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Princeton Mathematician Speaks at CMI Inauguration

By Adam Brown
STAFF REPORTER

A brass quartet, unveiling of a sculpted logo, a number of notable mathematicians, and an audience of over 450 celebrated the formation of the Clay Mathematics Institute yesterday in Room 10-250. Andrew Wiles, the Princeton University mathematician who proved Fermat’s Last Theorem, delivered the keynote address.

The Clay Mathematics Institute (CMI) was formed in September 1998, according to Director Arthur Jaffe. Yesterday’s lecture was its first public event. Many notable mathematicians and others gave brief welcomes.

These welcomes included “three soundbites” from CMI Adviser Edward Witten of the Institute for Advanced Study: Mathematics is a pillar of modern civilization because it is ancient (though it is not, panel moderator and Editor at Large of U.S. News & World Report David Gergen later pointed out, the oldest profession); the strongest aspect of modern civilization due to rigor in proofs; and the broadest, because mathematics supports the creative enterprise of most of science.

Wiles discusses recent advances

Wiles explained recent advances in number theory, the field of mathematics devoted to finding integer and rational solutions to equations. Wiles began by telling the story of Fermat’s Last Theorem (FLT) -- Fermat wrote it in the margin of his copy of Diophantus’s Arithmetic without proof. Wiles moved on to describe number theory proofs and attempted proofs of FLT. Finally, Wiles explained his own proof, incorporating the work of other mathematicians. He ended by displaying other problems related to right triangles, as well as explaining Diffie-Helman and RSA cryptography.

Fermat’s Last Theorem states that the equation xn+yn=zn has no integer solutions if n is greater than 2. This had been proved for special cases of n = 3, 4, and a few other small numbers, but the generalized theorem has evaded proof for over 350 years.

Herschbach, Odon on math in life

A small panel moderated by Gergen, discussed their experiences in the world of mathematics. The panelists were Dudley Herschbach, a Harvard chemist, and General William Odon, former director of the National Security Agency.

Herschbach described his experience as a mathematics undergraduate at Stanford in classes with mathematicians such as George Polya and Gabor SzegÖ, and told a story of how Polya, who studied probability theory, was prompted to study randomwalks in the plane, and eventually other dimensia, when he ran into an “amorous couple” several times one day in a maze-like forest.

Herschbach spoke of the need for increased access to mathematics -- higher, interesting mathematics rather than elementary school arithmetic -- for young students. He mentioned the falling U.S. performance between the fourth, eighth, and twelfth grade levels.

Asked about mathematics applications and science, Herschbach said, “science has so far used only a tiny fraction of the richness that math has provided.”

Odon, who described himself repeatedly as a “layman,” described problems that arose at the National Security Agency when there were few mathematicians, and spoke on what should be done to further the discipline in terms of government.

CMI logo is a work of art, math

The head of the CMI, Arthur Jaffe of Harvard University, began the event by introducing Landon Clay, CMI founder, as well as Charles Vest, who spoke briefly about the future of research in general, saying “I feel we still lack that deep-seated commitment” in regard to the government’s recent cuts in funding.

Helaman Ferguson, a sculptor and mathematician, was commissioned to design the CMI logo. His sculpture is called “Figure Eight Knot Complement,” and is made of black granite. Ferguson described the sculpture’s elements of topology, non-Euclidean geometry, and arithmetic. The sculpture originated as a visualization of complex matrices. A small bronze replica of the logo was also presented to Wiles, and CMI advisors said that mathematical awards in years to come may be similar replicas.

The president of the International Mathematical Union, Director of the National Science Foundation, and the President of the American Mathematical Society attended ceremonies, as did two winners of the Fields Medal, the equivalent of the Nobel Prize in mathematics, and numerous students from several schools.

Karen Robinson contributed to the reporting of this story.