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No. 1971:
Lame, Cauchy, and Kummer

John H. Lienhard presents guest Andrew Boyd

Gabriel Lamé
Gabriel Lamé

Today, guest scientist Andrew Boyd relives a race. The University of Houston presents this series about the machines that make our civilization run, and the people whose ingenuity created them.

On March 1st 1847, the atmosphere at the French Academy of Sciences was electric. Author Simon Singh tells how Gabriel Lamé had just finished announcing to a crowd of eminent mathematicians that he was on the verge of solving an infamously difficult problem – a problem that had defied the efforts of the world's greatest minds for over two centuries.

It was no surprise that Lamé was working on it. The salons in Paris were abuzz ever since the French Academy had offered a gold medal and a prize of 3000 francs for the problem's solution. Still, when such an esteemed mathematician stepped forward to proclaim that a proof was imminent, this was cause for excitement.

When Lamé finished his presentation, Augustin Cauchy stepped forward and asked for permission to speak. He, too, had been working on the problem using techniques very similar to those of Lamé, and was about to publish a proof of his own.

Augustin Cauchy

Augustin Cauchy

The race was on. Through March, April, and May, Lamé and Cauchy continued to share details of their work before the Academy – albeit, sketchy ones – and anticipation grew. Who would be first? What thrilling new mathematics would bring this notorious problem to its knees?

Twelve weeks after the race began, speculation came to an end as Joseph Liouville stood before the French Academy. In his hands was a note from German mathematician Ernst Kummer. Kummer, who when he was young had lost his father as the result of a Napoleonic campaign, had no great love for the French. From a distance, he followed the proceedings of the Academy, and concluded that Lamé and Cauchy were headed down a dead end. His note described why.

Lamé immediately realized his mistake. Feeling humiliated, he sent a letter to a close colleague in Berlin. "If only you had been here in Paris," wrote Lamé, "or I in Berlin, all of this would not have happened."

Ernst Kummer

Ernst Kummer

Cauchy, on the other hand, felt he could overcome the barriers raised by Kummer. He continued to publish results on the problem for several weeks, but eventually realized his efforts were fruitless.

Ten years later, it would be Cauchy who would write the closing report on the prize competition, stating, "the question remains … where Monsieur Kummer left it … the Academy would make an honorable and useful decision if, by withdrawing the question from competition, it would [give] the medal to [him]." With that, the French conceded the medal to the German.

As for the problem, the public failure of two leading mathematicians only served to enhance its mystique and its allure to future generations. For decades thereafter it would continue to tantalize people from all walks of life.

Finally, in June of 1993, a prominent article on the front page of the New York Times declared "At Last, Shout of 'Eureka!' In Age-Old Math Mystery." After more than 350 years Andrew Wiles had finally laid it to rest. In doing so, he opened new research vistas, and carved his place in history by proving one of the most famous mathematical results ever known -- a result that you've read about -- Fermat's Last Theorem.

I'm Andy Boyd at the University of Houston, where we're interested in the way inventive minds work.

I'm John Lienhard, at the University of Houston, where we're interested in the way inventive minds work.

(Theme music)

Dr. Andrew Boyd is Chief Scientist and Senior Vice President at PROS, a provider of pricing and revenue optimization solutions. Dr. Boyd received his A.B. with Honors at Oberlin College with majors in Mathematics and Economics in 1981, and his Ph.D. in Operations Research from MIT in 1987. Prior to joining PROS, he enjoyed a successful ten year career as a university professor.

The material in this essay is taken from the delightful book Fermat's Enigma by Simon Singh, First Anchor Books, a division of Random House, New York, 1998.

See also Kolata, G., "At Last, Shout of 'Eureka!' In Age-Old Math Mystery, New York Times, Monday, June 28, 1993, pp. A1 and A11.

The statement of Fermat's last theorem is remarkably simply, considering all the drama surrounding it. It says merely that the equation xn + yn = zn has no non-zero integer solutions for x, y and z when n > 2.