Evariste Galois (1811-1832) was a great mathematician, led a tumultuous life, and was killed under mysterious circumstances at the age of 20. The book under review is a novel based on his life, aimed at the general reading public.

What do we know about the real Evariste Galois? Certainly, he was a visionary mathematician. He was the first to truly understand the concept of a finite group. More spectacularly, he applied this emerging group theory to an outstanding problem of his time: he gave a necessary and sufficient group-theoretic condition for a polynomial to be solvable by radicals.

We know also a great deal of his involvement in the revolution of 1830 and its aftermath. For example, none other than the novelist Alexandre Dumas was among the witnesses when Galois made threatening remarks about King Louis-Philippe, while brandishing a knife; this led to the first of his two jail terms.

We know too how the work and the tumult came together most dramatically on the night of May 29, 1832, when Galois wrote a long letter to his friend Auguste Chevalier. This letter makes clear that he expected to be killed the next morning. It is also his clearest and most-cited work, summarizing and correcting his previous work, and indicating other areas in which he had thought deeply. The next day, he indeed got himself shot, and the letter played a central role in the later recognition of his work.

There is also a lot we don't know. What was in his various lost manuscripts? To what exactly do the cryptic hints in his final testament refer? We have very fragmentary evidence of a brief and amorous relationship with a Stéphanie DuMotel. What really happened? And, of course, what were the exact circumstances of his death?

What a grand and tragic life! What tantalizing questions! Galois' life story has given rise to a large literature, with works ranging from purely historical to semi-fictional. Most authors have Galois dying in a duel over DuMotel, with various details depending on the author. On the other hand, a 1996 biography by Toti Rigotelli gives a completely different account of the shooting.

If you are interested in systematically learning about Galois' life, I would recommend starting with Toti Rigotelli's biography and its useful 12-page bibliography. Among the works cited there, I would particularly recommend Rothman's 1982 Monthly article, which nicely sifts fact from fiction.

What about the book under review? We must judge it on its own terms. First, since it is aimed at a general readership, we can only demand that it do superficial justice to Galois' mathematical work. Second, we must accept the self-contained format of a novel. The line between fact and guesses is not investigated here. Even an occasional purely fictional scene is to be allowed, as well as attempts on many levels to add beauty to the tale and depth to the characters.

Petsinis' stated goal is much more ambitious than to simply capture the drama of the known and guessed-at events. He is aiming for a higher psychological truth and to this end has Galois himself narrate the novel. The jacket says that "Galois springs off these pages". Among other things, we must judge whether we think the Galois here is plausibly the real Galois.

I give Petsinis very high marks for incorporating the known events of Galois' life into the book. There is accuracy not just in the many basic events, but in their many small details as well. Some of the small details are worked in quite cleverly. Readers who fact-check will be rewarded.

I also give Petsinis high marks for making plausible and consistent choices when required to fill in the historical record. For example, he gives Galois an aversion to sex, a conjecture which can be supported by the documentary evidence. This aversion plays an important role in a great fictional scene: Petsinis has Galois react angrily to Delacroix's famous painting *Liberty leading the people*. It is also blended in well with a touching and suitably brief imagined version of his relationship with DuMotel.

Fairly high marks too for enriching the tale in the telling. The many real secondary characters are generally portrayed well. The ever-changing scenes are sketched well. I particularly liked how Petsinis catches the horror of a cholera epidemic in just a few words. One can hardly imagine adding drama to the night of May 29. But even here I think Petsinis' embellishments help: lamp oil is dwindling as the clock strikes later and later hours...

Petsinis tries hard to give the reader some intimation of Galois' mathematical genius. A device he uses repeatedly is to give Galois a stray mathematical thought in the midst of other thoughts. This device is a perfect match for the constraints of the book, and sometimes he uses it expertly. For example, a pigeons-in-triangles thought deftly communicates to a lay reader one sort of thing that goes on in a mathematician's mind. But often Petsinis uses this stray-thought technique poorly, at times even giving Galois thoughts that are mathematically incorrect. His attempts to convey Galois' mathematical genius with other techniques also range from very good to poor.

My biggest objection is that, in an important respect, it is a fake Galois which springs off the pages. A lot of space is given to Galois' internal thoughts. Some of these thoughts are copied or extrapolated from the historical record. But a majority are wild dreams or trite philosophical thoughts, often repeated with slight variations. These invented thoughts are meant to convey genius, but to me they convey only a crazy dreaminess. They are meant to ring true, but to me they clang false. For the real Galois to spring off the pages, he must be made to think his own thoughts again, with the depth that he thought them.

But I shouldn't conclude too critically. In his acknowledgements, Petsinis says he seeks to "build bridges...between Mathematics and Literature". Such bridges are rare and valuable, and Petsinis has built us one more.

**References:**

- Laura Toti Rigatelli, Evariste Galois 1811-1832 (Vita Mathematica, Vol 11). Birkhauser, 1996. ISBN 3764354100. (See also the review by Roger Cooke in the March 1998 issue of the
*American Mathematical Monthly*.)
- Tony Rothman, "Genius and biographers: the fictionalization of Evariste Galois."
*American Mathematical Monthly* **89** (1982), no. 2, 84--106.

David Roberts is currently assistant professor of mathematics at Rutgers University. His research speciality can be described as "Computational motivic Galois theory". Non-work time is spent with wife Windy, and kids Angela 15, Emma 6, and Thomas 4.