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How to Free Your Inner MathematicianNotes on Mathematics and Life$
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Susan D'Agostino

Print publication date: 2020

Print ISBN-13: 9780198843597

Published to Oxford Scholarship Online: April 2020

DOI: 10.1093/oso/9780198843597.001.0001

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Be grateful when a solution exists, because of Brouwer’s Fixed Point Theorem

Be grateful when a solution exists, because of Brouwer’s Fixed Point Theorem

Chapter:
(p.227) 37 Be grateful when a solution exists, because of Brouwer’s Fixed Point Theorem
Source:
How to Free Your Inner Mathematician
Author(s):

Susan D'Agostino

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198843597.003.0038

“Be grateful when solutions exist, because of Brouwer’s Fixed Point Theorem” offers a introduction to a mathematical theorem asserting the existence of solutions to problems in engineering, medicine, economics, and other fields, as long as certain criteria are satisfied. The discussion is illustrated with numerous hand-drawn sketches. While this theorem assures the existence of a solution—a “fixed point”—it does not provide insight on how to find it. Still, it can be reassuring to know that a solution exists. For example, economist John von Newmann used this theorem in his 1937 economic model establishing that there exist prices at which supply equals demand. Mathematics students and enthusiasts are encouraged to be grateful for knowledge that a solution exists in mathematical and life pursuits, even when the solution itself remains elusive. At the chapter’s end, readers may check their understanding by working on a problem. A solution is provided.

Keywords:   Brouwer’s Fixed Point Theorem, fixed point, von Newmann, math, student

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