The French Mathematician, Tom Petsinis

The French Mathematician

By Tom Petsinis

Penguin, 1997. 422 pp., $17.95 (pb)

Review by Phil Shannon

http://www.greenleft.org.au/node/16082

"I refuse to be a mathematician in a prison, and Paris will continue to be a prison until King Charles and the Church are overthrown", declares the student Evariste Galois in the revolutionary year of 1830 in a new novel by Tom Petsinis.

Petsinis, a lecturer at the Victorian University of Technology in Footscray, has recreated with artistic flair the turbulent politics of post-Napoleon France and their impact on that seemingly remote and tranquil science of mathematics, as embodied in the person of Galois.

Galois was a precocious mathematical genius killed when only 21 years old in a duel in 1832 but whose scattered writings (less than 100 pages in all) have opened up a new branch of modern mathematics known as group theory, which underpins nuclear physics and genetic engineering.

Galois takes most of his short life to overcome his disinterest in politics. After constraining the "emotional chaos" of his unhappy childhood with the discovery of "the order and certainty of geometry" and the intellectual purity of algebra, the young Galois is beset by doubts about the relevance of mathematics and his life to "the struggle against oppression", but he rejects the approaches made to him by republicans, anarchists, Blanquists and utopian socialists.

Galois immerses himself in "the noblest pursuit" of mathematics as a refuge against "the corrupting influences of the world" — such as politics and sex — until the death of his father, a republican driven to suicide by his royalist enemies.

At his father's funeral, Galois discovers solidarity and belonging, "strengthened by the sight of hundreds of people chanting support", feeling "a kinship towards complete strangers" united by a passion for a just and democratic republic.

Seeking to avenge his father's death, Galois becomes a zealous republican. His commitment is further firmed when he faces victimisation by the royalist mathematical establishment, which keeps "losing" his manuscripts and thwarting his career.

Once resisting anything that interfered with mathematics, Galois "now resists anything that interferes with the Republic". Mathematics loses its obsessive hold as he questions whether his ethereal thoughts are "nothing but an escape into fantasy, a timid mind fleeing the world of flesh and fact".

Galois attempts to hurl himself into the July revolution in 1830, which overthrew the Bourbon monarchy only to be betrayed by "liberal politicians" and the bourgeoisie, who immediately set up a "bourgeois monarchy" under whose patronage they proceeded to steal the economic and political fruits of victory from the labouring poor who had fought the street battles.

Galois is at the centre of a number of aftershocks — failed revolts, church desecrations — as a swarm of communist and socialist sects, some with a mass following, agitate for a thoroughgoing revolution amongst an organised working-class movement that was to crucially impress Marx when he moved to Paris in the 1840s.

Galois, arrested and imprisoned, maintains a rage and purity of republican passion that most others can not maintain. He takes on republican notorieties such as the writer Alexander Dumas ("You exploit those who give their blood for an ideal in order to satisfy your craving for wealth and fame") and the painter Delacroix (whose Liberty Leading the People is an icon of rebellion) for being a "parasite" and whose use of the bare-breasted Liberty is "unbecoming of a true Republican".

Galois had never been able to shake off a puritanical aloofness and a feeling of superiority. This elitist attitude kept him from identification with artisans, workers and the unemployed, whose coarseness repelled him. He was unable to tolerate or understand the vices which stain the ordinary people of the revolutionary forces in an oppressive society.

Galois does achieve some self-understanding, as well as his flaw of being "too impatient, too excitable" which make him unsuited to be a political leader and tactician.

Prison and illness prompt a return to mathematics until a duel with a fellow republican over a love affair signals the end of Evariste Galois, but not before the frantic rush to record and order his mathematical insights for posterity in the last 11 hours of his life.

These revolutionary decades in France were also decades of revolution in mathematics. Not only was Galois' search for a general theory of equations a radical departure, but there was equal intellectual daring by his contemporary, the Russian mathematician Lobachevsky, who overthrew solid Euclidean certainties (such as parallel lines never meeting and the three angles of a triangle always summing to 180 degrees) by adopting the framework of curved space instead of the flat surfaces of Euclid's ancient, flat-earth Greeks.

Revolutions in mathematics and other sciences are not mere echoes of political and social revolution (even Galois' political opponents, like the mathematician Cauchy, subsequently adopted Galois' theories).

It took an extended period of intensive revolutionary ferment to fertilise the ground for the questioning not only of monarchical, church and class power but for challenging what was held by long intellectual tradition to be "natural" and "normal" in mathematics. It was only in the 19th century that irrational numbers (the square root of 2) and imaginary numbers (the square root of -1) were accepted.

In some individuals, scientific and political revolution were captured together and magnified. Galois, revolutionary republican and mathematician, was one such person. He has found a sympathetic author who writes with creative speculation and a sure artistic touch, with not a word or symbol wasted — like the most profound and elegant mathematical theorem.