A Princeton Massacree
I worked at Princeton a number of years, took classes, helped “A Beautiful Mind”, John Nash. Many people there other than my boss and immediate coworkers thought me strange, arrogant, too tall and good looking, and a complete Roosevelt University lightweight and hotdog but I was having too much fun to worry about this.
Dozing, this Saturday afternoon, over this BBC program about the discovery of a proof for “Fermat’s Last Theorem”. I was a fly on the wall from 1987 through 1992 as regards Princeton maths.
It won’t help you to understand the math beyond the broad implication structure: “if we solve Taniyama-Shimura then for no x>2 does m**x + n**x = p**x (Fermat)” but it shows the astounding geek (Andrew Wiles) who proved this and the affable bearded John Horton Conway, the inventor of cellular automata and the Game of Life which I discovered in 1970 in Scientific American and programmed on an old IBM mainframe.
That beautiful river and towpath that you’ll see in the program is Princeton’s answer to the Cam in Cambridge: the Delaware-Raritan Canal, constructed in the early 19th century before railways to expedite passenger travel and shipping in New Jersey.
At Princeton, that canal expands into “Lake Carnegie”. In the late 19th century a Princeton man met Andrew Carnegie on the Dinky, a small passenger train operated ONLY for the convenience of Princeton students to hook them up with the main line of the Pennsylvania Railroad at Princeton Junction…I was struck how traditionally Princeton “men” were given all sorts of perks, but this is changing: more than 50% of Princeton’s student body is female today. Princeton men could get a Gentleman’s C as I could at uni: not so any more.
Any roads, the Princeton boy complained to the steel magnate that Princeton could not beat Harvard at rowing since the canal was so shallow, affording insufficient space for rowers to train for their meets, so Carnegie had a lake dug at his expense. Andrew Wiles sought peace through long walks down the towpath as I did by running it, for people who work with math and numbers are often subject to fits of mental anguish.
I could not help but notice that on Princeton’s rowing teams, the coxswains, who shouted both the time and encouragement, were highly fit women (underweight and under-muscled so as not to burden the boat) whereas the actual hard work of rowing was male. Hmm.
I would see John Horton Conway in the WaWa (convenience store), poking through logic and Sodoku magazines for the 1980s were the zenith of Conway’s interest in recreational math, where he made several important discoveries. And, of course, I’d see John Nash because Nash, unlike many mathematicians including Wiles, didn’t hate and mistrust computers.
Wiles would never have used a computer for his proof although a team at the University of Illinois did so to check millions of cases to prove that “for any map, at most four colors suffice to color countries and the ocean such that all adjacent countries including the “country” of the ocean will be of different colors”. Mathematicians objected saying that the computer hardware, or software supporting the program checking the cases, or the program itself may have had a bug and after some to and fro, a non-computer proof was found.
You see, there are three major philosophies of mathematics: logicism or Platonism, which believes that mathematical objects are real if perhaps resident in a higher world: formalism, which denies this and declares that math is just a game with meaningless symbols (and that mathematicians are paid an unholy amount of money for essentially playing Sodoku): and strangest of all, intuitionism, the belief that math is about the Kantian apparatus of our perception and that oh by the way thou shouldn’t reason based on p or ~p (any proposition is true or false) for some propositions (consider the antinomies of Kant, such as “time is infinite”) are neither true nor false.
Real mathematicians are mostly “logicists” aka “Platonists”. Wiles certainly was, as was Nash, for both were seduced and held in awe by the idea that they could “voyage strange seas of thought” and discover new worlds, “and the Anthropophagi, whose heads/Do grow beneath their shoulders”, as Othello discovered. They didn’t want the trustees of Princeton to think they were playing Sodoku on company time, and Kant, and consequently intuitionism, is little understood in England or America.
13 May 2013 Added this change record: minor corrections