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Science in the Looking GlassWhat Do Scientists Really Know?$
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E. Brian Davies

Print publication date: 2007

Print ISBN-13: 9780199219186

Published to Oxford Scholarship Online: September 2008

DOI: 10.1093/acprof:oso/9780199219186.001.0001

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How Hard can Problems Get?

How Hard can Problems Get?

(p.85) 4 How Hard can Problems Get?
Science in the Looking Glass

E. Brian Davies

Oxford University Press

This chapter describes some of the outstanding mathematical discoveries which have taken place during the last half century, focusing on what they say about how far human mathematical powers extend. They suggest that we are already quite close to our biological limits as far as the difficulty of proven theorems is concerned. Topics discussed include the four colour problem, Goldbach's conjecture, Fermat's last theorem, finite simple groups, algorithms, and how to handle hard problems.

Keywords:   mathematics, four colour problem, Goldbach's conjecture, Fermat's last theorem, finite simple groups, algorithms

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