In a recent blog post discussing a recent Quanta Magazine article on symplectic geometry, I told you that I was rather confident that feminism and lesbian activism has affected the stories, and how they were presented.
This contribution wasn't 100% and in this text, I want to argue that another part of the "identity politics", namely the unpopularity of the Asian mathematicians within a certain clique of Western mathematicians, has been important, too.
First, let me remind you that I am confident that feminism and related politics has influenced the tone of the Quanta Magazine article about symplectic geometry because the author admits that he hasn't interviewed the main heroine, Dr Katrin Wehrheim, but he read an "MIT Women in Mathematics" article about her which was all about the beauty of affirmative action and where Dr Wehrheim also claimed that it is a characteristically female virtue to focus on things that she doesn't understand (in mathematics). So she basically identified her critical attitude to proofs by Dr Fukaya as a feminist, women's contribution to mathematics that men are less capable of making. Kevin Hartnett has demonstrably read that feminist profile and I know too much to have serious doubts that it was a main reason why he decided about the "heroes" and "villains" in the way he did. He shouldn't have taken sides at all because he doesn't understand these technical issues at a sufficiently deep leve.
But Dr Wehrheim and Mr Hartnett aren't the only players in this strange confrontation in the symplectic geometry circles.
A disagreement emerged in the discussion under the Quanta Magazine article. I don't know the true identities of everybody who participated but I know most of them and the wording conveys some information in the remaining cases, too. Everything is compatible with the idea that within mathematics, this tension is basically a conflict between the Asian and "organized Caucasian" mathematicians. The commenter named "a reader" says many interesting things about the mental world of the latter group. I described the second group as "organized Caucasian" mathematicians because I am convinced that most of the best white mathematicians just don't give a damn about the nationality of the colleagues who make important contributions and in this sense, they are not organized.
If true, and I think that it is true, it is unfortunate that this kind of a split has emerged. And I believe that the political interests in the Western, Caucasian circles should be blamed for a big part of this tension. I needed some time to realize the remarkable double standards that the Western journalists as a class have exposed when they were discussing the "not so direct" path towards the completely rigorous and acknowledged proof of two different theorems.
Let's return to 2006. Grigory Perelman's proof of the Poincaré conjecture (all three-dimensional manifolds that look, smell, and quack like three-dimensional spheres are topologically three-dimensional spheres), based on Ricci flows the Hamilton program, was getting its final rigorous form, thanks to some professional hard-working mathematicians around Shing-Tung Yau – who was my "colleague in the adjacent building" at Harvard at that time (and he often came to our building).
The New Yorker published a disgusting article "The Manifold Destiny" which was really a hit piece against Shing-Tung Yau. I wrote about it a few times, e.g. here, and Yau wrote some letters to protest because he was really painted as a criminal of a sort.
Yau didn't deserve such a treatment. He's done lots of remarkable things for mathematics – and also for the organization of mathematics. It means that various brilliant junior people could have become researchers because of his organizational work. Also, in the Perelman case, Yau and everyone around him had a great respect towards Perelman and his profound ideas. None of them expected to share the credit and top medals with Perelman for their technical work. "The Manifold Destiny" was lying about all these things.
Now, years later, the proof of the Arnold conjecture and related ideas in the symplectic geometry was discussed. McDuff and Wehrheim were similarly pointing out something that looked like gaps in Fukaya's proof. There were differences and all of those should be normally counted as Yau's advantages. First, unlike Yau and pals, McDuff and especially Wehrheim were really trying to oversell their dissatisfaction with Fukaya's proof. Second, when the holes were being fixed, most of the work was done by Yau et al. in the case of Perelman's proof, but by Fukaya and OOO in the case of Fukaya's work. McDuff and Wehrheim did write related work as well but I think it's clear that they actually wanted to be celebrated for their complaints themselves.
If there is a difference between the two situations, the difference is that Yau et al. have actually done more useful work than McDuff and Wehrheim – and they did it more modestly, too! Nevertheless, the message of the popular articles, "The Manifold Destiny" and "A Fight to Fix Geometry’s Foundations", respectively, seems to be exactly the opposite. For some reasons, it's always the Caucasian people, especially women, who are the heroes; and it's the Asians who are the villains.
It seems rather obvious to me that this bias does affect the way how these "not so straightforward" advances to mathematics are being developed. I also think that it's clearly the "Western cliques" that should be blamed for these basically racist confrontations. And I claim to know quite something about the way how these pathological political mechanisms work.
The generic jobs in the Western – Caucasian – institutions (and let me say that I do believe that it's much better at the top places) are largely controlled by a more or less political group that suffers from a group think of amazing proportions. I do think that all of them have the same political opinions and the members of this clique apparently believe that they have the monopoly on the truth and the credit in mathematics. When they have the ability to influence things, they hire their friends or people with the same political opinions or those who will help them personally.
It's really exactly the same toxic approach that is sometimes referred to as the "consensus science". These people agree with some colleagues who are effectively members of a political movement and they believe that this agreement between themselves means that they have the right to define the truth about mathematics and about the credits in mathematics globally. It's just not the case and you, the politically organized nominal mathematicians, don't really possess most of mathematics. You know, people like Yau and Fukaya aren't really a part of your clique and that is already a huge subtraction.
I have never shared anything from this racism and people from all racial and cultural backgrounds were always and still are equally good in my view on mathematics and science. It looks unbelievable to me that someone may have all the biases. For decades, I was aware of the fact that Einstein and most other top theoretical physicists were Jewish. I've never thought that they were different or less likable as scientists (or even their results) for that reason. Theoretical physics was "a largely Jewish enterprise" and I have always loved it equally – because I loved it because of the content – and maybe the content was even precious enough for me to be (even) more enthusiastic about the Jews and to ambitiously consider myself a "spiritual honorary Jew". ;-)
In the same way, the European science and mathematics has historically been largely a German, British, French, and to some extent Italian, Danish, and Dutch enterprise. There have been exceptions but this perspective makes it clear which nations have been and mostly still are the true pillars of the modern European civilization. Ethnic Czechs (Brahe was Danish and Kepler was German – their affiliation with the Prague Castle didn't make them Czech, at least not according to the Czechs' conventions) haven't been historically important in physics or theoretical physics and I would always find it totally silly to obfuscate this fact. A 19th century guy at the Charles University was writing rants against James Clerk Maxwell and his theory. He was a complete loser because he was doing totally analogous things to the likes of Woit and Smolin, and it always looked unimaginable that I would be rooting for that man just because he was Czech.
When I learned about the great ideas by Ramanujan or Bose, I realized I loved Indian mathematics and physics. Salam has clearly been a comparably great scientist as other co-fathers of the Standard Model even though he was a Pakistani Muslim. Many colleagues I have had and known in person over the years were doing pretty much the same physics and the same string theory as I did. When you're doing things seriously, you will easily find out that the cutting-edge physics research really does transcend the races, nationalities, and genders. It's mainly some "sociological enterprise" at lower levels – some average professional scientists in each nation etc. – where the nationality and culture seem to play a larger role.
If my education in history were better, I would be much more familiar with the various Persian or Arab mathematicians who have invented some key things in mathematics or astronomy or other fields. I have no doubt that many such people have lived and I do realize that when I only mention some Western counterparts, this way of assigning the credits is only legitimate "regionally" and it is only justifiable because the civilizations were and still partly are separated from each other.
The first modern book about string theory that I read in late 1992 had an article about the Kyoto group string field theory. Over the years, I decided that this work was less important and less correct than I originally thought but there's no doubt that Japanese string theorists were shaping me when I was getting started with string theory and Japan was subjectively punching above its weight. It was always funny to discuss the "Japanese [IKKT] matrix model", a 0+0-dimensional counterpart of the 0+1-dimensional "BFSS matrix model". I mostly tend to think that the Japanese matrix model doesn't work but it could. There are obviously folks in all the civilized nation who can contribute to these top scientific questions pretty much equally.
But there are communities in the West that simply don't have much respect towards this universality of mathematics and science. The glassy-eyed cult – which is how Will Happer of Princeton, a candidate for Trump's science adviser, named the alarmist movement in climatology, is clearly the most shocking example of this politically driven group think. But to a lesser extent, these pathologically political cliques have grown in much more prestigious disciplines of science and mathematics in the West, too.
You know, when someone's references point to a shockingly high percentage of Caucasian authors, or female authors, or even lesbian authors, or if journalists' articles always seem to celebrate those who are more convenient for a political party or a movement, something smells badly. Every top physicist who has worked on a sufficiently wide subject must know that there are important serious people of many nationalities and usually several races and there are even important left-wing as well as right-wing folks, and so on. A top physicist would feel extremely constrained and squeezed if he or she had to restrict himself or herself to European or American physicists etc. – those continents may be rather large but they're still too small for someone who is really doing world-class research.
Some nations in the real world have a much lower probability to do important things in mathematics. So it is indeed unreasonable to believe the first newspaper article that informs you that a Nigerian man has proven the Riemann Hypothesis. But there are still many nations that have about the same chances as your nation, or a bit higher or lower, and the people in these nations belong to several races. Prejudices aren't the assumptions that Nigerian men are less likely to settle the deepest problems in mathematics – because these assumptions are clearly true. Prejudices are similar assumptions directed against nations and other groups of people that have already demonstrably contributed a lot to mathematics and science, e.g. against Japanese and Chinese mathematicians.
In the case of Fukaya, the "auditors" must know that his work is more important than theirs. After all, their "audit" is a derivative work whose very existence depends on Fukaya's original work. The only way how a vitriolic criticism by the "auditors" may turn out to be right is the outcome that Fukaya's mistakes can't really be fixed by local patches, the claims must be changed qualitatively, and one needs to start from scratch. It seems that people agree that this is not what has happened. So the "auditors" did end up to be counterparts of "language editors" who are looking for typos or localized linguistic imperfections that may be fixed independently of the "big picture".
I am confident that a big majority of the really best mathematicians and scientists agrees with me and has no problem to interact with equally good mathematicians and scientists regardless of their nationality or race – and give them the credit they deserve. But there is a layer of less important, less achieved mathematicians and scientists who love to create cliques that want the monopoly on the truth although they have in no way contributed the majority of insights to their discipline of science or mathematics. Such people have tried to defame Yau, Fukaya, and others. Their behavior is analogous and has similar reasons to the behavior of the Aryan Physics in Nazi Germany. Some of the members of that movement were decent scientists but it's still true that most of the truly top scientists didn't belong to that cult. In particular, Werner Heisenberg – despite his being a conservative German patriot compatible with many novelties that the Third Reich brought them – was not an Aryan Physicist at all. He was labeled a "White Jew" by them because he dared to constructively elaborate on theories discovered by the Jews.
Needless to say, Heisenberg was such a great physicist – and basically helpful for the fame of Germany – that even the Nazi regime was totally aware of the fact that it would be painful to spit on him. And at the end, Heisenberg, the "White Jew", did become a key figure of the German scientific establishment during the war while the Aryan Physics movement quickly became irrelevant. In some sense, this outcome suggests that the members of the Aryan Physics movement were more fanatical racists than the Nazi apparatchiks themselves. They hated the people just because they worked on Einstein's ideas – while the Chancellor and people close to him didn't really have a problem with that.
There are some aspects in people's behavior that make me believe that someone is similarly trying to politicize mathematics and science as the Aryan Physics movement did. Dr Chris Wendl started our confrontation in the Quanta Magazine by pointing out that he had tenure in Berlin. Good for him but what is it supposed to prove? After all, Fukaya also has tenure (while the author of the Quanta Magazine hasn't ever worked as a researcher) and neither of the two tenures is an argument. But people like Wendl do think that the political decisions such as someone's tenure or a vote by a committee is what "defines the truth and assigns the credit" and because they care about their power and credit a lot, they simply get politically involved. The unequal, hostile treatment of Asian mathematicians is among the first things that all these people easily agree about. It's sad.
The world of genuine mathematics and science is much grander than the petty world of these people's consensus, committees, and tenures they collectively assign to each other. If they're not willing to fairly look beyond the boundaries of their "community in consensus", it means that they are simply not world-class researchers.