Very excited to share our interview with @polynoamial on AI for math — the Erdős unit distance problem, saturating the IMO, the future of math research, and more!
[1/7] Recent breakthroughs in LLMs’ mathematical ability are genuinely surprising.
I recently solved a problem I had been unable to solve for seven years: the optimal acceleration rate for first-order methods under high-order smoothness assumptions in nonconvex optimization.
Earlier this month I volunteered at Stanford’s Future of Math symposium, and ever since, I've been puzzling through what it now means to pursue mathematics as a student in the age of AI. I wrote an essay to make sense of it all: apoorvapanidapu.substack.com/p/a-new-consci…
I've recently got in on the act of getting AI to solve open problems in mathematics. More precisely, I gave some questions asked by Melvyn Nathanson to ChatGPT 5.5 Pro, to which I have been given access, and it answered them. 🧵
What do the smartest kids in the world do when they grow up?
I did the largest study of ~18,000 International Olympiad medalists (IMO, IOI and IPhO) over the last 25yrs, arguably the sharpest analytical minds of the world in high school, to see where they ended up and traced ~50% of them.
Founders of ~20 unicorns and ~7 decacorns and ~10 billionaires: OpenAI, Cursor, Stripe, Databricks, Perplexity, Ethereum, Cognition, Hyperliquid, Fireworks, Modal, Quora, Parallel, Cartesia, Wispr
Most kids went to MIT, a whopping 12% of them, followed by Cambridge (7%) and Sharif (3%)!
The career paths they chose (of those who graduated) were:
— 36% Academia (professors)
— 26% Other
— 22% in Software / Tech
— 12% in Quant / Finance
— 5% Founders!
The biggest employer was Google, by far, at 6%.
Others interesting tidbits were:
— 47 of them work at Jane Street (#3)
— 38 at OpenAI (#5)
— 15 at Anthropic
— 8 at Cognition
— 6 at Isomorphic Labs
Olympiaders were 1500x more likely to be billionaires and 4000x more likely to be unicorn founders than the average person!
@TRBRajaa@IPeriyasamy_@VckBalaji Who is/are the political in-charge for the roads/lights/other infra within SIPCOT IT Park, Siruseri? This person(s) should be in jail for the horrible conditions here. This is the situation after collecting tons of tax from companies and apts.
STAN WAWRINKA. 🤯🤯🤯🤯
The last one handed backhand winner he ever hit at the Australian Open.
It’s enough to send chills down your spine.
One of the most beautiful shots in the history of tennis… it’s not up for debate. 🥹
My friend just got placed on Day 1 at IITM with a 60 LPA package.
People love to criticise JEE, but they forget it’s actually the simplest path in the long run. Crack it and you get four years of clarity, structure, and opportunity. Miss it, end up in a tier-3 college, and suddenly you’re juggling DSA, dev, communication skills, side projects, and five other things, just to land 4 LPA.
Sometimes the “hard” thing is actually the easiest route forward. Study hard, that’s it. people who have genuinely prepared for JEE would relate!
The uncomfortable truth is: everyone has to go through a phase of intense hard work at least once in their life.
For some, it's during school.
For others, it hits in college.
And for many, it comes later during their first job, first switch, second switch, or even beyond.
The catch?
The later you push that phase, the tougher it gets.
Early in life, the competition is smaller, the responsibilities are fewer, and the stakes are low. That’s when excellence is cheapest, in terms of effort, stress, and sacrifice.
But once reality hits, when bills show up, when you see your peers pulling ahead, when survival and growth clash, the grind becomes ten times harder. Because now you're competing with thousands who are hungry, experienced, and desperate for the same opportunity.
So yes, cracking something early (be it JEE, exams, a skill, or a career break) doesn’t “guarantee” life, but it gives you leverage. And leverage compounds.
Early excellence isn’t about privilege, it’s about momentum.
The sooner you build it, the longer you benefit from it.
My friend just got placed on Day 1 at IITM with a 60 LPA package.
People love to criticise JEE, but they forget it’s actually the simplest path in the long run. Crack it and you get four years of clarity, structure, and opportunity. Miss it, end up in a tier-3 college, and
Recently came across this fantastic talk by @ccanonne_ on deterministic amplification via expander graphs—elegant ideas, crystal-clear exposition. A real gem!
youtube.com/watch?v=3AAUqW…
Gilbert Strang's "A Vision of Linear Algebra"
Presents Professor Strang’s updated vision of how linear algebra could be taught.
Youtube Playlist: youtube.com/playlist?list=…
Course Website: ocw.mit.edu/courses/res-18…
Hi new followers! I’m a mathematician at Harvard. I have a YouTube channel, where I discuss math the way I think about it, with now two playlists on differential geometry and complex geometry (in progress). Comments welcome!
DG: youtube.com/watch?v=rVTN7V…
CG: youtube.com/watch?v=N5FQHg…
Yes.
Given a Hamiltonian cycle C of the n-hypercube, we can construct one for the (n+1)-hypercube inductively by listing the elements of C in order and concatenating it with a 0, followed by the elements of C in reverse order concatenated with a 1.
It is possible to walk a loop through all two-digit sequences of 0s and 1s, changing one digit at a time: 00->10->11->10->00.
Can do the same for all three-digit sequences of 0s and 1s.
All four-digit sequences? All n-digit sequences?
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