Thursday, September 07, 2006

Mathematics vs. Talmud

Grigory Perelman, the man who solved one of the seven most difficult mathematics problems in the world, is such an other-worldly character that he actually refused the Field Prize, which in the eyes of many, is even more prestigious than the Nobel Prize. Dr. Perelman, 40, has declined previous mathematical prizes and has spurned offers from Princeton, Stanford and other universities.

Dr Perelman resigned from his academic position, perhaps because of anti Semitism. He lives with his mother. Apparently he does not want to emigrate. Even more remarkable is the fact that he has shown no interest in pursuing the $1 million that the Clay Mathematics Institute is offering to anyone who solves the Poincare conjecture. All that would be required is for him to publish his results in a recognized journal, and show up at an award ceremony. Having finally solved the problem after more than 10 years' work, he posted his conclusion on the internet, rather than publishing his explanation in a recognized journal. "If anybody is interested in my way of solving the problem, it's all there - let them go and read about it," said Dr Perelman. "I have published all my calculations. This is what I can offer the public." Interviewed in St Petersburg last week, Dr Perelman insisted that he was unworthy of all the attention, and was uninterested in his windfall. "I do not think anything that I say can be of the slightest public interest," he said. "I am not saying that because I value my privacy or that I am doing anything I want to hide. I just believe the public has no interest in me.” He continued: "I know that self-promotion happens a lot and if people want to do that, good luck to them, but I do not regard it as a positive thing.”

I am convinced that, although he lives IN this world, he really is not OF this world, but resides in some higher realm where us mortals cannot enter. I don’t think such an idea is particularly mystical. If one takes a Platonist line on the reality of mathematics, there is no reason why such a transcendental world must be equally available to everyone. Maybe great mathematicians are like idiot savants that can calculate calendars into perpetuity or factor the primes of very large numbers in their heads.

There has been a long discussion over at DovBear on the relative merits of advanced Talmudic study and Mathematics. The issue became confused right from the start because it was conflated with a second and independent question whether Torah study has any practical value. So after endless comments, the Philistine question “What do you do with Torah?” is still raging. My response to that question is Torah study need not have any practical value. No different than art for arts sake, or pure mathematics for mathematics sake. The purpose of Torah is more Torah. Jews are Torah’s way of creating more Torah.

The more interesting question is how does one compare the greatness of a Perelman with the greatness of accomplished Talmudic scholars? The consensus of the DovBear crowd seems to be that the scholars are clearly inferior. I both agree and disagree. My view is that mathematics at the level of Perelman is much more difficult than any individual problem in Talmud. Most, if not all Talmud scholars, would fail to get anywhere close to the mathematical depth required to solve such world class problems. Talmud people would like to believe that if they turned their full attention to the arts and sciences they would be enormously successful. The view is a conceit based on ignorance and narcissism.

There are different kinds of intellectual power. Talmud requires an enormous scope over a large literature; it requires certain strength of character, and a different kind of creativity. I would say not only Talmudists but almost every great philosopher would not get close to solving Poincare’s conjecture. But who was greater, Plato, Kant, Nietzsche to name just three or Perelman, Wiles (of Fermat’s Last Theorem fame), etc? In my mind, Plato and the other great philosophers are far greater in intellectual creativity than any mathematician, even though they are incapable of doing what mathematicians do. In the same way, great Talmudist /Rabbis are just greater people all around; they are humanly deeper and have a more comprehensive vision. They frequently are first rate politicians and leaders.


At 9:00 AM, Anonymous Some Guy said...

I wonder what his mother said when he declined to pursue the $1 million prize. "You good-for-nothing loafer, you ..."

At 3:10 PM, Blogger Baalabus said...

Agree with everything except:

... Torah study need not have any practical value.

The consensus even amoung litvaks is that minimally, Torah study ought to provide knowledge about how to do the mitzvoth. But yes, someone who has that level of knowledge ought to study even those unpractable portions of Torah, similarly, as you say that one might study art for art's sake. I doubt you'll disagree with my stipulation to your blanket statement.

In the same way, great Talmudist /Rabbis are just greater people all around; they are humanly deeper and have a more comprehensive vision. They frequently are first rate politicians and leaders.

Let's not conflate Talmudists with rabbinical leaders. The latter, yes, are first-rate politicians. Some the greatest Talmudists were skirted aside from or plainly unfit for leadership positions, e.g. R. Hayyim Heller; some leaders were weak Talmudists, e.g. ..., well, I'd better not say. The point is sometimes the greatest of Talmudists are not good politicians or leaders at all. I'd say this happens more often then people commonly believe.


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