"While asleep, I had an unusual experience. There was a red screen formed by flowing blood, as it were. I was observing it. Suddenly a hand began to write on the screen [...] a number of elliptic integrals. They stuck to my mind." — Srinivasa Ramanujan

Physics professor discloses in 1 minute the full insight of Quantum Mechanics.

$610,000,000 of Health Science projects funded by the National Cancer Institute include far-left political/DEI language like "latinx" -- 11% of Cancer awards by dollars $315,000,000 of those by the National Inst on Minority Health & Health Disparities -- a whopping 48% of theirs

Mathematicians are deeply delusional about normal humans

The most intuitive explanation of floats I've ever come across, courtesy of @fabynou fabiensanglard.net/floating_…

I crossed an interesting threshold yesterday, which I think many other mathematicians have been crossing recently as well. In the middle of trying to prove a result, I identified a statement that looked true and that would, if true, be useful to me. 1/3

Andrew Wiles on the morning he discovered how to fix his proof of Fermat's Last Theorem

Very revealing exchange here IMO. You can judge the quality of the claims yourself but fwiw this seems to me to be an argument against publicly funding public goods in general.

If "real" numbers are so "real", then why can't we implement them on computers?

The simple fact is that if you care more about understanding things than making money, the academy is, despite its many flaws, your best option.

Philosophers: logic is the foundation of mathematics. Mathematicians:

The article also slanders non-commutative algebra.

I have taught kids before, and you have to understand that half of the population is below 100 IQ. Getting them to memorize some mechanical techniques and then apply them to pass a state test is the best you are ever going to do with them.

Math is a skill— like music or sports. Yet somehow, it's treated it differently. We’d never accept anti-practice attitudes in other domains, so why do we tolerate it in math? Here's @AlexKontorovich talking about this in my latest podcast episode. Link to full episode below.

The US National Science Foundation spends about $250 million (yes, that’s “million” with an “m”) funding math research (pure and applied) per year. ROI is actually incredible.

My article on IQ. Turning out to be a small booklet. medium.com/incerto/iq-is-lar…

Well the mathematicians, neuroscientists, and geneticists here are wrong. They probably don’t understand the difference between skills and abilities. Quantitative reasoning, sequential reasoning, etc. are important abilities for developing math skills.

This speech is a disgrace. As a young mathematician, I stopped talking with my physicist friends for the same exact reason: their reply to all my questions was always: "no, no, don't try to understand it intuitively." Nothing is counterintuitive by nature, unless you decide so.

the IQ pill is absolutely brutal. Game Theory, The Manhattan Project, Quantum Mechanics, Monte Carlo Methods, Entirety of Modern Computing, Entropy, Numerical Weather Prediction, Stochastic Computing, you just can’t compete with this.

starting to learn about grothendieck's model of practice via @davidbessis' phenomenal "mathematica" -- math is the act of refining your intuition by constantly exposing its weakness no surprise then that the main challenge can be the pain

tl;dr this is an iq 120 guy trying to debunk 160+ iq historical genius accomplishments using iq 100 normie standards for what genius is in(mental calculations in his head(which ironically von neumann was excellent at)/ memorization of facts and books/speaking 4 languages instead of eight from historians confused about sources) in a situation where normie iq 80 people can tell it has nearly zero relevance(the question of the correctness of hereditarian views is about intelligence in groups, not n=1 individual) usually i won't even bother to get on my high horse but since he has proven to be a continuous source of retarded takes about intelligence research (see his previous article on aristocratic tutoring and his attacks on the studies of precocious youth when he maliciously frame the studies as purporting to be useless because they are not rcts when anyone that actually read the studies would know that immediately because it is a study of seeing the effect of intervening on the smartest kids and their outcome! of course it is not a pure "rct") let's address the obvious elephant in the room. Erick Hoel have no understanding of the real significance of Von Neumann's work in any of the fields he mentioned(not including all the important things he just passed over and did not even mention or flat out got completely wrong in a way that suggest he did not bother with reading a wikipedia/or getting a llm to explain it to him) already we see the limits of this article proposing to explain "the myth of von neumann shooting lighting from his ass" The core problem is I see it is that he doesn't understand the phenomenology of being an incredible mogger like von Neumann and thus he debunks some silly stories told about von Neumann to impress normies but no one smart is impressed because von Neumann being able to multiple large numbers inside of his head or speak four languages or have a party trick for memorizing large amounts of texts at will(there are incredible dumb people who are capable of being all of these) impresses preciously no one important! the important bits of von Neumann's intelligence(like the stories of Danzig and linear algebra or Nash coming to explain his embedding theorems being immediately told by von Neumann what the real theorem should be)(or every version of stories like this or actual examples of his impressive mental calculation story is left out of the article for some reason) like maybe i am a elitist snob to demand he has a real understanding of anything von neumann did, but you can just read the stories of people who are remembered as the founders of entire fields and got nobels and countless other awards who come to von neumann to be immediately told they were boring and wasting his time essentially and he(von neumann) had the real theory! and then demonstrating it to them! Von Neumann had no need to steal other people's ideas, he was already an all knowing oracle in some ways!(he wasn't perfect and some of his fellow mathematicians also told stories where he lacked basic knowledge in some other areas of math and had to prove things inelegantly) (but there is no other mathematician who you would expect to know random areas they don't even work on, and von neumann famously knew "three tricks" let me steal the full quote here(it's ulam who he falsely say von neuman took cellular automata ideas from) "Von Neumann was different. He also had several quite independent techniques at his fingertips. (It is rare to have more than two or three.) These included a facility for symbolic manipulation of linear operators. He also had an undefinable "common sense" feeling for logical structure and for both the skeleton and the combinatorial superstructure in new mathematical theories. This stood him in good stead much later, when he became interested in the notion of a possible theory of automata, and when he undertook both the conception and the construction of electronic computing machines. He attempted to define and to pursue some of the formal analogies between the workings of the nervous system in general and of the human brain itself." (page 96) on the retarded shit he says about godel making von neumann's work on the foundations useless(completely stupid and wrong by the way, his method on transinduction stands see: en.wikipedia.org/wiki/Von_Ne…(there is a funny thing here where zermelo supposedly had publishing priority on some of the ideas) and see: en.wikipedia.org/wiki/Von_Ne… "In actual fact, during the Königsberg Congress, none of the eminent participants realized the full import and implications of the result announced by Gödel – with one exception: von Neumann. After the discussion the latter rushed up to Gödel and took him aside in order to get a better understanding of his demonstration. He then left the Congress in a state of extraordinary excitement and spent the next month working on the issue. Less than two months later he wrote to Gödel to announce he had demonstrated, as a consequence of the theorem of incompleteness, that the consistency of arithmetic cannot be proved. Gödel replied that he had in the meantime succeeded in obtaining this demonstration and sent him a copy of the article that had already been presented for publication." (Chapter 2, page 30, ISBN 978-3-7643-9895-8 Birkhäuser Verlag AG, Basel - Boston - Berlin The World as a Mathematical Game (by Giorgio Israel and Ana Millán Gasca)) as we can see here, von neumann was not just taking other people's original ideas and extending them(he was mostly independently proving things once he starts to think about a particular type of problem) he completely misconstrue the nature of dirac's book on quantum mechanics(the principles of quantum mechanics) what von neumann wrote in his book was not what dirac did! it was not just a notation equivalence. Dirac did not invent operator algebras or what later leds to c* shape algebras or any of the work von neumann did. Von Neumann(along with stone and banach established both the basic of functional analysis )and independently proved theorems that dirac did not consider and went beyond his papers on quantum mechanics) Indeed, he did this work because he viewed dirac's books and papers as not being fully rigorious enough for a mathematician!!(this part pissed me off the most since i actually read all of dirac's book on qm and most of von neumann's book(some of the math was beyond me at that point in my life and i can't claim to understand all of it) he notes that von neuman's proof that the hidden variables is impossible is wrong(but this seems to be argued by people who thinks following up people have misread von neumann or fallen prey to german translation issues see: arxiv.org/html/2401.04002v2) this doesn't even begin to cover the achievements of von neumann in domains of mathematics that i know nearly nothing about(ergodic theory and computational fluid dynamics being two simple examples) really I haven't mastered a fraction of all the stuff he got up to(i have read the theory of games and the theory of self reproducing automata that is coauthored by burks) but hoel's article is just wrong on every single point i do know about! it's crap. bro does not know jackshit about von neumann but he is here comparing his achievements to einstein and others(does he know anything about special or general relativity i wonder) he lacks the basic qualifications to even assess the smallest part of von neumann's works and he is here deunking what? some biographical details that got mixed up over time? his arguments about hereditarianism is laughable! he falls prey to the same mistakes that everyone trying to say educational interventions work/explain variance(he does not control for genetics, it's so funny his own sources note the ridiculous amount of jews in hungary at the time, if this is just the outcome of intense tutoring and good schooling(then why did not the crop of hungarian mega-geniuses continue!!) indeed, they were mostly the product of immigrant jews(who are strongly filtered on ability already by dint of being able to immigrant) his arguments against the role of ethnicity just highlighted the very thing HE THINKS ISN'T IMPORTANT. (what about class-mates who went to the same schools but did not turn out to be world class mathematicians?? what explains them) it isn't even worth considering. it is a terrible way to argue about group differences focused on one individual(or his fellow martians for that matter) (the ideal condition is to consider randomized people placed in schools/tutoring at the quality he demanded and see the outcome)(do the the asian cram schools produce mega-geniuses???they do exactly this! there are other striver cultures that rival anything von neumann went through in terms of sheer pressure and quality and they mostly don't produce shit) I suppose i should link to let the fair reader evaluate his words against what i have presented here but if you care to you can google erick hoel's substack because frankly i consider all of that article to be entirely trash misinformation and i am not about to give it anymore attention than it deserve(this is mostly catharsis for me)