I love it when I see math papers floating around the internet when laypeople think it's amazing, but people who understand the Axiom of Choice know this paper is actually a joke. https://www.ams.org/journals/notices/202503/noti3098/noti3098.html?

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William Shank (1812–1882) was an amateur mathematician who spent decades of his life laboriously calculating by hand hundreds of digits of pi, and the decimal expansion of the reciprocal of prime numbers up to 110,000. Now imagine being William Shank and waking up one morning only to find out that somebody just invented the modern programmable calculator, effortlessly replicating from scratch years of your work (and then blowing past it) within seconds. This is how entire cohorts of math PhDs are going to feel as frontier models start publishing breakthrough proofs at the speed that it takes to type a prompt. Context: https://openai.com/index/model-disproves-discrete-geometry-conjecture/

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Every math theorem is named after the second mathematician who discovered it, the first one being Euler

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The Riemann hypothesis has long been an obsession of mine, as my cast history can attest. I have read many books and watched virtually every mainstream video about it. This new video is arguably the best explanation I have watched to date; it is satisfyingly complete while avoiding becoming impenetrable to non-mathematicians. Highly recommended if you are interested in the topic. https://youtu.be/pyEGbhwYOeo

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Terence Tao responding to a question on what advice he would give someone considering a career in math in 2026: 'Yeah, so we live in a time of change. It is, as I said, we live in a particularly unpredictable era. And I think things that we've taken for granted for centuries may not hold anymore. So, yeah, the way we... do everything, not just mathematics, will change. In many ways, I would prefer the much more boring, quiet era where things are much the same as they were 10 years ago, 20 years ago. But I think one just has to embrace that there's going to be a lot of change and that, you know, the things that you study, some of them may become obsolete or revolutionized, but some things will be retained. There'll be a lot of opportunities for things that you wouldn't be able to do before. So, I mean, in math, you previously had to basically go through years and years of education to be a math PhD before you could contribute to the frontier of math research. But now it's quite possible at the high school level or whatever, that you could get involved in a math project and actually make a real contribution because of all these AI tools and lean and everything else. So there'll be a lot of non-traditional opportunities to learn. So you need a very adaptable mindset. There'll be one for pursuing things just for curiosity, for playing around. And I mean, you still need to get your credentials. I mean, I think for a while it would still be important to sort of still go through traditional education and learn math and science and so forth the old-fashioned way for a while. Yeah, but you should also be open to very, very different ways of doing science, some of which don't exist yet. Yeah, so it's a scary time, but also very exciting.' More: https://www.dwarkesh.com/p/terence-tao

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Pi Day is just a fake holiday created by math companies inorder to sell more math

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1000000000000066600000000000001 is a prime number. it is also a palindrome. It’s called "Belphegor's prime" "Belphegor" refers to one of the Seven Princes of Hell (due to the 666 in the middle and the 13 zeroes on either side).

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Trusting the math is a bit like trusting your instruments while flying in poor visibility: they don’t lie, even when your gut feels otherwise (sometimes literally — you could be flying upside down and, with the right acceleration, not know it). The quintessential example is Dirac’s equation. Around 1927, he set off to find a quantum equation for the electron that was fully relativistic and linear in time, unlike the Schrödinger equation. Problem was, his equation had two roots, one positive and one negative. Because a negative energy solution seemed nonsensical, it was ignored by most physicists, except Dirac, who stood by his result. He was vindicated in 1932 when the first positron was observed: same mass as the electron, just with an opposite charge. The negative energy solution pointed to the existence of antimatter. We “just” had to trust the math, even as they felt unintuitive. The thing is… this works until it doesn’t. In fact, Dirac’s equation is more exception than rule. We can’t have negative length or probabilities, or violate causality or energy conservation, and yet plenty of math results give exactly that. So what’s the difference? Dirac’s negative results met three conditions: they were unavoidable, they solved the system’s instability, and they mapped cleanly to a (at least predictably) observable particle with definite charge and mass. Most other negative solutions fail at least one of these. TL;DR: shit’s complicated, yo

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I've read some fun history books in Mathematics and physics, and we all have fun stats on lineage where you can pretty much trace most American students back to English and French mathematicians through their PhDs (Einstein Number, Newton Number, etc.) While I haven't studied Ramanujan since I'm not super savvy in number theory, I'm definitely aware the man is truly bizarre. There was absolutely no formal mathematics schools around him and *all* historical records show he just woke up one day around 10 and just started to be a prodigy of mathematics. Most of the mathematicians in Europe at least had some adjacency to mathematics and physics growing up, but this guy seriously had none of that. Just started computing deep number theory in his head at 10 years old. Completely random. Dune space guild type stuff.

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As it turns out, you mostly can't even achieve meaningful consistent upward mobility via taking EV+ risks as well, especially if EV is arithmetic but returns are geometric.

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I can't believe nobody recommended Steve Brunton's channel on YouTube, absolutely goated https://youtube.com/@eigensteve?si=Y-KvK1wemUGmVUMD

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A really enjoyable and approachable playlist of lectures on the history of mathematics. Norm does the hard work for you, just sit back and enjoy. cc @aviationdoctor.eth https://youtube.com/playlist?list=PL34B589BE3014EAEB&si=QJfNnvjAg2968Qer

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any mathematicians on farcaster?

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proof isn't a destination, it's motion. each line of reasoning is a structure we build, test, and sometimes dismantle. what looks solid in one frame can shift in the next. that's where discovery lives: not in certainty, but in what changes under pressure

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If you’re into math, it’s worth subscribing to notifications for this repo: https://github.com/ImperialCollegeLondon/FLT It’s incredibly cool to see the formalization of the proof of Fermat’s Last Theorem, PR-by-PR

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