*E. Brian Davies*

- Published in print:
- 2007
- Published Online:
- September 2008
- ISBN:
- 9780199219186
- eISBN:
- 9780191711695
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199219186.003.0004
- Subject:
- Physics, History of Physics

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. ...
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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.Less

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.

*LOWELL BEINEKE and ROBIN WILSON*

- Published in print:
- 2013
- Published Online:
- September 2013
- ISBN:
- 9780199656592
- eISBN:
- 9780191748059
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199656592.003.0015
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics, History of Mathematics

During the first half of the 20th century many classic theorems about graphs were discovered, but it was not until the second half of the century that graph theory emerged as an important field in ...
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During the first half of the 20th century many classic theorems about graphs were discovered, but it was not until the second half of the century that graph theory emerged as an important field in its own right. In this chapter we develop themes arising from the four-colour problem, before focusing on three specific subject areas — the factorization of graphs, connectivity, and graph algorithms.Less

During the first half of the 20th century many classic theorems about graphs were discovered, but it was not until the second half of the century that graph theory emerged as an important field in its own right. In this chapter we develop themes arising from the four-colour problem, before focusing on three specific subject areas — the factorization of graphs, connectivity, and graph algorithms.