Alexandre Grothendieck: A Mathematical Portrait

... [The contributors] write with great insight on Grothendieck’s mathematical legacy. What comes over strongly is his immense productivity during the early decades of his career, often relying on students and colleagues to write up his prodigious output, and his desire for mathematics to be as natural and as general as possible, often delaying publication until the exposition fitted perfectly into his global view of mathematics.

This collage of viewpoints provides a fascinating cubist portrait of Grothendieck, which will form an excellent complement to the multi-part biography which Wilfried Scharlau is writing...

… [The authors’] aim is to provide some explanation of what made Grothendieck such a unique mathematician, what the nature of his mathematical thought was, and how his overall mathematical impact shaped their own research work. Accordingly, these articles do not concentrate on specific mathematical contents of Grothendieck’s gigantic work, but instead on the characteristic traits of his tackling of problems: maximum generality, structuralism, fundamental simplicity of new approaches, ingenious generalizations of classical concepts, technical prowess, etc. Each of the articles is devoted to one or another aspect of Grothendieck’s contributions, accompanied with personal impressions, memories, anecdotes, and biographical insertions.

… Altogether, this book makes the reader see Alexandre Grothendieck through the eyes of people who knew him and his mathematics very well. The mathematical portrait painted here provides a better understanding of what his unique contribution to mathematics really was, in particular with a view toward further generations of mathematicians.

The present book is a compendium or a collage of articles having to do with the different facets of Grothendieck both as a hugely important and influential scholar and as an ultimately enigmatic individual with a remarkable history, including a past filled with childhood tragedy and strife, and a present full of mystery. There are articles by mathematicians, experts all, on the major themes of Grothendieck as an unsurpassed algebraic geometer.

The book under review is irresistible to anyone who has even a mild interest in and acquaintance with algebraic geometry … and who is fascinated by Grothendieck’s remarkable life, including a trajectory from a fatherless childhood as a refugee from the Nazis sheltered in southern France, to early adulthood as an outsider who nonetheless absorbed mathematics through his pores, to a stellar career as one of the unquestioned grand masters of algebraic geometry, doing things in magical and radical ways in a style all his own, and then to the mystery that he now poses. The authors represented in this “Mathematical Portrait” are uniquely positioned to comment not only on Grothendieck’s mathematics but on the man himself, his personality, his influence (and his influence on them), and his uniqueness. Yes indeed, I think the book is altogether irresistible.

...a fascinating (if technical) collection of essays about the man who wholly remade mathematics in the middle of the 20th century...

The remarkable life of Grothendieck has shaped not only the work but also the lives of the authors in this book and many more. What the readers will find in this fascinating collection of articles is not only valuable overviews of aspects of Grothendieck’s work but vivid glimpses of what it was like to be drawn into Grothendieck’s orbit.