Chapter

How Hard can Problems Get?

E. Brian Davies

in Science in the Looking Glass

Published in print June 2007 | ISBN: 9780199219186
Published online September 2008 | e-ISBN: 9780191711695 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199219186.003.0004
 How Hard can Problems Get?

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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

Chapter.  5586 words.  Illustrated.

Subjects: History of Science and Technology

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