This book makes mathematics both understandable and interesting! It is an incredibly well-told story about the nature of mathematics and mathematicians and the search for the proof of Pierre Fermat's last theorem. It explains what the theorem is and the nature of mathematical proof and it comes as close as imaginably possible to explaining how mathematical techniques and knowledge developed until a proof of the theorem could be devised.
Pythagoras's famous equation ("for a right-angled triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides") leads to a simple mathematical equation. Pierre Fermat, in 1637 or thereabouts, wondered whether you could have an equivalent equation using cubes rather than squares, or indeed any higher power. He claimed, in a marginal note, that "I have discovered a truly marvellous proof of this, which this margin is too narrow to contain". But in the ensuing 350 years no mathematician could prove 'Fermat's Last Theorem' (last because it was the last to be confirmed). Then, in 1993, Andrew Wiles claimed to have a proof. But did he?
There are some brilliant anecdotes, some wonderful curiosities from the world of mathematics, and the following:
- "Mathematical logic ... a way of achieving truth which is beyond the fallibility of human judgement." (Ch 1)
- "The growth of any discipline depends on the ability to communicate and develop ideas, and this in turn relies on a language which is sufficiently detailed and flexible." (Ch 2)
- "Creating mathematics is a painful and mysterious experience. Often the object of the proof is clear, but the route is shrouded in fog, and the mathematician stumbles through a calculation, terrified that each step might be taking the argument in completely the wrong direction. Additionally there is the fear that no route exists." (Ch 3)
- "Mathematics consists of islands of knowledge in a sea of ignorance." (Ch 5)
Fascination and wonderfully explained. June 2021; 345 pages
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