by Nathan Collins

        After talking about how he realized that he was going to be doing math for a career, Arkady was asked about a number of things such as the Indian mathematician Ramanujan, and also knot theory. Knot theory started as part of physics in the 1860's. The physicists were working with tubes of ether and discovered these knots in a physical form. By the 1870's the physicists had "classified" all of the knots, but when asked by a mathematician how they knew that they had finished, they could only explain that they had tried to find other knots and couldn't. So the mathematician started looking at it in a more rigorous mathematical approach. Around 1899 knot theory became part of topology. By the 1930's knot theorists thought they had solved all of the problems of knot theory. Around 1984 a mathematical physicist discovered a powerful tool to distinguish lots of knots, which reopened the theory. A good book to learn about knots is The Knot Book by Collin C. Adams.  A side note is that Professor Vaintrob once found a knot theory book located in the sailing section of a bookstore.
         The last topic that I will discuss is Professor Vaintrob's opinion on Fermat's "proof" of "Fermat's last theorem"  (xⁿ + yⁿ = zⁿ for x, y, z > 0 and integers is not solveable for n > 2). When asked if he believed that Fermat had actually given a proof of this, Professor Vaintrob said that he believes that Fermat's "proof" was only for the case when n = 4. Fermat had actually proved that x⁴ + y⁴ = z² is not solvable for integers x, y, z > 0, a stronger case than n = 4. A note about "Fermat's last theorem" is that it had been unsolved for hundreds of years and was finally proven in the 1990's by Andrew Wiles of Princeton. Fermat claimed that his proof was written somewhere other than his book because it was too big for the margin (where he wrote most of his proofs). The proof using Andrew Wiles' method is hundreds of pages, making the phrase "too big for the margin" seem like a great understatement.
         If you are interested in the topics and are beating yourself up for missing the tea, don't worry, there will be another one coming up around the corner. For questions about the next tea, talk to the head math Peer Advisor, David Jordan in the Hilbert Space.

         There are (at least) two interesting undergraduate competitions for interested undergrads during the fall. If this has piqued your interest keep reading. The Putnam Competion is held in December (this year it is the 4th, although I don't know if that's standard) and is open to any undergraduate who has not participated more than three times previously. As far as I can gather it is only open to American students, with the exception of Canada. 
         The Putnam competition is an individual event (although individual scores are combined to form team scores, collaboration is strictly prohibited). There are twelve problems, broken into two sets of six, and ordered in increasing order. Ordinarily people try to tackle easier problems first, although the order doesn't actually matter and most people are happy to even solve one. The competition is six hours long. Participants are given the first six problems and have three hours to make what progress they can. Then there is a half hour lunch break and finally another six problems with an additional three hours. The problems are graded on a one to ten scale, although it is uncommon to get between three and seven points (inclusive). Since the problems mostly fall under the category of mathematical proof there is no simple way to grae them and hence you have to wait a few months to find out exactly how you did (although you should have a pretty good idea when the competition is over, especially when  you don't turn anything in).