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Structure of Crystal, Bucket of Dust

Peter Galison

in Circles Disturbed: The Interplay of Mathematics and Narrative

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691149042
eISBN:
9781400842681
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691149042.003.0002
Subject:
Mathematics, History of Mathematics

This chapter advances the idea that every mathematical argument tells a story by focusing on the biographies of two pioneers: American physicist John Archibald Wheeler and the Bourbaki collective of ... More


Vividness in Mathematics and Narrative

Timothy Gowers

in Circles Disturbed: The Interplay of Mathematics and Narrative

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691149042
eISBN:
9781400842681
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691149042.003.0007
Subject:
Mathematics, History of Mathematics

This chapter examines vividness in mathematics and narrative. It first gives two presentations of the mathematical notion of a group before explaining how to calculate highest common factors. It then ... More


Conclusion

Joseph Mazur

in Enlightening Symbols: A Short History of Mathematical Notation and Its Hidden Powers

Published in print:
2016
Published Online:
January 2018
ISBN:
9780691173375
eISBN:
9781400850112
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691173375.003.0024
Subject:
Mathematics, History of Mathematics

This concluding chapter argues that symbols contribute to the beauty in mathematics—the elegance of proofs, simplicity of exposition, ingenuities, simplification of complexities, making sensible ... More


Introduction

Roi Wagner

in Making and Breaking Mathematical Sense: Histories and Philosophies of Mathematical Practice

Published in print:
2017
Published Online:
January 2018
ISBN:
9780691171715
eISBN:
9781400883783
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691171715.003.0001
Subject:
Mathematics, History of Mathematics

This book examines the force of mathematics, what this force builds on, and how it works in practice by discussing mathematics not only from the point of view of applications but also from the point ... More


Mathematics and Cognition

Roi Wagner

in Making and Breaking Mathematical Sense: Histories and Philosophies of Mathematical Practice

Published in print:
2017
Published Online:
January 2018
ISBN:
9780691171715
eISBN:
9781400883783
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691171715.003.0006
Subject:
Mathematics, History of Mathematics

This chapter introduces the notion of embodied mathematical cognition by reviewing some neuro-cognitive theories of mathematical concept formation. It first considers the neuro-cognitive debate on ... More


Mathematical Metaphors Gone Wild

Roi Wagner

in Making and Breaking Mathematical Sense: Histories and Philosophies of Mathematical Practice

Published in print:
2017
Published Online:
January 2018
ISBN:
9780691171715
eISBN:
9781400883783
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691171715.003.0007
Subject:
Mathematics, History of Mathematics

This chapter examines two case studies that illustrate the limitations of the cognitive theory of mathematical metaphor in accounting for the formation of actual historical mathematical life worlds. ... More


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