Ian Stewart: From Here to Infinity (1996)

Edition: Oxford University Press, 1996
Review number: 315

Ian Stewart has written several versions of a survey of the current state of mathematics, dating back as far as 1975 with Concepts of Modern Mathematics. The more snappily titled From Here to Infinity, published in 1998, is the latest version of his 1987 book, The Problems of Mathematics. As mathematics progresses, the important and interesting areas change rapidly, as new breakthroughs come and new applications and connections spark renewed interest in hitherto obscure areas. Thus a considerable revision has been made with each new incarnation.

The original book has had a considerable influence on my own life. It helped confirm my desire, as an A-level student, to study mathematics at university. From Here to Infinity is as inspiring as this suggests, and made me want to return to some of the books I have not opened for years.

Stewart tends to focus on those areas which are of interest to him personally, and his enthusiasm helps to make his account more accessible. There is one part of the book which reads as though it was included because he felt he had to rather than because he wanted to, and that is the section on Fermat's Last Theorem. However, his writing is never opaque, and should be comprehensible to the (more or less) general reader. He gives a picture of the mindset behind modern mathematics, something very difficult to obtain in the English and American school systems, where little more recent in date than 1900 is taught even under the "new maths" banner. The change between school and undergraduate mathematics is marked, and at a very fundamental level, as proof rather than correct calculation becomes the important skill.