in 1889, it is the state's flagship academic institution and the largest by enrollment, with over 25,400 ...

since 1964, where he was professor emeritus.

Academic career

Hersh wrote a number of technical articles on

partial differential equation In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a Multivariable calculus, multivariable function. The function is often thought of as an "unknown" to be sol ...

probability Probability is the branch of mathematics concerning numerical descriptions of how likely an Event (probability theory), event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and ...

, random evolutions
example
, and

linear operator In mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping V \to W between two vector spaces that pre ...

equations. He was the co-author of four articles in ''

'', and 12 articles in the ''

Mathematical Intelligencer ''The Mathematical Intelligencer'' is a mathematical journal published by Springer Verlag that aims at a conversational and scholarly tone, rather than the technical and specialist tone more common among academic journals. Volumes are released qua ...

''. Hersh was best known as the co-author with

Philip J. Davis Philip J. Davis (January 2, 1923 – March 14, 2018) was an American academic applied mathematician. Davis was born in Lawrence, Massachusetts. He was known for his work in numerical analysis and approximation theory, as well as his investigati ...

of ''

The Mathematical Experience ''The Mathematical Experience'' (1981) is a book by Philip J. Davis and Reuben Hersh that discusses the practice of modern mathematics from a historical and philosophical perspective. The book discusses the psychology of mathematicians, and giv ...

'' (1981), which won a

National Book Award The National Book Awards are a set of annual U.S. literary awards. At the final National Book Awards Ceremony every November, the National Book Foundation presents the National Book Awards and two lifetime achievement awards to authors. The Nat ...

in Science."National Book Awards – 1983"

National Book Foundation The National Book Foundation (NBF) is an American nonprofit organization established, "to raise the cultural appreciation of great writing in America". Established in 1989 by National Book Awards, Inc.,Edwin McDowell. "Book Notes: 'The Joy Luc ...

. Retrieved 2012-03-07. This was the 1983 award for paperback Science.
From 1980 to 1983 in National Book Award history there were dual hardcover and paperback awards in most categories, and several nonfiction subcategories including General Nonfiction. Most of the paperback award-winners were reprints, including this one. Hersh and Martin Davis won the 1984

Chauvenet Prize The Chauvenet Prize is the highest award for mathematical expository writing. It consists of a prize of $1,000 and a certificate, and is awarded yearly by the Mathematical Association of America in recognition of an outstanding expository article ...

for their

article on

Hilbert's tenth problem Hilbert's tenth problem is the tenth on the list of mathematical problems that the German mathematician David Hilbert posed in 1900. It is the challenge to provide a general algorithm which, for any given Diophantine equation (a polynomial equat ...

. Hersh advocated what he called a "humanist" philosophy of mathematics, opposed to both Platonism (so-called "realism") and its rivals nominalism/fictionalism/formalism. He held that mathematics is real, and its reality is social-cultural-historical, located in the shared thoughts of those who learn it, teach it, and create it. His article "The Kingdom of Math is Within You" (a chapter in his ''Experiencing Mathematics'', 2014) explains how mathematicians' proofs compel agreement, even when they are inadequate as formal logic. He sympathized with the perspectives on mathematics of

Imre Lakatos Imre Lakatos (, ; hu, Lakatos Imre ; 9 November 1922 – 2 February 1974) was a Hungarian philosopher of mathematics and science, known for his thesis of the fallibility of mathematics and its "methodology of proofs and refutations" in its pr ...

and ''

Where Mathematics Comes From ''Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being'' (hereinafter ''WMCF'') is a book by George Lakoff, a cognitive linguistics, cognitive linguist, and Rafael E. Núñez, a psychologist. Published in 2000, ''WMCF' ...

'', George Lakoff and Rafael Nunez, Basic Books.

Books

* 1981, Hersh and Philip Davis. ''

''. (Mariner Books, 1999). * 1986, Hersh and Philip Davis. ''Descartes' Dream: The World According to Mathematics''. (Dover, 2005) * 1997
''What Is Mathematics, Really?''
Oxford Univ. Press. * 2006, edited by Hersh.
18 Unconventional Essays on the Nature of Mathematics.
' Springer Verlag. * 2009, Hersh and Vera John-Steiner
''Loving and Hating Mathematics''
Princeton University Press *Greenwood, P.; Hersh, R. "Stochastic differentials and quasi-standard random variables", ''Probabilistic methods in differential equations'' (Proc. Conf., Univ. Victoria, Victoria, B. C., 1974), pp. 35–62. Lecture Notes in Math., Vol. 451, Springer, Berlin, 1975. *2014, Reuben Hersh
''Experiencing Mathematics: What do we do, when we do mathematics?''
American Mathematical Society. *2015, Reuben Hersh
''Peter Lax: Mathematician''
American Mathematical Society.

Notes

References

External links

Humanizing Mathematics and its Philosophy: ''Essays celebrating the 90th Birthday of Reuben Hersh''

The Ideal Mathematician, with Phillip Davis
(Note: Google.com, somewhat unfortunately, decides to redirect this link weirdly, as of May 2018).
Web page
at the Univ. of New Mexico.
Published Articles
at googlesites.
AMS video interview with Reuben Hersh part 1
{{DEFAULTSORT:Hersh, Reuben 20th-century American mathematicians 21st-century American mathematicians Mathematics writers National Book Award winners Philosophers of mathematics 2020 deaths 1927 births American science writers Harvard University alumni Courant Institute of Mathematical Sciences alumni University of New Mexico faculty