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Reuben Hersh
18 unconventional essays on the nature of mathematics
Of all subjects, mathematics is the one which is supposed to be based on firm ground. But what is it really based on - is it just manipulation of meaningless symbols, or is there a Platonic world of mathematical forms? In 18 unconventional essays on the nature of mathematics different authors present their views on the status of mathematics. For instance acceptance of a mathematical proof is seen to be very much a social phenomenon. I recommend the essay by William P Thurston on how his early mathematical career was too successful - no one else wanted to enter his field. So in later work he made sure that there was plenty of opportunity for others to participate.
The essays are bit of a mixed bag, and it seemed that there was less editorial involvement than in similar books. There is no index and one of the articles clearly has not been fully proof read after being scanned in. Some of the philosophical and sociological articles are a bit wordy, but if you're interested in the nature of mathematics then you might appreciate the range of viewpoints. Alternatively you might just be interested in inividual essays. As well as Thurstons's essay, I also enjoyed those by Donald MacKenzie on the status of computer based proofs, and Rafael Núñez on how, despite expressing mathematics as static symbols, our internal view of the subject is based on movement.
