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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😏

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Probably the funniest thing you'll read today, quant larpers have found a new home in prediction markets 😂 https://x.com/Prithvir12/status/1968941775323590841

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Unless ofc when sample mean = true mean 😂

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It took me a second to realize what July meant and I feel stupid bc of it

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I can’t believe we’ve had thousands of years of math progress, and the way to make compute fast enough for LLMs is to let go of associativity 😭

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Thinking of math things like machines helps my brain process them. Should I post more notes on Lagrange interpolation?

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