What Frenkel and Ross did not tell us is that the “math” that led to the discovery of the Higgs boson is not their kind of (pure-and-rigorous) math, but the much more effective, and efficient, nonrigorous mathematics practiced by theoretical physicists called quantum field theory. This highly successful (and precise!) mathematical theory would not be considered mathematics by most members of the American Mathematical Society, since it is completely nonrigorous.I would not phrase it that way. I agree that the nonrigorous math is not really math, and that this is a dividing issue between mathematicians and physicists. Most physicists are sloppy in their math and do not really appreciate mathematical rigor.
But there is a lot of legitimate math behind quantum field theory, even if most physicists ignore it.
He appears to have a legitimate gripe about how the math community devalues computational math.
Proof is the only way to determine mathematical truth, and experiment (or observation) is the only way to determine scientific truth. When you have neither, then you have abominations like string theory.
He doubles down:
Traditional “rigorous proof” is yet another religious dogma, which did some good for a long time (as did the belief in God). Of course, it is not surprising that people can get deeply offended when someone denies the existence of their “God”.The Annals of Mathematics does not prohibit computer-assisted proofs. It published this paper of mine. It was a rigorous proof, not a heuristic or experiment.
But the God of (alleged!) rigorous proof is dead (well, not yet, but it should be!), and we should allow diversity. Rigorous proofs should still be tolerated, but they should lose their dominance, and the Annals of Mathematics should mostly accept articles with mathematics that has only semi-rigorous or non-rigorous proofs (of course, aided by our much more powerful and superior silicon brethren), because this way the horizon of mathematical knowledge (and mathematical insight!), broadly defined, would grow exponentially wider.
Yes, rigorous has been the standard for a long time. Ever since Euclid's Elements in 300 BC.
His web site has many opinions, starting with this:
First Published (in Hebrew): ... The history of science supplied us with many examples of true "geniuses" that were kicked out of high school because of poor achievements, and one of the most prominent examples is the greatest scientist of our time, the physicist Albert Einstein. But Einstein was the greatest scientist of all times, and hence he managed somehow to find his way in life (but it wasn't easy, even for him).No, Einstein was not kicked out of school or anything like that. He had very good grades and progressed thru a fairly rigid system to get a doctoral degree in physics.
Einstein did not succeed in doing any rigorous math. I am not sure he ever proved anything. Relativity is very mathematical, and he needed mathematicians Poincare and Minkowski to figure out the special theory, and Grossmann and Hilbert for the general theory.
For an example of math that seems sloppy but can actually be made rigorous, see
this NY Times account of how the natural numbers sum to -1/12. Or read Terry Tao's rigorous explanation or others.