From the preface: The first edition of this book was written in 1986 and published in 1988 [see Mathematics: the new golden age, Penguin, New York (1988; Zbl 0702.00001)]. In preparing this new, American edition, I have changed the text to make it better suited to American readers and to take account of various developments that have taken place in the intervening ten years, but the choice of topics remains the same. Again, my intention was never to cover all of mathematics – an impossible task in a discipline that, in terms of published new results, has, throughout my mathematical career, doubled in size roughly every ten years. Rather, I have tried to convey something of the richness and diversity of present-day mathematics.
Other than the addition of new material updating the original account and the correction of minor errors and misprints pointed out to me by various readers of the first edition, the most significant change made in this second edition is the complete rewriting of the chapter on Fermat’s last theorem to take account of the 1994 proof of the theorem. This new treatment of Fermat’s last theorem required moving the chapter to follow the discussion of topology; thus, what was chapter 8 in the first edition is now chapter 10, and chapters 9 and 10 of the first edition now appear as chapters 8 and 9, respectively. The other major change is in the chapter on knots and topology, chapter 10 of the first edition and chapter 9 of this edition. This has been renamed and expanded to take account of some dramatic developments in topology that have occurred over the past five years.