知乎上的张学军对陶哲轩(tao)不太看好

知乎上有个张学军,介绍里有“复旦大学”,“数学”,“高等教育”。然后他的回答大多将如何纯数学在走向衰落,因为重要的有价值的东西已经做得差不多了,现在的菲尔兹奖是一届不如一届,一代不如一代,劝年轻人退出。他对陶哲轩不太看好,并为此写了几个回答。

我今天工作(做我的disqussearch.com的事情)加写作已经累了,所以就不写太多了。就把几个关于tao的回答复制到这上面吧。

陶哲轩的太太外貌一般,其实不难理解。按美国人的刻板印象,陶哲轩是典型的东亚男性:数学天才、书呆子、老好人、不擅与异性交往。这种样子怎么能找到很漂亮的女人?像陶那样,找一个崇拜自己的女学生,不失为解决终身大事的好办法。

陶哲轩和杨振宁不能比。杨振宁那一辈搞学术的,很多出身大户人家,见过大世面,风流倜傥,吟诗作画,追女人是小case。而陶出身医生、老师家庭,很大概率是nerd。

老婆外貌一般也就罢了,还是韩国人。美国华裔那么多,为什么不找个华裔?

陶不仅讨个韩国老婆,还不会中文,这就彻底断了自己和中国在文化上的联系。虽然陶的父亲解释过,为什么陶没有学中文,但是那个理由听上去非常牵强。

在印象中,陶只来过中国大陆一次,还是参加与数学竞赛有关的活动,与学术无关。

种种迹象表明,陶对中国不大友好,有成见。很可能像很多华裔小孩那样,对自己的中国血统困惑、嫌弃。

陶哲轩的父亲,解放前从上海逃往香港,想必在思想上反g恐g。后来可能又觉得香港随时会被“解放”,又前往澳大利亚,离中国越远越好。陶哲轩出生在这样的家庭,他的一些行为就不难理解了。

算了,不叫他陶哲轩了,以后还是叫他Tao。因为他实在是愧为华裔。

作者:张学军
链接:https://www.zhihu.com/question/271890712/answer/368024252
来源:知乎
著作权归作者所有。商业转载请联系作者获得授权,非商业转载请注明出处。

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A revisit of the chosen people (the Jews)

From almost two years ago: https://gmachine1729.com/2017/07/13/the-chosen-people/.

After I sent this to a physicist, he responded:

I scanned that article a long time ago to see who you are
it is out of date just like my vixra article, because after UNZ showing that jewish achievement is way down now, there is no longer any question that the main reason is jewish people favoring other jews and lying and hyping all the time. you see it in academia all the time – and whites as well as asians slurp it up hook line and sinker. sad

This physicist is also quite obsessed with psychometrics and hypothesizes that verbal IQ is associated with self-deception, which also, according to him, is inversely correlated with autism/Aspergers. Sounds roughly right to me.

I wrote in response to his message above

I would bet JvN’s intelligence was also vastly exaggerated and hyped. Surely he was outlier in intelligence but the eidetic memory stuff and multiplying six digit numbers easily in his head stuff I now have hard time believing.

Genius tends to be exaggerated in biographies. That stuff doesn’t help for teaching young people. Much of the stuff in popular math and science books including of mathematicians and scientists is actually kind of a negative for actually learning the math and science.

The way to excel in anything is not to sensationalize it but to realize the simple and systematic ways and thought processes behind it. Once they are grasped there is nothing much more to it and they are straightforward. But you know many scientists for grants and misleading young people won’t do that and I would bet that Jews do more in that direction. I think Asians are probably the least in this regard though there are exceptions like Michio Kaku so they come across as uncharismatic/uncool. It’s uncool to say that there is actually a surplus of scientists (and engineers too in many fields) though it should be obvious if one examines closely. Jews are good at and inclined to hype and exaggerate especially in Anglo context.

His response:

yeah – the jews hype their jews that way – einstein was not all that clever either – he was not the one who first and best understood relativity, nor did he grasp quantum mechanics. the jews still today try to falsify the record on that – see the attachement – (did I send it to you – I just have it on this desktop for some reason)

That attachment I have uploaded to https://gmachine1729.com/wp-content/uploads/2019/03/Winterberg0715.pdf.

I had also written to him:

I think it’s still pretty high at the highest level especially in academic research. They do have the advantages of access to older generation. But in terms of test scores and contest results and maybe grades too they’ve surely declined. But they can always say those don’t matter as much as research/work.

But yeah the Jewish social science people they need to go.

Relatedly, http://kskedlaya.org/putnam-archive/putnam2018results.html came out lately. While the problems do not involve any deep mathematics, they do require some cleverness to solve, and to be able to solve them under the 6 hour time constraint is even more impressive,. There are a total of 12 problem each worth 10 points. To place top 5 required 100, top 15 87, top 25 79, top 100 56, top 500 23, according to https://kskedlaya.org/putnam-archive/putnam2018stats.html. And there’s no subjective component. So it does say something Continue reading “A revisit of the chosen people (the Jews)”

不知为何,突然想起测度论里的不可测度的维塔利集合

复制以我写的知乎文章

我在知乎上写的目前竟是一些有关于美国华人和ABC和犹太人的政治话题,自己快成了民族活动家了,其实对于学理工科的人而言,民族活动家比较贬义。民族活动家似的言论与活动,尤其在美国,其实是自然被有能力的人所藐视的,这原则很简单,它根本就是不“专业”的表现,甚至可以说是一种流氓耍诬赖的作为。在美国,中国人政治上都是特别老实的,从来不闹事儿,不抗议,就服从性的低调的埋头苦干。相反,我看到过一位根本不黑但有黑人血统的数学研究生,他的数学水平其实很差的,与其他人相比,可是他却公开的支持Black Lives Matter,然后学校媒体却非常支持他,以他宣传自己的diversity,公布的视频里还有他说I didn’t have to think about race。有意思的是他根本不黑,要他不说,其实都看不出来他是黑人。所预料,这些在学校没人敢说的,说了都怕给自己惹麻烦,其实好多人都为此感到不满,但不得不不了了之,最终政治赢者是谁就毫无疑问了。

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A revisit of the drama behind the Poincaré

I recall back in 2008, when I first cared enough to learn about mathematicians, I read a fair bit of the media articles on the proof of the Poincaré conjecture. At that time, I was clueless about math, and these mathematicians seemed to me like these otherworldly geniuses. I do remember thinking once to myself that maybe it would be kind of cool to part of that world. Except at that time, I was way too dumb, and maybe I still am. However, now I actually have some idea of what math research is about, unlike back then, when my conception of math and mathematicians was more of a naive popular one.

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Luboš Motl, and some thoughts on monopolies

I had the pleasure of reading some blog posts of Luboš Motl on present day academia. I first learned of him when I was a clueless undergrad. He seemed like this insanely smart theoretical physicist. Of course back then I was dumb and in awe of everything, so what else could I think? I know that he pissed off so many people that he was forced from resign from his tenure track position at Harvard physics in string theory. His academic work I am of course nowhere close to qualified to comment on, but people have said it’s first rate, and I’ll take their word. I even thought the guy was crazy. My very smart friend, in some online interaction with him, was scoffed off with: “You don’t understand vectors!” That guy later characterized the hypothetical combination of Luboš and this other guy I know, a PhD student in string theory, who is quite academically elitist and also so in terms of expecting good values and a fair degree of cultural/historical knowledge, as “a match made in heaven.” I also recall a commenter on Steve Hsu’s blog remark that Luboš has Aspergers syndrome or something like that. Anyhow, this time when reading the blog of Luboš, I no longer felt a sense of awe but rather a strong sense of clarity and reasonability in his thinking. He can be quite abrasive in some other contexts maybe, such as in his campaign against the climate change advocates (oh, on that I recently learned Freeman Dyson is also on the same side as Luboš on this one), but I believe it arises purely out of positive intentions on his part for the future of humanity, which many view as on a course of decline.

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Understanding Human History

I had the pleasure to read parts of Understanding Human History: An Analysis Including the Effects of Geography and Differential Evolution by Michael H. Hart. He has astrophysics PhD from Princeton, which implies that he is a serious intellectual, though it doesn’t seem like he was quite so brilliant that he could do good research in theoretical physics, though an unofficial source says he worked at NASA and was a physics professor at Trinity University who picked up a law degree along the way. I would estimate that intellectually, he is Steve Hsu level, perhaps a little below, though surely in the high verbal popularization aspect, he is more prolific, as evidenced by that book, among many others, such as one on the 100 most influential historical figures. He is active in white separatist causes (heh) and appears to have had ties with the infamous and now deceased Rushton.

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My awesome roommate

I recently met this cool guy because we live in the same place. Though he’s not that nerdy (by that, I mean super mathy), we still share many common interests. For instance, he expressed interest when I told him a bit about 艾思奇(Ai Siqi). Additionally, he told me about his appreciation for André Weil and Simone Weil, particularly her mysticism, which I found quite pleasing as I was reading about them not long ago. He also told me about this guy who is trying to understand Mochizuki’s “proof” of the abc conjecture despite being not long out of undergrad, who has plenty of other quirks and eccentric behaviors. Like, that guy joined some Marxist collective, and goes on drunken rants at 3 am, and is in general “aspie af,” something that he described me as too when messaging that guy himself. There is also, “he would literally kill himself if he had to do a tech job.” (laughter) That guy’s dad happens to be a (tenured) math professor from mainland China, more evidence that madness runs in families. Continue reading “My awesome roommate”

Oleg

Oleg is one of my ubermensch Soviet (and also part Jewish) friends. He has placed at (or at least near) the top on the most elite of math contests. He is now a math PhD student with an advisor even crazier than he is, who he says sometimes makes him feel bad, because he has done too little math research wise. However, this persona alone is not that rare. Oleg’s sheer impressiveness largely stems from that on top of this, he is a terrific athlete, extremely buff and coordinated, enough that he can do handstand pushups, to the extent that he regards such as routine. Yes, it is routine for a guy contending for a spot on a legit gymnastics team, but you wouldn’t expect this from a math nerd huh?

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Innate mathematical ability

This morning I had the great pleasure of reading an article on LessWrong on innate ability by Jonah Sinick. Jonah has been one of my greatest influences and inspirations, having interacted with him substantially. He is unusual in one of the best ways possible. I would not be surprised if he goes on to do something extraordinary.

When I catch up with Jonah, I like to talk with him about math, mathematicians, and IQ, which happens to be what that article of his on LessWrong is about. 😉 That article resonates with me deeply because I myself had similar experiences as he did. It is hypothesized by me that I was also twice exceptional, albeit in different ways, with its effects compounded by my unusual background, all of which mediocrities within the American public school system are not good at dealing with in an effectual way.

This writing of Jonah has brought forth reflections in my own mind with regard to mathematical ability, development, and style. I’ll say that as a little kid under 6, I was very good at arithmetic and even engaged in it obsessively. However, by age 8, after two years of adjusting to life in America starting off not knowing a word of English, I had forgotten most of that. I was known to be good at math among the normal normal students; of course, that doesn’t mean much. In grade school, I was not terribly interested in math or anything academic; I was more interested in playing and watching sports, particularly basketball and baseball.

I didn’t have any mathematical enrichment outside of school other than this silly after school math olympiad program. Nonetheless, I managed to test into two year accelerated math once I reached junior high, not that it means anything. In junior high, we were doing this stupid “core math” with graphing calculators and “experiments.” I didn’t realize that I was actually a joke at math until I failed miserably at the state mathcounts contest, having not prepared for it, unlike all those other tiger mommed Asian kids, who to me seemed way beyond me at that time. It only occurred to me that I might have some real talent for math when I made the AIME in 10th grade, taking the AMCs for the first time, being one of four in my high school of about 2000 to do so. I thought it was fun solving some of those math contest problems, which were more g-loaded, with an emphasis on the pattern recognition side.

It was after that I started to read up on the history of mathematics and mathematicians. I taught myself some calculus and was fascinated by it, not that I understood it very well. But I could easily sense that this was much more significant than many of those contrived contest problems, and soon, I began to lose interest in the contest stuff. It was also after that that I learned about proving things, which the American public school math doesn’t teach. I finally realized what mathematics is really about.

Like Jonah, I had some difficulties with careless errors and mental organization. I don’t think my raw intellectual horsepower was very high back in high school, but fortunately, it has improved substantially since then that it is for the most part no longer the major impediment.

I took calculus officially in 11th grade, and it was a breeze for me. I could easily compute the areas and volumes and such but the entire time, I felt quite dissatisfied, because I could not actually understand that stuff at a rigorous, theoretical level as I poured through our textbook that went up to vector calculus during lecture, which was rather inane, expected if one considers the mismatch between cognitive threshold relative to the distribution of ability of the students. I knew from reading online the rich world of math far beyond what we were covering, most of which I was not intellectually mature enough to access at that time. However, I vividly remember during summer after 11th grade, while attending a math summer program, I was able to comfortably write out the delta epsilon definition of limit with understanding of why it was reasonably defined that way. Still, I would say I was still quite weak in terms of both my mathematical maturity and overall intellectual ability. There were too many things I wasn’t aware of, including the g factor, that I easily would have been had I been higher in verbal ability, which would have enabled me to read, absorb, and internalize information much more rapidly and broadly. In contrast, Jonah had discovered independently, or so he says, the lack of free will at the age of 7!

I made some incremental advances in my math knowledge from reading and thinking outside of school the next year. As for contest math, I almost made the USAMO. Though I had improved, I was still not terribly quick and careful with solving contest style problems and doing computations. I think close to graduation, I also solved some Putnam problems.

Only in undergrad did I learn real math more seriously, but even there, nothing too advanced. US undergrad is a joke, and I also was one, just to a lesser extent than most of my “peers.” Almost certainly, Jonah, based on he’s told me, had gained much deeper and broader knowledge at the same stage, from the reading works of giants like Euler and Riemann.

I’ve noticed how there are a lot of Chinese-(American) kids really into those high school math contests, and they now also dominate USAMO and Putnam (though careful, as in the latter, there you’ve got some of Chinese internationals drawn from the elite from China). I will say that at the lower levels, many of those kids have some pretty low taste and an inability to think outside the system that would enable them to discover the existence of real math, as opposed to this artificial math game that they enjoy playing or are pressured to doing so for college. Though those contests have a high pattern recognition component to them, there is not really much depth or substantial math knowledge. It is also my belief, with reference to Jonah’s article, that math contests are mostly M loaded while real math is more V loaded. So this behavior is consistent with the lopsidedness in favor of M and perhaps also short term working memory of Chinese students. It has also been Jonah’s belief that controlling for g, these contests select for low taste and value judgement, and I surely identify with that perspective. So maybe college admissions are somewhat fair to assess an Asian penalty?

Of the thesis of Jonah’s article, a representative figure is Terry Tao. There, Jonah also pointed out that Tao’s research in math is more concrete and problem solving oriented by pure math standards, in line with what appears to be the same lopsided (modulo the absolute level, as Terry is a far far outlier) cognitive profile of his based on testing at age 9 and 10. Again, people enjoy what they are best at, and though, Terry Tao is almost certainly at least +3 sigma at verbal, he is far more rare, at least +5 sigma, a real übermensch, in the (in some sense dual) pattern recognition component, which means he leans towards the areas of math more loaded on the latter. I have heard the saying that even other Fields medalists are intimidated by Terry Tao. The breadth and volume and technical power of his work is almost unrivaled and otherworldly. The media makes it seem like Terry is a league above even the other Fields medalists. However, Jonah seems to believe that the deepest and most leading of mathematicians are the ones who are more theory builders, who create through leaps of insight and synthesis new fields and directions that keep mathematicians busy for decades, and even centuries. That would be say Grothendieck or SS Chern, and an ability that is more loaded on verbal ability, crudely speaking. Again, I have felt the same. This might explain why the advantage of Chinese students is not anywhere near as pronounced in math research as in contests, and why some people say that generally speaking, the Chinese mathematicians are more problem solving and technical than theoretical, more analysis than algebra. Likewise, we can predict the opposite for Jews who are skewed in favor of verbal. A corollary of this would be that the Jews produce the deepest thinkers, adjusted somewhat for population, which is almost certainly the case, if you look at the giants of mathematics and theoretical physics.

I’ll conclude with the following remark. I used to revere somewhat those who placed very highly on those contests, until I realized that many of them are actually somewhat weak in terms of deep understanding and thinking at a more theoretical level. Yes, I have met MOSPers who got destroyed by real math and who are not very intellectually versatile, with glaring weaknesses; I was quite surprised initially that even I seemed to be smarter if not a lot than some of them. Once upon a time, I couldn’t understand those who appeared very strong at real math (and often also science and/or engineering and/or humanities) who struggled with more concrete math and/or contest-style problem solving, like Jonah, who has written on LessWrong of his difficulties with accuracy on the trivial math SAT. I’ve met this other guy, who I thought was an idiot for being unable to perform simple computations, who is leagues beyond me in the most abstract of math, who writes prolifically about partially V-loaded areas of math like model theory. Now, the more metacognitive me has awakened to the reality that I may never by deficit of my neurobiology be able to fathom and experience what they’re capable of. After all, there are plenty I am almost certain are and are essentially doomed to be very delusional by nature relative to me, and since I’m at the far tail but not quite so much, there are bound to be people who view me the same. I can only hope that I can become more like them through some combination of exposure and organic neurobiological growth, but I as a realist will not deem that very likely.

Math sunday

I had a chill day thinking about math today without any pressure whatsoever. First I figured out, calculating inductively, that the order of GL_n(\mathbb{F}_p) is (p^n - 1)(p^n - p)(p^n - p^2)\cdots (p^n - p^{n-1}). You calculate the number of k-tuples of column vectors linear independent and from there derive p^k as the number of vectors that cannot be appended if linear independence is to be preserved. A Sylow p-group of that is the group of upper triangular matrices with ones on the diagonal, which has the order p^{n(n-1)/2} that we want.

I also find the proof of the first Sylow theorem much easier to understand now, the inspiration of it. I had always remembered that the Sylow p-group we are looking for can be the stabilizer subgroup of some set of p^k elements of the group where p^k divides the order of the group. By the pigeonhole principle, there can be no more than p^k elements in it. The part to prove that kept boggling my mind was the reverse inequality via orbits. It turns out that that can be viewed in a way that makes its logic feel much more natural than it did before, which like many a proof not understood, seems to spring out of the blue.

We wish to show that the number of times, letting p^r be the largest pth power dividing n, that the order of some orbit is divided by p is no more than r-k. To do that it suffices to show that the sum of the orders of the orbits, \binom{n}{p^k} is divided by p no more than that many times. To show that is very mechanical. Write out as m\displaystyle\prod_{j = 1}^{p^k-1} \frac{p^k m - j}{p^k - j} and divide out each element of the product on both the numerator and denominator by p to the number of times j divides it. With this, the denominator of the product is not a multiple of p, which means the number of times p divides the sum of the orders of the orbits is the number of times it divides m, which is r-k.

Following this, Brian Bi told me about this problem, starred in Artin, which means it was considered by the author to be difficult, that he was stuck on. To my great surprise, I managed to solve it under half an hour. The problem is:

Let H be a proper subgroup of a finite group G. Prove that the conjugate subgroups of H don’t cover G.

For this, I remembered the relation |G| = |N(H)||Cl(H)|, where Cl(H) denotes the number of conjugate subgroups of H, which is a special case of the orbit-stabilizer theorem, as conjugation is a group action after all. With this, given that |N(H)| \geq |H| and that conjugate subgroups share the identity, the union of them has less than |G| elements.

I remember Jonah Sinick’s once saying that finite group theory is one of the most g-loaded parts of math. I’m not sure what his rationale is for that exactly. I’ll say that I have a taste for finite group theory though I can’t say I’m a freak at it, unlike Aschbacher, but I guess I’m not bad at it either. Sure, it requires some form of pattern recognition and abstraction visualization that is not so loaded on the prior knowledge front. Brian Bi keeps telling me about how hard finite group theory is, relative to the continuous version of group theory, the Lie groups, which I know next to nothing about at present.

Oleg Olegovich, who told me today that he had proved “some generalization of something to semi-simple groups,” but needs a bit more to earn the label of Permanent Head Damage, suggested upon my asking him what he considers as good mathematics that I look into Arnold’s classic on classical mechanics, which was first to come to mind on his response of “stuff that is geometric and springs out of classical mechanics.” I found a PDF of it online and browsed through it but did not feel it was that tasteful, perhaps because I’m been a bit immersed lately in the number theoretic and abstract algebraic side of math that intersects not with physics, though I had before an inclination towards more physicsy math. I thought of possibly learning PDEs and some physics as a byproduct of it, but I’m also worried about lack of focus. Maybe eventually I can do that casually without having to try too hard as I have done lately for number theory. At least, I have not the right combination of brainpower and interest sufficient for that in my current state of mind.

一说起偏微分方程,想到此行有不少杰出的浙江裔学者,最典型的可以说是谷超豪。想起,华盛顿大学一位做非交换代数几何的教授,浙江裔也,的儿子,曾经说起他们回国时谷超豪,复旦的,如他父亲一样,逝世了,又半开玩笑言,“据说谷超豪被选为院士,是因为他曾经当过地下党。”记得看到杨振宁对谷超豪有极高的评价,大大出于谷超豪在杨七十年代访问复旦的促动下解决了一系列有关于杨-米尔斯理论的数学问题。之外,还有林芳华,陈贵强,都是非常有名气的这套数学的教授,也都是浙江人。我们都知道浙江人是中国的犹太人,昨天Brian Bi还在说”there are four times more Zhejiangnese than Jews.” 可惜我不是浙江人,所以成为数学家可能希望不大了。:(