| | Ivars Peterson's MathTrek |
March 1, 1999
Most people owe what they know about Galois to a stirring account written in 1937 by the mathematician Eric Temple Bell in his book Men of Mathematics. In a chapter titled "Genius and Stupidity," he described the young Galois and his tormented state of mind on the night before the ill-fated duel.
Bell wrote: "All night ... he had spent the fleeting hours feverishly dashing off his last will and testament, writing against time to glean a few of the great things in his teeming mind before the death which he foresaw could overtake him. Time after time he broke off to scribble in the margin 'I have not time; I have not time,' and passed on to the next frantically scrawled outline. What he wrote in those desperate last hours before the dawn will keep generations of mathematicians busy for hundreds of years."
Évariste Galois
Great stuff--the sort of tragic but inspiring tale that readily gets passed on from one generation of math students to another. Indeed, Bell's account is echoed in numerous textbooks, articles, and other material.
The facts, however, do not support the picture that Bell painted of a misunderstood boy genius, hindered and persecuted by those around him too stupid to understand his mathematical achievements and appreciate his talent.
In a chapter of the book Science à la Mode, cosmologist Tony Rothman, now at Illinois Wesleyan University in Bloomington, tries to set the record straight. He demonstrates where Bell went astray and introduces evidence to clear up apparent mysteries surrounding the circumstances that led to Galois's death in a duel--including the name of his opponent and the identity of the woman over whom the duel was fought.
Rothman points out that Galois's own arrogance, erratic temperament, and self-destructive tendencies contributed greatly to his difficulties in getting his mathematical ideas accepted, to his failure to pass the exam necessary to get into the prestigious École Polytechnique, and to his political misfortunes and eventual downfall.
In the quirky, recently published Norton History of the Mathematical Sciences, Ivor Grattan-Guinness declares that "Galois was known around town as a loud-mouthed and opinionated republican, not a good reputation to have either before or after the 1830 revolution."
As for Galois's final night, Rothman debunks the romantic notion of a doomed genius working feverishly by candlelight to commit his revolutionary theory of equations and groups to paper. In fact, Galois had been writing papers on the subject since the age of 17, and the new idea of "group" that he had introduced is found in all of them. Nonetheless, Galois did help create a field that would keep mathematicians busy for hundreds of years, but not in one night!
What about the famous inscription "I have not the time"? It appears only once in a final letter to a friend, scrawled next to a particular theorem after he had written the words, "There are a few things left to be completed in this proof."
Ironically, the account that seems closest to the facts of Galois's brief life is a recent novel called The French Mathematician by Tom Petsinis, a novelist, poet, playwright, and math instructor in Melbourne, Australia. It's an intriguing book, presenting the tragic tale as if it were told by Galois himself.
I'm not convinced that Petsinis has truly captured Galois's evolving state of mind. Many times, Galois's mathematical thoughts seem too modern--too informed by recent developments in mathematics to be genuinely his. Similarly, I find his depiction of the psychological transformations that distract Galois away from his mathematical studies into politics sometimes less than compelling.
Petsinis does, however, bring to vivid life the passions, complexities, and uncertainties of life in Paris during the tumultuous years of conflict between royalists and republicans after the exile of Napoleon Bonaparte. And Galois's story remains as dramatic and engrossing as ever.
Copyright 1999 by Ivars Peterson
References:
Bell, E.T. 1937. Men of Mathematics. New York: Simon & Schuster.
Devlin, K. 1996. Of men, mathematics, and myths. MAA Online (August). Available at http://www.maa.org/devlin/devlin_aug.html.
Grattan-Guinness, I. 1998. The Norton History of the Mathematical Sciences: The Rainbow of Mathematics. New York: Norton.
Katz, V.J. 1998. History or mythology? Math Horizons (April):22.
Muir, J. 1996. Of Men and Numbers: The Story of the Great Mathematicians. Mineola, N.Y.: Dover.
Petsinis, T. 1998. The French Mathematician. New York: Walker.
Rothman, T. 1991. Science à la Mode. Princeton, N.J.: Princeton University Press.
______. 1982. Genius and biographers: The fictionalization of Evariste Galois. American Mathematical Monthly 89:84.
You can find a brief biography of Galois at http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Galois.html.
Comments are welcome. Please send messages to Ivars Peterson at ipeterson@maa.org.