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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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Do Androids Prove Theorems in Their Sleep?

Do Androids Prove Theorems in Their Sleep?

(p.130) Chapter 5 Do Androids Prove Theorems in Their Sleep?
Circles Disturbed

Michael Harris

Princeton University Press

This chapter examines the role of dreams in mathematics by focusing on Robert Thomason's decision to add as co-author of an important paper his deceased friend Tom Trobaugh, a non-mathematician. The reason Thomason gave was that Trobaugh, who had committed suicide a few months earlier, appeared to him in a dream and helped him complete a particularly difficult proof. The chapter first considers what the dream tells us about the narrative structure of a mathematical proof before discussing the use of automated theorem provers in creating new proofs. It also explores how K-ness can be defined and whether it can be calculated in the context of the Thomason–Trobaugh article. Finally, it describes the division in the mathematical literature between ghost and ghostwriter, citing as an example the work done regarding Grigori Perelman's proof of the Poincaré conjecture.

Keywords:   dreams, mathematics, Robert Thomason, Tom Trobaugh, proof, automated theorem provers, K-ness, Thomason–Trobaugh article, ghost, ghostwriter

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