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6. Abstract Generality, Simplicity, Forgetting, and Discovery

  • 2022
  • OriginalPaper
  • Chapter
Published in:
Author
Colin McLarty
Published in
Axiomatic Thinking II
Publisher
Springer International Publishing

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Abstract

The chapter delves into the intricate relationship between mathematical rigor, simplicity, and generalization. It challenges the notion that rigor and simplicity are mutually exclusive, arguing that the pursuit of rigor often leads to the discovery of simpler proof methods. The author explores various examples of unifying generalizations, including Grothendieck's theory of schemes in algebraic geometry, which is highlighted as a particularly influential generalization. The chapter also discusses the role of forgetting specific details to uncover more general principles, as exemplified by Emmy Noether's work. Throughout, the text offers a fresh perspective on how abstraction can lead to both simplification and deeper understanding in mathematics.
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previous chapter Reflections on the Axiomatic Approach to Continuity
next chapter Varieties of Infiniteness in the Existence of Infinitely Many Primes
Title
Abstract Generality, Simplicity, Forgetting, and Discovery
Author
Colin McLarty
Copyright Year
2022
Book
Axiomatic Thinking II

Print ISBN: 978-3-030-77798-2

Electronic ISBN: 978-3-030-77799-9

Copyright Year: 2022

DOI
https://doi.org/10.1007/978-3-030-77799-9_6
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