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{{Short description|American mathematician (1927–2020)}}
[[File:Reuben Hersh.jpg|thumb|220px|Reuben Hersh]]
[[File:Reuben Hersh.jpg|thumb|220px|Hersh in 1979]]


'''Reuben Hersh''' (born 1927) is an [[United States|American]] [[mathematician]] and [[academic]], best known for his writings on the nature, practice, and social impact of mathematics. This work challenges and complements mainstream [[philosophy of mathematics]]. ("Hersh" is his professional or [[pen name]]. His family name is Reuben Laznovsky.)
'''Reuben Hersh''' (December 9, 1927 – January 3, 2020) was an American [[mathematician]] and [[academic]], 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]].


== Education ==
After receiving a B.A. in [[English literature]] from [[Harvard University]] in 1946, Hersh spent a decade writing for ''[[Scientific American]]'' 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]]. In 1962, he was awarded a Ph.D. in mathematics from [[New York University]]; his advisor was [[Peter Lax|P.D. Lax]]. He has been affiliated with the [[University of New Mexico]] since 1964, where he is now professor emeritus.
After receiving a B.A. in [[English literature]] from [[Harvard University]] in 1946, Hersh spent a decade writing for ''[[Scientific American]]'' 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]]. In 1962, he was awarded a Ph.D. in mathematics from [[New York University]]; his advisor was [[Peter Lax|P.D. Lax]]. He was affiliated with the [[University of New Mexico]] since 1964, where he was professor emeritus.


== Academic career ==
Hersh has written a number of technical articles on [[partial differential equation]]s, [[probability]], random evolutions ([https://www.jstor.org/stable/44236397 example]), and [[linear operator]] equations. He is the (co)author of four articles in ''[[Scientific American]]'', and 12 articles in the ''[[Mathematical Intelligencer]]''.
Hersh wrote a number of technical articles on [[partial differential equation]]s, [[probability]], random evolutions ([https://www.jstor.org/stable/44236397 example]), and [[linear operator]] equations. He was the co-author of four articles in ''[[Scientific American]]'', and 12 articles in the ''[[Mathematical Intelligencer]]''.


Hersh is best known as the coauthor with [[Philip J. Davis]] of ''[[The Mathematical Experience]]'' (1981), which won a [[National Book Award]] in Science.<ref name=nba1983>
Hersh was best known as the co-author with [[Philip J. Davis]] of ''[[The Mathematical Experience]]'' (1981), which won a [[National Book Award]] in Science.<ref name="nba1983">
[https://www.nationalbook.org/awards-prizes/national-book-awards-1983 "National Book Awards – 1983"]. [[National Book Foundation]]. Retrieved 2012-03-07.</ref><ref group=lower-alpha>
[https://www.nationalbook.org/awards-prizes/national-book-awards-1983 "National Book Awards – 1983"]. [[National Book Foundation]]. Retrieved 2012-03-07.</ref><ref group="lower-alpha">
This was the 1983 [[List of winners of the National Book Award#Science|award for paperback Science]].
This was the 1983 [[List of winners of the National Book Award#Science|award for paperback Science]].
<br>From 1980 to 1983 in [[National Book Award#History|National Book Award history]] there were dual hardcover and paperback awards in most categories, and [[National Book Award for Nonfiction#nonfiction categories|several nonfiction subcategories]] including General Nonfiction. Most of the paperback award-winners were reprints, including this one.</ref>
<br />From 1980 to 1983 in [[National Book Award#History|National Book Award history]] there were dual hardcover and paperback awards in most categories, and [[National Book Award for Nonfiction#nonfiction categories|several nonfiction subcategories]] including General Nonfiction. Most of the paperback award-winners were reprints, including this one.</ref> Hersh and [[Martin Davis (mathematician)|Martin Davis]] won the 1984 [[Chauvenet Prize]] for their [[Scientific American]]<ref name="Davis Hersh Hilbert 10th">{{cite journal |last1=Davis |first1=Martin |last2=Hersh |first2=Reuben |year=1973 |title=Hilbert's 10th Problem |journal=Scientific American |publisher=Springer Science and Business Media LLC |volume=229 |issue=5 |pages=84–91 |doi=10.1038/scientificamerican1173-84 |bibcode=1973SciAm.229e..84D |issn=0036-8733}}</ref> article on [[Hilbert's tenth problem]].


Hersh advocates what he calls a "humanist" philosophy of mathematics, opposed to both Platonism (so-called "realism") and its rivals nominalism/fictionalism/formalism. He holds 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 sympathizes with the perspectives on mathematics of [[Imre Lakatos]] and ''[[Where Mathematics Comes From]]'', George Lakoff and Rafael Nunez, Basic Books.{{clarify|date=March 2012}}{{citation needed|date=March 2012}}
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]] and ''[[Where Mathematics Comes From]]'', George Lakoff and Rafael Nunez, Basic Books.{{clarify|date=March 2012}}{{citation needed|date=March 2012}}


==Books==
==Books==
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* 1981, Hersh and Philip Davis. ''[[The Mathematical Experience]]''. (Mariner Books, 1999).
* 1981, Hersh and Philip Davis. ''[[The Mathematical Experience]]''. (Mariner Books, 1999).
* 1986, Hersh and Philip Davis. ''Descartes' Dream: The World According to Mathematics''. (Dover, 2005)
* 1986, Hersh and Philip Davis. ''Descartes' Dream: The World According to Mathematics''. (Dover, 2005)
* 1997. ''What Is Mathematics, Really?'' Oxford Univ. Press.
* 1997. [https://books.google.com/books?id=cocpm4oBKqwC ''What Is Mathematics, Really?''] Oxford Univ. Press.
* 2006, edited by Hersh. ''[http://www.math.unm.edu/%7Erhersh/Intro_to_Unconventional.doc 18 Unconventional Essays on the Nature of Mathematics.]'' Springer Verlag.
* 2006, edited by Hersh. ''[http://www.math.unm.edu/%7Erhersh/Intro_to_Unconventional.doc 18 Unconventional Essays on the Nature of Mathematics.]'' Springer Verlag.
* 2009, Hersh and Vera John-Steiner. ''Loving and Hating Mathematics''.Princeton University Press
* 2009, Hersh and [[Vera John-Steiner]]. [https://books.google.com/books?id=gvsHAnAuIp4C ''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.&nbsp;35–62. Lecture Notes in Math., Vol. 451, Springer, Berlin, 1975.
*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.&nbsp;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.
*2014, Reuben Hersh. [https://books.google.com/books?id=8YkCAQAAQBAJ ''Experiencing Mathematics: What do we do, when we do mathematics?''] American Mathematical Society.
*2015, Reuben Hersh. ''Peter Lax: Mathematician''. American Mathematical Society.
*2015, Reuben Hersh. [https://books.google.com/books?id=ammxBgAAQBAJ ''Peter Lax: Mathematician'']. American Mathematical Society.


==See also==
==See also==
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== External links ==
== External links ==
*[https://link.springer.com/content/pdf/bfm%3A978-3-319-61231-7%2F1.pdf Humanizing Mathematics and its Philosophy: ''Essays celebrating the 90th Birthday of Reuben Hersh'']
*[https://ff3df8c5-a-62cb3a1a-s-sites.googlegroups.com/site/reubenhersharticlesetc/home/articles/ideal.pdf The Ideal Mathematician, with Phillip Davis] (Note: Google.com, somewhat unfortunately, decides to redirect this link weirdly, as of May 2018).
*[https://ff3df8c5-a-62cb3a1a-s-sites.googlegroups.com/site/reubenhersharticlesetc/home/articles/ideal.pdf The Ideal Mathematician, with Phillip Davis] (Note: Google.com, somewhat unfortunately, decides to redirect this link weirdly, as of May 2018).
*[http://www.math.unm.edu/%7Erhersh/ Web page] at the Univ. of New Mexico.
*[http://www.math.unm.edu/%7Erhersh/ Web page] at the Univ. of New Mexico.
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[[Category:Mathematics writers]]
[[Category:Mathematics writers]]
[[Category:National Book Award winners]]
[[Category:National Book Award winners]]
[[Category:Philosophers of mathematics]]
[[Category:American philosophers of mathematics]]
[[Category:Living people]]
[[Category:2020 deaths]]
[[Category:1927 births]]
[[Category:1927 births]]
[[Category:American science writers]]
[[Category:American science writers]]

Latest revision as of 11:53, 12 April 2024

Hersh in 1979

Reuben Hersh (December 9, 1927 – January 3, 2020) was an American mathematician and academic, 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.

Education

[edit]

After receiving a B.A. in English literature from Harvard University in 1946, Hersh spent a decade writing for Scientific American 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. In 1962, he was awarded a Ph.D. in mathematics from New York University; his advisor was P.D. Lax. He was affiliated with the University of New Mexico since 1964, where he was professor emeritus.

Academic career

[edit]

Hersh wrote a number of technical articles on partial differential equations, probability, random evolutions (example), and linear operator equations. He was the co-author of four articles in Scientific American, and 12 articles in the Mathematical Intelligencer.

Hersh was best known as the co-author with Philip J. Davis of The Mathematical Experience (1981), which won a National Book Award in Science.[1][a] Hersh and Martin Davis won the 1984 Chauvenet Prize for their Scientific American[2] article on Hilbert's tenth problem.

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 and Where Mathematics Comes From, George Lakoff and Rafael Nunez, Basic Books.[clarification needed][citation needed]

Books

[edit]

See also

[edit]

Notes

[edit]
  1. ^ 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.

References

[edit]
  1. ^ "National Book Awards – 1983". National Book Foundation. Retrieved 2012-03-07.
  2. ^ Davis, Martin; Hersh, Reuben (1973). "Hilbert's 10th Problem". Scientific American. 229 (5). Springer Science and Business Media LLC: 84–91. Bibcode:1973SciAm.229e..84D. doi:10.1038/scientificamerican1173-84. ISSN 0036-8733.
[edit]
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