nrqed said:
I apologize if I have insulted people by putting weight on the fact that the claim of a proof had been made by someone who has earned both a Fields medal and an Abel prize.
We need to put weight on the claims of such people in an intellectual community such as academia;
what else are these prizes good for if not to publicize the towering proven intellect of these remarkable individuals? It is no coincidence that although tonnes of people, many of them even extremely skilled experts, work in mathematics and physics today, not just anyone of the experts is or can be regarded as a Newton, a Gauss or a von Neumann. This can be encapsulated in the difference between being capable of inventing calculus in the 1600s by yourself with no clear precedent and merely being able to do calculus, after being spoonfed a rigorous theory of calculus in undergraduate mathematics courses.
Moreover, this doesn't seem to be that well of a known fact among scientists and mathematicians generally (there are notable exceptions), but there is even a striking statistical demonstration (
NB: first discovered empirically in the social sciences (!) and then generalized mathematically) which justifies this argument, namely that for any valuable skill(set) which one can be better at then some other and the results of which are generally valued by others, there exists a distribution such that the most valued results produced by all practitioners of such a skill is disproportionately produced by a small subset of the entire population of practitioners; among that small subpopulation of skilled people the same thing holds again i.e. an even smaller subset in approximately the same proportion is again responsible for the production of the large majority of the most valued results.
What this means in this discussion is that there are some scientific works that are much more read than others, generally indicating their superior perceived value, and a small number of works which practically everyone has read. For those who already do know this, they will recognize immediately that I am speaking about none other than the Zipf-Pareto principle which can be described by a very simple power law and/or further mathematicized into a very special kind of probability distribution; what most people (probably) do not yet know is that there is even an elegant piece of pure mathematics underlying the scale-invariant self-similarity of this ubiquitously occurring distribution, which ties together the mathematics underlying probability theory, modern network theory, fractal geometry and (nonlinear) dynamical systems theory among others, but I digress.
To get back to my point, Sir Michael Atiyah is exactly the towering kind of intellect, that has shaped not just the physics and mathematics of his time but an entire generation of thinkers probably in more ways than they can or indeed do realize; Edward Witten for heaven's sake is directly among the man's mathematical offspring. To even try and compare yourself, let alone put your mind above his, would mean that you are not merely some celebrated expert in a particular field of mathematics such as algebraic geometry, but simultaneously an expert in mathematical physics, having contributed to countless related mathematical fields and having almost 70 years of experience of being an expert and letting all that knowledge and experience shape his thoughts; just try and let that thought sink in for a moment.
Mathematicians like Atiyah are a class apart from pedestrians such as you and me, who are literally runts trying to mimic the gods themselves; although the gods may be fallible, so much more can we be. Not being able to recognize the limits of one's own intellect is a very common fault and feature of those not lucky enough to be counted as part of the pantheon (yet). The only living public figures in science I can even think of who are somewhat properly comparable to Atiyah, and I say this with very much a reserved judgement, are themselves lone stellar intellects, namely Roger Penrose and Gerard 't Hooft; anyone who knows anything about the average scientists' perception of these two distinguished gentlemen will fully understand that it is the shame of our generation, as it is of those before them, that we do not venerate our heroes more during their life.
It is in this respect that especially scientists can still learn an awful lot (both good and bad) from the general public, i.e. ordinary citizens of the world: publically celebrating the birthdays of our living heroes en masse for example wherein we celebrate both their life and work, instead of only suddenly finding the inspiration to publically appreciate their life and work when their death is announced, while in the meantime pushing nonsensical trends such as Pi Day in a hopeless effort to try and connect with the public; a real and honest public display of affection from scientists for their own heroes would do very much for the public appreciation and dissemination of science. To end on a positive note, here is a piece about another mathematical giant, written posthumously by Atiyah:
a tribute to Hermann Weyl. I just hope that others will show the same kind of care and respect for Atiyah, not just after he has gone and left us, but more importantly while he is still with us.
