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it is out of date just like my vixra article, because after UNZ showing that jewish achievement is way down now, there is no longer any question that the main reason is jewish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.

The people at the top 25 are almost all East Asian with a few whites (whose names don’t seem to be Jewish) and Indians, and almost half (if not more) of the ones on the honorable mention list are East Asian as well. Upon seeing this, my reaction is that the ethnic Chinese students are really bastardizing contest math now, turning it into ping pong.

My white friend who placed at least honorable mention on this contest multiple times once surprised me by saying “to be honest, intellectually, it’s East Asians > Jews > whites.” Before he said that, this was actually somewhat unthinkable to me. But we have more evidence that that he might be right.

Let’s see the Jewish geniuses with ton of hype in the media that I can immediately think of: Einstein, Feynman, von Neumann, Erdos. No doubt that these people were real geniuses but it’s fair to say what we’ve heard of them in the English media is exaggerated or at least disproportionate. That physicist similarly has said that Stephen Hawking is Stephen Hawking mostly because of his disability, and I would be much inclined to believe that.

I was talking today with someone a bit about AI, saying how that’s also overhyped, with a ton of bullshit propaganda. And on that, I could immediately think of Ray Kurzweil and Marvin Minsky.

The Jews were certainly quite dominant in science in the US from WWII on. There was a golden era of science during the Cold War, especially in theoretical physics, that many Jews shined in in both America and the Soviet Union. There weren’t very many East Asians in America during that period but there were some top Chinese who came to US before founding of PRC or afterwards from Taiwan/Hong Kong who did breakthrough work. Like Chen Ning Yang, Tsung-Dao Lee (1957 Nobel laureates in theoretical physics) and Shiing-shen Chern (Wolf Prize winner, revolutionized differential geometry). There was also Qian Xuesen who was high up enough to be a professor at Caltech and tasked with getting information on Nazi rocket technology from Wernher von Braun after surrender but he returned to China in the 50s.

Nowadays science is so specialized that it’s pretty much impossible to make a fundamental contribution as did the geniuses listed above.

The Japanese certainly achieved much more than Chinese in science during the same period and many if not most of their geniuses did in Japan as opposed to in the West. The name Michio Kaku was mentioned here, but almost certainly he’s not a genius by achievement though he was also born later. Many more people have heard of Michio Kaku than of Hideki Yukawa, Sin-Itiro Tomonaga, Yoichiro Nambu, Makoto Kobayashi, Toshihide Maskawa all Japanese Nobel laureates in theoretical physics who made everlasting fundamental contribution to high energy physics (I don’t actually know their work but I place enough faith on Nobel Prize here to make such an assertion).

I wrote that I much dislike hyping of science and of genius. Its not conducive to actual learning. Much of the stuff in popular science books is quite disingenuous and reading them I would say actually has negative value. Chen-Ning Yang has actually publicly said that the high energy physics party is pretty much over (the fruit has been picked and what hasn’t even if it’s picked can’t really be tested). He’s honest enough to oppose funding of this supercollider in China that is estimated to cost $100 billion. As far as I know, he’s never said serious bullshit that misleads young people, unlike many scientists after they attain fame for some breakthrough, and I much respect that. I’ve heard from a Chinese physicist that he has also privately expressed disapproval of Jews. I told this to my friend who was a student at top university pretty much run by Jews and his response was pretty much that very few people aren’t at least somewhat averse to Jews but most self-censor.

I also remember a Chinese scientist who knows high energy theory along with chemistry and biology regarding Stephen Wolfram’s behavior as utterly shameful and sad. He basically used his reputation and money to start a company making mathematical software that he pays quantitative PhDs like shit to make because he can and misleads the public into thinking he’s the genius behind it all.

Oh yeah as for (non-Jewish) whites, there are too many geniuses to name, who did more classic work than Jews earlier on in history. Newton, Euler, Lagrange, Galois, Gauss, Riemann, Maxwell, Lorentz, Poincare, etc. So maybe we have reason to be suspicious. Maybe Jews actually stole some scientific glory later on from whites and got away with it.

As for East Asians, nowadays, it’s so much harder to do real breakthrough work in math and theoretical physics as the low hanging fruit’s been picked, so it’s hard to prove anything through that. But there were some truly important results in the 20th century, and the Japanese had the massive advantage of starting earlier than the Chinese did. Tenure at elite university and prizes nowadays still mean stuff even if there isn’t as much scientific value in the work. Contest results might in some sense be a better indicator of raw talent/intelligence given how brutally objective they are. For those, there is the preparation component (though preparation clearly has limits, you do need to be a genius in ability to make it to the top). One could similarly say that genius level scientific achievement has a cultural and access component especially earlier on in history so those are even less purely meritocratic.



Apparently, another one of Ren Zhengfei’s daughters is a computer science undergraduate at Harvard

The detaining of Meng Wanzhou, CFO of Huawei and daughter of its founder Ren Zhengfei, at Canadian airport on behest of the US authorities has made headlines the past several days. On that, I have little to say other than that she is quite attractive and also that the half-closeted nepotism via mother’s surname is both amusing and somewhat gross.

Reading her Wikipedia page, I pulled the following

Ren’s first wife was Meng Jun, the daughter of Meng Dongbo, a former deputy governor of Sichuan Province. They had two children: daughter Meng Wanzhou and son Meng Ping, both of whom took up their mother’s surname.[14] After their divorce, he married Yao Ling, with whom he had another daughter, Annabel Yao, who is 25 years younger than Meng Wanzhou. Annabel is a computer science student at Harvard University who made a high-profile debut at Le Bal des Débutantes in Paris in 2018.[14] Ren married for the third time to Su Wei, who was reportedly his former secretary.[14]

Ren’s eldest daughter, Meng Wanzhou, is deputy chairperson and chief financial officer (CFO) of Huawei.[15]

I’m somewhat surprised and also rather disappointed that Ren Zhengfei sent his other daughter, who also took her mother’s surname (and this is a different mother), to Harvard for undergrad. It reminds of how Xi Jinping’s daughter transferred to Harvard from Zhejiang University after her freshman year. I hate to say it but it’ll be hard to take the PRC elites too seriously when they send their children to elite US schools for undergrad. It is a sign that they still lack independence with a need to associate with global homo Anglo elite institutions. On the Chinese internet, people are questioning what other passports besides the Chinese one is possessed by Meng Wanzhou, and it was revealed somewhere that she had a green card from Canada.

Meng for undergraduate merely attended a good but not great university in China. That was when her father, who started Huawei in his 40s, was still a relative nobody. Remember that in China, aside from regional discrimination, wherein Beijing residents are allocated like 10 times more slots at Beida/Qinghua adjusted for population than residents in the provinces, admissions is based purely on gaokao and automatic admission via top performance on the national math and science olympiads. It’s basically impossible for filthy rich and/or well-connected parents to buy one’s kid’s way into Beida/Qinghua in China. So I guess when the kid of someone super high up in China turns out to be intellectually mediocre, attending an elite US school for undergrad becomes the default, sadly.

Something to note, relatedly, is that 富二代 (second generation rich) is a relatively new phenomenon in China. After all, after the communists took power, the rich people had their assets confiscated (like my amusingly pro-communist ABC friend stuck in the US at least for the near future, his family ended up sharing their four story house/building with a bunch of a poor people), and afterwards, people in high up positions did not make much more than the ordinary worker, with the salary difference, based on what I’ve heard, at most a factor of 10, barring very exceptional cases. It was really only after 1980 when it became possible for one to become extremely rich doing business. Between 1980 and 2010. there was a lot of low hanging fruit in China, economically. Plenty of mediocre people with the right entrepreneurial energy/personality became rich. And by that, the class of second generation rich was born, and it seems now they are forming their own culture, with studying abroad paying ridiculous tuition at US universities common, as well as their parents investing in US real estate. It’s very possible and perhaps likely that the class structure in China will solidify over the next generation, as is already the case in the US. How much so, that remains to be seen.

I’ve had some interactions with 富二代 kids and their parents in the US. Many of them are, predictably, not very smart academically. They are basically on permanent vacation in America. Their career/employment prospects in America are not surely not good for obvious reasons. It doesn’t seem like they’re well treated in school by their white peers in America. Yes, their families are economically well off, but that doesn’t mean they can integrate into American society. Their families are able to invest in real estate in America for now; even so, their existence in the US will be a marginal one much confined to the Chinese community. Many of them do not even know English well and are mostly here to invest in real estate, enjoy some material comfort and fresh air, and also send their kids to school here. In most cases, the father based in China only visits every once in a while. They’re obviously not really wanted in America other than for their money, spent on international tuition and luxury brands and so on.

As the reader can tell, I don’t have a high opinion of those 富二代 who send their kids to America and invest in real estate there. Being in China now, I’m sure I’ll learn more about them, including the process they go through to transfer all that money to the US, and maybe I can even influence them a bit. As one can see from the detention of Meng Wanzhou in Canada, there is little guarantee for them on US soil. Finance/economics tells us there is no such thing as a free lunch. They may feel they are winning now and that their assets in America are safe, but this could very much be a process of 温水煮青蛙 (a frog boiled in warm water), where initially one feels warmth, until one gets burned. They may own real estate in America on paper for now, but that real estate is physically in America, where the Chinese do not really control anything. They have no media power, no legal power, no military power there. It’s totally possible for them to suddenly lose everything. Unlikely, but it can happen and only needs to happen once.

The Meng Wanzhou incident has been in Chinese media tied to the death of Stanford physics professor Shoucheng Zhang at age 55 which happened on the same day. The family statement said that it was due to depression, which we all know is just a euphemism. There has been speculation that it was related to the alleged tanking of his Chinese venture capital firm in Silicon Valley. It’s quite tragic that he took his ambition/careerism too far, assuming that his death was related to his VC activity. Had he just remained purely academic, he would have survived and likely eventually won his Nobel. Needless to say, using the prestige of a rare Stanford tenured professorship in physics to raise a Chinese VC is not really what he should be doing while officially in that position. Stanford probably should be somewhat embarrassed about his case as well, in addition to the recent Elizabeth Holmes case that was magnitudes worse. On this, I also have in mind the cases of Lucas Duplan and Evan Spiegel, both quite shameful.

It is my hope that talented, elite Chinese can focus more on developing their institutions at home instead of wasting so much money and energy associating with and working for elite US institutions for signaling. Doing so only inflates the value of a system hostile to Chinese while at the same time de-valuing Chinese institutions. If Chinese are really serious about this trade war, they should be going out of their way to devalue Harvard and Stanford, to devalue Google and Facebook, not eagerly trying to attend those schools for undergrad for a rather mediocre academic educational experience and making such a big deal about working for those companies, whose programmers are generally no better than ones in a good internet company in China as far as I can tell. If Chinese want other people to respect and value them, then they ought to first have confidence in their own institutions. I say this having been in prestigious US institutions myself, interacted substantially with numerous people from there, and frankly, many of them are not all that great, with some depressingly mediocre or even problematic. Of course, there are also plenty of genuinely brilliant, accomplished people in America in top American institutions. Overall, my point is that it’s clear that America will not judge the Chinese well, so why expend so much trying to associate and fit in with America? Why not instead expend more energy into creating a system where what America thinks simply becomes more or less irrelevant?



周四,我认识的一位同样搞理论凝聚态物理的人微信发给我了张首晟去世的消息,让我感到吃惊。这么牛逼的人,不光有资格得诺贝尔奖的理论物理学家,而且还很有钱,好像他90年代末凭他斯坦福大学教授的关系做了搞虚拟机器(virtual machine)的VMware(其创始人是斯坦福大学计算机系教授)的天使投资,赚了一大笔钱,也得到了为后来做风险投资的资历和关系。一流理论物理学家很少是多么有钱的,美国名校物理教授每年也就15万,最多30万的工资(当然,现在极少数最牛的理论物理学家可以通过什么突破奖发点大财了),而张首晟成为了极其罕见的即大物理学家又大发财的人,一种几乎不存在的令人惊叹不已的人生赢家。可惜他近年做得过度了,最终出现了悲剧。可以说他当初运气太好了,拿到的教职确是斯坦福的,才得到了这种天使投资的机会。反而他要是是什么麻省理工或哈弗的,很难想象到他这么去做。可是,反过来,也可以说最终好事变成了坏事,他的这种运气所迎来的成功引发了他后来自以为是的做一件物理教授不应该做的事情而运气不好彻底倒闭了,英年夭折失去了得诺贝尔奖的机会。




我还记得有一次网上看到了他的一个视频,是在斯坦福大学举行的那种启发美国华裔中学生那种活动,网上可以搜到,那里边他讲了他的一些人生故事和价值观。记得一开始他说起他长大的文革时期中国的气候是不鼓励学习的,然后又说起他父母是工程师,然后家人有好多学过文科的人,自己小时候多么多么善于自己读书学习。然后还开始扯美国建国的人如Benjamin Franklin, John Adams的一些理念,说什么我自己要做一些实用的挣钱的事情,为了我的孩子或孙子能够从事更创造性的如艺术之类的工作。他说同样,我们这一代移民来到美国好多为了留下,为了挣钱,却选择了工程,他属于少数坚持他对理论物理热爱的人,但第二代就比他们有远远更好的条件,应该去追求自己的梦想,最自己喜欢的东西。他说的这些也有一定道理了,当然,他扯美国建国人的时候我有点感到不舒服,我想他是不是觉得自己在美国名校斯坦福举行这种明目张胆的华人利益活动有点不要脸了,他真的觉得中国人应该学习美国建国人那套吗,以白人至上主义和暴力逐出印第安土著人建设一个华人没有什么真正地位的国家吗?他跟那些孩子讲完了之后,在旧金山的中国领事馆的一个代表又开始采访他了。在那一段谈话里,我记得他说中国人在美国都混得不错,大多是在做工程。是,那些科技移民在硅谷都有比较好的工程工作,整一个相当高的工资,不过相当少能成为经理,很少能够创办自己的公司,也没有那么好,在美国依然算相对边缘。还记得他又提到自己的儿子在哈弗上学第一学期在上一门中国近代历史的课,不过都是用英文以美国的眼光讲,同时儿子中文也不错,也读了陈独秀的一些中文文集。我想这活动肯定是那儿的中国领事馆组织的,由于张首晟当时是拿了政府的钱本科时去德国留学的,中国政府的人依然觉得有资格“利用”他一下。





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。


好,说起数学,我想稍微写写关于我对某非常具有纯数学性质又非常基础重要及美妙的一个观念和例子,那就是不可测度集合的体会。我记得曾经把他的英文维基百科页发给某北大物理毕业的人看了,他的反应就是这种鬼东西只有脱离现实的数学家才会在乎。其实测度这个观念大家是有的,即使不喜欢数学的人,长度宽度这些都是对人很直觉的。形式化一些,我们以实数集合模拟,一个实数集合的子集的度量,勒贝格度量(Lebesgue measure)定义为

\mu^*(E) = \inf\{\displaystyle\sum_{k=1}^{\infty} I_k : (I_k)_{n \in \mathbb{N}} \text{as open intervals}, \displaystyle\bigcup_{k=1}^{\infty} I_k \supset E\}

这个其实是勒贝格外测度,是否可勒贝格测度有条件,那就是所有实数子集A 符合

\displaystyle \mu ^{*}(A)=\mu ^{*}(A\cap E)+\mu ^{*}(A\cap E^{c})



  • 测度平移守恒,那就是 \mu(S) = \mu(x+S), \forall x \in \mathbb{R}
  • \{A_k\}_{k \in \mathbb{N}} 互相不交则 \mu(\bigcup_{k=1}^{\infty} A_k) = \sum_{k=1}^{\infty} \mu(A_k)
  • S \subset T\mu(S) \leq \mu(T)


以前两点,我们发觉任何可以表示为可数无限多个平移同等的不交集的测度比为 0\infty ,因为所有不交集测度一样所以总测度必然是无限个零或无限个有限数。

我们先取商加法群 \mathbb{R} / \mathbb{Q} ,并以选择公理在其所有同价类选在 [0,1] 范围内的一个元素构建一个集合,称之 V 。我们在以每一个 \mathbb{Q} \cap [-1,1] 的元素将 V 平移,这些平移互相不交叉,其并集又包含 [0,1] (也就是我们选择不大不小 [-1,1] ),但 [-1,2] 之内,所以以第三点,他的测度又在 13 之间。所以他若可测度就矛盾了。




What’s wrong with the Ivy League

Very recently, a Chinese-American Yale undergrad cold emailed me expressing approval of this blog, and we not long after began to talk regularly.

A few days ago, in an email to Steve Hsu, me, and some others, he wrote:

I think the Ivy League is best understood as a giant money-making organism. Attached to it like a leech is a seminary for training priests and spreading the gospel of the American progressive religion. Attached to that leech is an even smaller leech which actually contains smart people doing good technical work. And gmachine1729 is right that the average Ivy student is not that great (but the top end does represent the best of the best).

Relatedly, I just saw an essay on Zhihu in Chinese by Yale finance professor Zhiwu Chen on the matter of 中国人那么优秀,为什么美国人还是更喜欢印度人?(Chinese are so exceptional, why do Americans still like Indians more). The essay was one of Chinese are smart and hardworking but modest, passive, conformist, filially pious per the Confucian tradition and emphasize hard skills at the expense of soft skills, while Indians, like Americans, are assertive and confident with strong leadership qualities. The comments, of which there were 27, were mostly dismissive. The first one, and the most memorable one was


In translation,

Can’t you better understand the situation by comparing Chairman Mao with Gandhi?

I’m very happy to see this. It means that Chinese are no longer dazed by Ivy League credentials. They are beginning to think more independently, to have more confidence in themselves. Maybe in another decade’s time, non-STEM professor at Ivy will become an explicit negative signal among Chinese in China.

On credentialism and selection systems

I’ve mentioned before that an Asian-American friend of mine, who is quite smart, disapproves of the whole campaign against Asian quotas spearheaded, or at least advocated, by Steve Hsu and others.

His words are the following:

  1. I don’t believe in legitimizing the credentialist culture of modern academia
  2. I don’t generically feel much kinship with Asian-Americans (who are the most affected by purported discrimination in admissions), even if I might feel more kinship with them on average than I would with any other large ethnic group in America (which is itself not necessarily true)
  3. I don’t find it implausible that there are legitimate reasons to discriminate against Asian-Americans in the admissions process, if by ‘discriminate’ we mean ‘weigh their formal accomplishments less than one would for a member of a different race’
  4. At the end of the line, I believe that persistent whining about this is a reflection of emotional immaturity on the part of Steve et al., in that they seem to have a ‘chip on their shoulder’ which they are incapable of overcoming, and if they were actually taking a principled approach, they would come together and try to create a superior alternative to the radically broken university system, which will likely not be saved by any infusion of Asian students

Here’s what I think.

On 1), I don’t like the credentialism culture of modern academia either. Much of it is a superficial and soulless arms race. Not that grades, test scores, publications, citations, impact factor aren’t strong signals but they are prone to manipulation and artificial inflation, and that there are qualities of work not well-captured by those metrics. People are more or less compelled to single-mindedly play this game, often at the expense of actually substantial scholarship, if they are to survive in academia nowadays.

On 2), I hate to say that this country has become more toxically consumed by identity politics over the years, not to mention that people are judged at least subconsciously by who one is associated with. So collective bargaining is crucial for a group’s position on the status hierarchy.

On 3), there is that due to Asian-Americans’ and Asians in general having traditionally been the underdog, as well as their lack of media presence, which is intimately tied to the alienness of their names in the Western linguistic context, some people are inclined to view Asians are grinds who aren’t actually as capable as they might appear on paper. Especially with the whole tiger mother phenomenon that Amy Chua popularized with her infamous book. Of course, China’s rise over the recent years has altered this perception somewhat, especially the one that Asians are smart but not creative, though surely, it does seem that controlling for grades and test scores, or IQ, Asians do seem less creative, though that may be due to environmental factors, such as de facto or implicit quotas imposed by diversity mandates and economic circumstances.

On 4), I mostly disagree. Asian-Americans don’t really have the power to create a sufficiently credible alternative in a world that runs so heavily on associating with prestigious, usually long-established, institutions like Harvard and Goldman-Sachs. In their ancestral countries, China and India, Asians can improve the university and research system and the economic and technological competitiveness of the country as a whole, so as to make their universities more credible as well. In America, all Asian-Americans can really do is make more noise around the issue to exert more pressure on the elite universities, and also donate more and enhance their media and political presence as their socioeconomic position improves, especially at the elite end, improves, so that the elite universities perceive themselves as having more to lose from discriminating against Asian-Americans based on race.

This is all I have to say as pertains exclusively to Asian-Americans. I shall now give my thoughts on credentialism and selection in general.

The job of admissions and hiring committees and HR is astronomically harder than in the pre-internet age. So many people apply for positions they are grossly under-qualified for, now that it’s so easy to shoot off a resume or application online. There are, of course, application fees for college and grad schools, but they are not enough to deter. This means in the selection process can be afford now significantly less time per candidate, and one can argue that as a consequence, the process becomes more bureaucratic and easier to game. Often, people will in the pre-screening stage eliminate all applicants who do not meet certain formal criteria, such as minimum GPA/test scores or a certain degree from a certain set of sufficiently credible universities. In the case of academia, to my limited second-hand knowledge, committees will look at publications lists with a focus on citation count and impact factor of the journals on which the papers were published and also verify the candidate against senior, tenured faculty in the same or at least similar area of research. In the case of industry jobs, what matters more is the interview, where for technical roles, technical questions will be asked to further test the technical aptitude and knowledge, as well as, the softer aspects of communication and personal chemistry. For non-technicals, I can only say it’s even more about credentials (school, companies, job titles, dates of employment) and how you present yourself. I can only conclude that way more energy is expended now in aggregate on application and selection than before, which is quite costly really. In the career world, people are mostly out for themselves and don’t really care about wasting other people’s time, so long as they can get away with it with impunity more or less.

I’ll say that there is a tradeoff between optimizing for one’s formal credentials and optimizing for one’s actual ability and knowledge. One loses out so much more now if one neglects the former too much due to more competition per position. Surely, there has been gross inflation of credentials. This is in its crudest form epitomized by college’s having become the new high school, thereby rendering prestige of institution a stronger signal. Furthermore, the largely consequent grade inflation and watering down of coursework has added more noise to school transcripts. Contest training, for math in particular, has become so much more popularized, that to not have credentials in those raises questions in some circles, and moreover, there is so much more of an obstacle course of summer programs and scholarships and grants and internships and jobs which one must pass through to some degree if one wants a reasonable chance of success at a specified level. In this sense, there is more pressure to conform to an existing, often complexity-ridden system. It may well be that people nowadays are not all that much better in terms of knowledge and proficiency than before, correcting for the positive effects of technology on learning, but they actually put in much more time and effort.

Now, if one expends much energy on actual substance, there is concern as to what would be lost if those translate not into formal credentials. Arguably more common is the other way round, where one turns into a soulless credential-chasing machine. I’ve been amazed at how many people manage to achieve much higher grades, test scores, and awards than what their knowledge and ability from interaction with them would reasonably indicate. Those people tend to be very boring and risk-averse, and they are often the types our current system selects for, like it or not.

I used to feel like to prove that one is actually smart, at least in STEM, one ought to do sufficiently well in one of those major math, physics, or computing olympiads or contests. I would say that for raw technical ability, that is probably still the strongest signal. Grades are somewhat noisy, because it’s not hard to copy or snipe homework solutions, and for tests, there is a large cramming and figuring out what’s gonna be on the test component. Perhaps they are more consequentially so as there are also some genuinely capable or even brilliant students who for related personality reasons have a hard time getting themselves to care too much about grades. I’ve personally seen some high GPA people, even in college, who signal in what they say or write complete idiocy that would make you wonder if they were pretending stupid, especially if said person were female. Some people learn much more deeply and also much more broadly, outside of what the system teaches them, to a high level of retention, much of which is not captured through any formal credential. From my personal experience, tests of a wide range of knowledge, sufficiently substantial but not too esoteric, are stronger signals since they cannot be crammed for, but they are, for the difficulty of organization, seldom administered.

In the real world and in academia though, what matters is the ability to deliver actual projects and conduct meaningful research, and those, while correlated with ability to learn, are not quite the same. Those are also way more context-dependent, which means more noise, both due to more variance and more ambiguity of judgment.

I will say that at times or even often, society is met with the problem of people finagling themselves into a position to judge what they are not really qualified to, per their ability and expertise, which means some resume-padding bozos rising up and actual competents being passed over. This problem I believe has been accentuated by the ever more credentialist culture that has emerged over the recent years. What’s kind of sad is how the more conformism and risk-aversion rises, the more these traits are pressured and selected for.

I’ve come to notice that there tends to be some difference between maverick genius and the conformist first-rate professional. If one looks at history, real genius, the ones who create paradigm shifts, tends to have more very lopsided profiles, though surely, it might go too far to say that *most* of the real geniuses were out of it in a Stallman or Galois like fashion, especially as it’s the deranged ones which garner more attention. But one can say with high level of confidence that there were many real geniuses who had a hard time fitting in even into the elite mainstream of his profession, who have even been marginalized. I’ve been told that the real genius mathematicians like Perelman, Langlands, and Shimura more or less cut contact with the mathematical community apparently out of disgust. There is also evidence that plenty would-be real geniuses did not actually make it, with their enormous potential having been thwarted by the system at some point and hardly realized. In an ideal world that optimizes for collective value, if somebody else can do the job much better than you and actually really wants to, you should let him do the job and get out of his way. Of course, reality is far from that. I have personally felt that way with regard to my mathematical ability, often feeling that I wasn’t good enough when I failed to derive something on my own, yet I see so many people worse than I am even so eager to play the whole credentialist game without recognizing how deficient they really are. This suggests that I am very partial towards a certain side of the spectrum. I even feel that in some sense, nothing is more embarrassing then formally being much higher than what one’s ability actually merits, since it demonstrates not only incompetence but poor character. However, I am, regrettably, or not, feeling that circumstances are pressuring me ever more towards the opposite direction.

On grad school, science, academia, and also a problem on Riemann surfaces

I like mathematics a ton and I am not bad at it. In fact, I am probably better than many math graduate students at math, though surely, they will have more knowledge than I do in some respects, or maybe even not that, because frankly, the American undergrad math major curriculum is often rather pathetic, well maybe largely because the students kind of suck. In some sense, you have to be pretty clueless to be majoring in just pure math if you’re not a real outlier at it, enough to have a chance at a serious academic career. Of course, math professors won’t say this. So we have now an excess of people who really shouldn’t be in science (because they much lack the technical power or an at least reasonable scientific taste/discernment, or more often both) adding noise to the job market. On this, Katz in his infamous Don’t Become a Scientist piece writes:

If you are in a position of leadership in science then you should try to persuade the funding agencies to train fewer Ph.D.s. The glut of scientists is entirely the consequence of funding policies (almost all graduate education is paid for by federal grants). The funding agencies are bemoaning the scarcity of young people interested in science when they themselves caused this scarcity by destroying science as a career. They could reverse this situation by matching the number trained to the demand, but they refuse to do so, or even to discuss the problem seriously (for many years the NSF propagated a dishonest prediction of a coming shortage of scientists, and most funding agencies still act as if this were true). The result is that the best young people, who should go into science, sensibly refuse to do so, and the graduate schools are filled with weak American students and with foreigners lured by the American student visa.

Even he believes that now the Americans who go into science are often the ones who are too dumb or clueless to realize that they basically have no future there. I can surely attest to how socially inept, or at least clueless, many math grad students are, as I interact with them much more now. The epidemic described by Katz is accentuated by the fact that professors in science are not encouraging of students who seek a plan B, which everyone should given the way the job market is right now, and even go as far as to create an atmosphere wherein even to express a desire to leave academia is a no-no. I am finding that this type of environment is even corroding my interest in mathematics itself, which is sad. In any case, I sort of disagree with Katz in that I feel like the very top scientific talent of my generation still mostly ends in top or at least good graduate schools, though surely there are many who feel alienated or don’t find the risk worth taking, and end up leaving science. I myself am thinking of forgetting about mathematics altogether. So that I can concentrate my motivation and time and energy on developing expertise in some area of software engineering that is in demand, for the money and (relative) job security, and hopefully also find it a sufficiently fulfilling experience. There are a lot of morons in tech of course, but certain corners of it do provide refuge. I had always thought of mathematics as being a field with a much higher threshold cognitively in its content, enough to filter out most of the uninteresting people, but that’s, to my disappointment, less so than I expected. I do have reason to be scared, because one of the smartest and most interesting people I know took like five years following his math PhD to make his way into full employment, in a programming/data science heavy role of course, despite being arguably much better at programming than most industry software engineers with a computer science degree, which he lacked, an indicator of the perverse extent to which our society now runs on risk-aversion and (artificial) credential signaling. I can only consider myself fortunate that I do have a computer science degree from a reputable place, and with that, I have already made a modest pot of gold, despite being frankly quite mediocre at real computer stuff, which I have had difficulty becoming as interested in as I have been in mathematics. Maybe I was even fortunate to have not been all that gifted in the first place, which in some sense compelled me to be more realistic, as there is arguably nothing worse than becoming an academic loser, which academia is full of nowadays, sadly. This type of thing can happen to real geniuses too. Look at Yitang Zhang for instance, the most prominent case to come to mind. Except he actually made it afterwards, spectacularly and miraculously, with his dogged belief in himself and perseverance under adversity. For every one of him, I would expect like 10 real geniuses (in ability) who were under-nurtured, under-recognized, or even screwed, left to fade into obscurity.

I’ll transition now to a problem that I’ve been asked to solve. Its statement is the following:

Let f be holomorphic on a simply-connected Riemann surface M, and assume that f never vanishes. Then there exists F holomorphic on M such that f = e^F. Show that harmonic functions on M have conjugate harmonic functions.

Every p_0 \in M corresponds to an open connected neighborhood U =  \{p : \lVert F(p) - F(p_0) \rVert < F(p_0)\}. Let \{U_{\alpha}\} be the system consisting of these neighborhoods, (\log F)_{\alpha} a continuous branch of the logarithm of F in U_{\alpha}. From this arises a family F_{\alpha} = \{(\log F)_{\alpha} + 2n\pi i, n \in \mathbb{Z}\}.

In Schlag, there is the following lemma.

Lemma 5.5. Suppose M is a simply-connected Riemann surface and

\{D_{\alpha} \subset M : \alpha \in A\}

is a collection of domains (connected, open). Assume further that these sets form an open cover M = \bigcup_{\alpha \in A} D_{\alpha} such that for each \alpha \in A there is a family F_{\alpha} of analytic functions f : D_{\alpha} \to N, where N is some other Riemann surface, with the following properties: if f \in F_{\alpha} and p \in D_{\alpha} \cap D_{\beta}, then there is some g \in F_{\beta} so that f = g near p. Then given \gamma \in A and some f \in F_{\gamma} there exists an analytic function \psi_{\gamma} : M \to N so that \psi_{\gamma} = f on D_{\gamma}.

Using the families of analytic function F_{\alpha} as given above, it is clear that near p \in D_{\alpha} \cap D_{\beta}, (\log F)_{\alpha} + 2n_{\alpha}\pi i = (\log F)_{\beta} + 2n_{\beta}\pi i when n_{\alpha} = n_{\beta}, which means the hypothesis of Lemma 5.5 is satisfied by the above families.

I’ll present the proof of the above lemma here, to consolidate my own understanding, and also out of its essentiality in the construction of a global holomorphic function matching some function in each family. It does so in generality of course, whereas in the problem we are trying to solve it is on a specific case.

Proof. Let

\mathcal{U} = \{(p, f) | p \in D_{\alpha}, f \in F_{\alpha}, \alpha \in A\} / \sim

where (p, f) \sim (q, g) iff p = q and f = g in a neighborhood of p. Let [p, f] denote the equivalence class of (p, f). As usual, \pi([p, f]) = p. For each f \in F_{\alpha}, let

D'_{\alpha, f} = \{[p, f] | p \in D_{\alpha}\}.

Clearly, \pi : D_{\alpha, f}' \to D_{\alpha} is bijective. We define a topology on \mathcal{U} as follows: \Omega \subset D_{\alpha, f}' is open iff \pi(\Omega) \subset D_{\alpha} is open for each \alpha, f \in F_{\alpha}. This does indeed define open sets in \mathcal{U}: since \pi(D'_{\alpha, f} \cap D'_{\beta, g}) is the union of connected components of D_{\alpha} \cap D_{\beta} by the uniqueness theorem (if it is not empty), it is open in M as needed. With this topology, \mathcal{U} is a Hausdorff space since M is Hausdorff (we use this if the base points differ) and because of the uniqueness theorem (which we use if the base points coincide). Note that by construction, we have made the fibers indexed by the functions in F_{\alpha} discrete in the topology of \mathcal{U}.

The main point is now to realize that if \widetilde{M} is a connected component of \mathcal{U}, then \pi : \widetilde{M} \to M is onto and in fact is a covering map. Let us check that it is onto. First, we claim that \pi(\widetilde{M}) \subset M is open. Thus, let [p, f] \in \widetilde{M} and pick D_{\alpha} with p \in D_{\alpha} and pick D_{\alpha} with p \in D_{\alpha} and f \in F_{\alpha}. Clearly, D'_{\alpha, f} \cap \widetilde{M} \neq \emptyset and since D_{\alpha}, and thus also D'_{\alpha, f}, is open and connected, the connected component \widetilde{M} has to contiain D'_{\alpha, f} entirely. Therefore, D_{\alpha} \subset \pi(\widetilde{M}) as claimed.

Next, we need to check that M \setminus \pi(\widetilde{M}) is open. Let p \in M \setminus \pi(\widetilde{M}) and pick D_{\beta} so that p \in D_{\beta}. If D_{\beta} \cap \pi(\widetilde{M}) = \emptyset, then we are done. Otherwise, let q \in D_{\beta} \cap \pi(\widetilde{M}) and pick D_{\alpha} containing q and some f \in F_{\alpha} with D'_{\alpha, f} \subset \widetilde{M} (using the same “nonempty intersection implies containment” argument as above). But now we can find g \in F_{\beta} with the property that f = g on a component of D_{\alpha} \cap D_{\beta}. As before, this implies that \widetilde{M} would have to contain D'_{\beta, g} which is a contradiction.

To see that \pi : \widetilde{M} \to M is a covering map, one verifies that

\pi^{-1}(D_{\alpha}) = \bigcup_{f \in F_{\alpha}} D'_{\alpha, f}.

The sets on the right-hand side are disjoint and in fact they are connected components of \pi^{-1}(D_{\alpha}).

Since M is simply-connected, \widetilde{M} is homeomorphic to M (proof given in the appendix). We thus infer the existence of a globally defined analytic function which agrees with some f \in F_{\alpha} on each D_{\alpha}. By picking the connected component that contains any given D_{\alpha, f}' one can fix the “sheet” locally on a given D_{\alpha}.     ▢

By this, we can construct an analytic F such that for all \alpha,

f_{|U_{\alpha}} = (\log F)_{\alpha} + n_{\alpha} \cdot 2\pi i, \qquad n_{\alpha} \in \mathbb{Z}.

from which follows e^F = f.

For the existence of harmonic conjugates, we do similarly. Take a connected open cover of M, \{U_{\alpha}\} where each U_{\alpha} is conformally equivalent to the unit disc, and v_{\alpha} is a harmonic conjugate of u in U_{\alpha} (which exists uniquely up to constant on the unit disc. Let F_{\alpha} = \{v_{\alpha} + c, \quad c \in \mathbb{R}\}. Then by the same lemma, there exists v such that for all \alpha,

v_{|U_{\alpha}} = v_{\alpha} + c_{\alpha}, \quad \text{some } c_{\alpha} \in \mathbb{R}

that is harmonic and conjugate to u since it is the harmonic conjugate to u on every element of the cover, again with choise of c_{\alpha}s to ensure that on intersection of cover elements there is a match.