THE FRENCH MATHEMATICIAN
By Tom Petsinis
Walker and Co., 426 pages, $24
`Hard task, vain hope, to analyse the mind,” says William Wordsworth, a great representative of the era to which Tom Petsinis’ novel returns us, in his extraordinary portrayal of a poetic mind (his own) in “The Prelude.”
This task is even harder when it is the mind of a scientist, given the divide, and sometimes abyss, between “two cultures,” scientific and humanistic, as C.P. Snow famously defined them a few decades ago. On the one hand, one wants lay readers to appreciate the scientific side of scientists’ minds and lives. On the other, one wants all readers, scientists included, to appreciate the human side of both. Neither is easy, especially when one deals with mathematics, the most abstract and arcane of sciences. To achieve both is a hard task, vain hope indeed.
This is, however, the task that Petsinis (who teaches mathematics in Australia) has to confront in his fictional portrayal of the real, and rare, genius of Evariste Galois (1811-1832), the French mathematician of his novel and one of the founding figures of modern algebra.
Galois’ life contains the kind of stuff of which novels are made. Besides being a great mathematical genius, Galois was a revolutionary, killed in a duel caused by a mysterious mixture of a love affair and political intrigue (perhaps a betrayal by a friend and a set-up by the police). A similar mystery surrounded the death of his father. Finally, some of Galois’ greatest ideas and findings were written hastily during a single sleepless night on the eve of his death at age 21. “I have no time” is Galois’ famous tragic remark, found in that final manuscript.
Galois’ mathematics, on the other hand, is well out of the reach of most lay readers. To make such a subject accessible to nonspecialists–to make mathematics nonmathematical enough, and yet to show it as mathematics–requires much talent and effort, a considerable degree of technical knowledge of mathematics, and quite a bit of philosophical thinking. Reading such works requires a major effort in turn.
When the authors and the readers succeed, there appear not only things philosophical or poetic about mathematics, but also things mathematical about philosophy and poetry. Galois’ writings clearly manifest this ability to think philosophically and indeed poetically about mathematics, and to convey it accordingly. “The French Mathematician” gives us glimpses of this ability.
Petsinis’ novel itself, however, does not belong, and does not appear to aim to belong, to this category of writing about mathematics. It attempts this type of writing only occasionally, and would have benefited from doing it more often.
Admittedly, it is not easy to do this in a novel. A good novel about a mathematician cannot, however, avoid reaching into the essence of the complex ideas defining modern mathematics.
But the substance of mathematical genius cannot be truly conveyed apart from, for most readers, prohibitively complex mathematics. In one of the most dramatic moments of the novel, Galois, in confronting the death of his father, makes one of his mathematical discoveries. “I heard the clear voice of mathematics: For an irreducible equation of prime degree to be solvable by radicals it is necessary and sufficient that all its roots be rational functions of any two of these roots. . . . (M)y discovery gave me the strength to face Father’s death.”
Some lay readers will be able to make sense of Galois’ formulation. But how many of them will respond to the profundity, significance and beauty of the theorem itself, still reasonably elementary by the standards of modern mathematics?
Indeed, far more elementary references in the book may not be sufficiently familiar to many readers, for example, those to imaginary numbers, such as the square root of negative 1, designated as i in mathematics. Petsinis uses it as the key metaphor for his novel, taking advantage of the pun on i and “I,” the first person singular. The book would have benefited from a glossary and nontechnical explanation of its key mathematical terms and ideas.
Galois’ work is the stratosphere of mathematical thought, and some of the most complex 20th Century mathematics is an extension of his ideas or is indebted to them. He is the mathematician’s mathematician and the genius’ genius, and is often seen as one of the greatest, perhaps the greatest, mathematician, who ever lived, even though, and in part because, he died at 21.
Petsinis’ main emphasis is on the primary role of intuition, rather than technical power, in Galois’ mathematical thought and work. This emphasis is not out of place or inconsistent with Galois’ own extant comments on the subject. Galois’ mathematical writings may, however, be better seen as revealing a remarkable combination of giant intuitive leaps and a manifest capacity for precise and rigorous analysis, a technical brilliance.
Perhaps most crucial is the more broadly conceptual and foundational nature of his work. At stake in it are the fundamental architecture of mathematical objects and concepts, and the fundamental ways of creating and dealing with them.
Galois’ architectonic thinking accounts best for the extraordinary significance of his work for the subsequent development of mathematics, including for mathematics yet to come. Dozens of mathematical books are devoted to the so-called Galois theory (a branch of modern mathematics dealing with the nature of polynomial equations and their role in algebra and number theory) and its implications. This number would be even greater were one to include those dealing with group theory, also introduced by Galois. The Galois theory played a significant role in the proof of Fermat’s theorem by Andrew Wiles a few years ago, one of the greatest achievements of 20th Century mathematics.
Galois’ mathematics is a mathematics that always moves forward and transforms itself in the process, a mathematics that is always and forever new, indeed always and forever the mathematics of the future–a permanent mathematical revolution.
Both in his temperament and in the nature of his thought and work, Galois may indeed be best seen as a revolutionary. As his writings suggest, the revolutionary nature of his thought is not restricted to mathematics but extends to politics as well. Petsinis makes one sense the conjunction of mathematics and revolution in Galois’ life and, to some degree, his thought, but does not take advantage of it. Indeed mathematics and revolution are juxtaposed or even antagonistic in the novel, rather than brought together. Nor does one find in the novel a full-fledged portrayal of Galois as a political revolutionary.
What, then, are we to do? How are we to have productive encounters with mathematics (or science), or to understand Galois’ life?
The answer, I think, is that we read. We read as well as we can, which is also to say, we think as hard as we can. We read historical novels (such as Petsinis’). We read biographies and autobiographies. We read letters of mathematicians and scientists. We read books about mathematics and science, perhaps even some technical works.
Reading may teach us something that is as necessary for understanding Galois’ mind and life as his mathematics, perhaps ultimately more so. For the ultimate mystery may be the human mind itself and hence our own minds, even when we are neither poets, nor mathematicians, nor revolutionaries.
