Opinion 56: The DisUnity of Mathematics

By Doron Zeilberger

Written: Nov. 7, 2003

When I was a kid there was a joke about Jerusalem. A tourist goes out of his hotel and asks a lady who happens to be standing outside. `Excuse me, where is the night-life of Jerusalem?', and the lady replies: I am the night-life of Jerusalem.

I was reminded of this joke when I attended the Unity of Mathematics conference in honor of Israel Gelfand's 90th birthday. Sadly enough, the (almost) unique embodiment of the Unity of Mathematics, today, is Gelfand.

The slate of speakers was very impressive, and some of them (for example Bernstein, Drinfeld, Kazhdan, Kontsevich) are direct disciples, while all the other speakers were influenced by Gelfand's outstanding and versatile contribution to mathematics (like almost all of us!).

So Gelfand succeeded spectacularly in raising and influencing many generations of brilliant mathematicians. Alas, he failed miserably in creating a true heir. All the speakers are brilliant men (and woman, I am sorry I can't say women) of mathematics and/or physics. Some of them are also brilliant speakers (Atiyah, Seiberg, Hopkins, Fadeev, Nekrasov, Connes), (while some of them are hopeless). BUT NONE OF THEM IS GELFAND. In fact, I was wrong when I called them "mathematicians". The only mathematician alive today is Israel Gelfand himself. Everybody else is either a topologist, analyst, geometer, algebraist, combinatorialist, etc. etc. With the exception of Atiyah's beautiful talk, all the talks were technical and specialized, and testified much more to the disunity of mathematics than to its unity.

Even more sadly, Gelfand's unique approach to learning and teaching by giving the simplest possible example, and that Gelfand enforces in his famous seminar, by constantly interrupting speakers and making them explain clearly and simply, was conspicuously missing from the conference. Because of the size of the conference, Gelfand did not feel comfortable enforcing his style, and must have been frustrated, since he did not show up to most of the talks.

Louis Nirenberg told the audience, in the beginning of his talk, how after his first visit to Moscow, with some other colleagues from Courant, they promised each other to start a seminar a la Gelfand, and "take turns being Gelfand". Unfortunately, no one rose to the occasion during the "Unity" conference, not even Gelfand himself, and consequently, most of the talks were given near the speed of light and were incomprehensible.

Let's hope that the breed of giants in the style of Hilbert, Poincare, Weyl, and Gelfand, will not die out (luckily, some of the great mathematicians (in the sense of technical wizardy) also have Universalist leanings (for example Atiyah, Cartier, Gowers), so there is hope. But even more important, let's hope that Gelfand's approach to teaching and learning will survive for ever.

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