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18 Unconventional Essays on the Nature of MathematicsOn Proof and Progress in Mathematics

18 Unconventional Essays on the Nature of Mathematics: On Proof and Progress in Mathematics On Proof and Progress in Mathematics WILLIAM P. THURSTON This essay on the nature of proof and progress in mathematics was stimulated by the article of Jaffe and Quinn, “Theoretical Mathematics: Toward a cultural synthesis of mathematics and theoretical physics”. Their article raises interesting issues that mathematicians should pay more attention to, but it also perpetuates some widely held beliefs and attitudes that need to be questioned and examined. The article had one paragraph portraying some of my work in a way that diverges from my experience, and it also diverges from the observations of people in the field whom I’ve discussed it with as a reality check. After some reflection, it seemed to me that what Jaffe and Quinn wrote was an example of the phenomenon that people see what they are tuned to see. Their portrayal of my work resulted from projecting the sociology of mathe- matics onto a one-dimensional scale (speculation versus rigor) that ignores many basic phenomena. Responses to the Jaffe-Quinn article have been invited from a number of mathematicians, and I expect it to receive plenty of specific analysis and criti- cism from others. Therefore, I will concentrate in this essay on the positive http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

18 Unconventional Essays on the Nature of MathematicsOn Proof and Progress in Mathematics

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References (1)

Publisher
Springer New York
Copyright
© Springer Science+Business Media, Inc. 2006
ISBN
978-0-387-25717-4
Pages
37 –55
DOI
10.1007/0-387-29831-2_3
Publisher site
See Chapter on Publisher Site

Abstract

On Proof and Progress in Mathematics WILLIAM P. THURSTON This essay on the nature of proof and progress in mathematics was stimulated by the article of Jaffe and Quinn, “Theoretical Mathematics: Toward a cultural synthesis of mathematics and theoretical physics”. Their article raises interesting issues that mathematicians should pay more attention to, but it also perpetuates some widely held beliefs and attitudes that need to be questioned and examined. The article had one paragraph portraying some of my work in a way that diverges from my experience, and it also diverges from the observations of people in the field whom I’ve discussed it with as a reality check. After some reflection, it seemed to me that what Jaffe and Quinn wrote was an example of the phenomenon that people see what they are tuned to see. Their portrayal of my work resulted from projecting the sociology of mathe- matics onto a one-dimensional scale (speculation versus rigor) that ignores many basic phenomena. Responses to the Jaffe-Quinn article have been invited from a number of mathematicians, and I expect it to receive plenty of specific analysis and criti- cism from others. Therefore, I will concentrate in this essay on the positive

Published: Jan 1, 2006

Keywords: Kleinian Group; Hyperbolic Geometry; Mathematical Community; Mathematical Language; Human Understanding

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