Thursday, 22 October 2009

The Lucasian Chair, From the FFT of Calculus, to String Theory

This month the Lucasian Chair of mathematics at Cambridge, just down the road from my school here in Lakenheath, was passed to Michael Green, a physicist and pioneer in String Theory. Officially, I believe, he will replace the retiring Stephen Hawking on November first.

The Lucasian Chair began with a grant of land (and a huge library of books)from the Member of Parliament to the university, Henry Lucas, to provide a 100 pounds sterling annual stipend. The first chair was Issac Barrow, a classical mathematician. It may be surprising to young people who are taught that Newton invented the Calculus, that Barrow, Newton's teacher, gave the first general proof of the First Fundamental Theorem of Calculus, the one that links integration and differentiation together.
Amazingly, after only five years, he gave up the chair to his student, Newton. Newton is probably one of the two most famous holders of the chair, the next most well known being the retiring emeritus chair, Stephen Hawking.

After Newton, the chair passed through a succession of mathematicians that would not be recognizable to the common lay person. In fact, his successor, William Whiston, would probably not be a name recognized by most mathematicians. Born in 1667, the year after the great fire of London, he was headed for the top, and rubbing elbows with the best for a while. He served as Newton’s deputy at Cambridge, where he was a fellow. He was one of the earliest proponents of the theory that comets had a periodic behavior, along with Halley. He was a classical scholar and mathematician who, if remembered at all, is remembered for his contributions to recreational mathematics. His translation of the works of Flavius Josephus may have contained a version of the famous Josephus Problem, and in 1702 Whiston's Euclid discusses the classic problem of the Rope Round the Earth, (if one foot of additional length is added, how high will the rope be). I am not sure of the dimensions in Whiston's problem, and would welcome input, I have searched the book and can not find the problem in it, but David Singmaster has said it is there, and he is not a easy source to reject. It is said that Ludwig Wittgenstein was fascinated by the problem and used to pose it to students regularly.
Whiston was expelled from his chair on 30 October 1710; at the appeal of the heads of colleges. Comets were also part of this disaster in his life. He had become famous for his studies that stated that the Biblical flood had been caused by a comet, and gave support for other geological impacts of comets on the Earth. Whiston was removed from his position at Cambridge, and denied membership in the Royal Society for his “heretical” views. He took the “wrong” side in the battle between Arianism and the Trinitarian view, but his brilliance still made the public attend to his proclamations. When he predicted the end of the world by a collision with a comet in October 16th of 1736 the Archbishop of Canterbury had to issue a denial to calm the panic.

After two holders who seemed to be little more than groveling toadies, (Saunderson and Colsen) the chair passed to Edward Waring in 1760. In number theory, Waring's problem, proposed in 1770, asks whether for every k there exists a positive integer n such that every natural number is the sum of at most n kth powers of natural numbers (for example, every number is the sum of at most 4 squares), . The problem and its affirmative solution is now called the Hilbert–Waring theorem, proven by Hilbert in 1909.

I will continue this study anon...
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