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Circles DisturbedThe Interplay of Mathematics and Narrative$
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Apostolos Doxiadis and Barry Mazur

Print publication date: 2012

Print ISBN-13: 9780691149042

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691149042.001.0001

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Visions, Dreams, and Mathematics

Visions, Dreams, and Mathematics

(p.183) Chapter 6 Visions, Dreams, and Mathematics
Circles Disturbed

Barry Mazur

Princeton University Press

This chapter considers the role of visions and dreams in mathematics by focusing on Leopold Kronecker's desire—or dream—to find solutions to a large and interesting collection of polynomial equations. It begins with a discussion of three kinds of storytelling in mathematics: origin stories, purpose stories, and raisins in the pudding. It then examines Kronecker's so-called liebster Jugendtraum, the “beloved dream of (his) youth,” arguing that the seed of this dream lay in Carl Friedrich Gauss's expression for square roots of integers as trigonometric sums. It also describes three truths about explanation as opposed to proof, along with basic concepts in the epistemology of mathematics, such as the difference between explicit and implicit statements. Finally, it speculates on how Girolamo Cardano, Gauss, Isaac Newton, and Kronecker might solve cubic equations.

Keywords:   visions, dreams, mathematics, Leopold Kronecker, polynomial equations, storytelling, Carl Friedrich Gauss, square roots, explanation, cubic equations

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