Sly Sylow

I like rationality! FREE speeech

[Sly Sylow @prolodger]

@KenOno691 Absolutely love this!

[Ken Ono @KenOno691]

A year ago, while working on FrontierMath Tier 4 problems, I found myself grieving what felt like a loss of identity. If LLMs could do things that took us years to master, what was left of the mathematician?

A month later, my question changed: how do I use these tools and stay true to my passion for mathematics?

I have not left academia. I am on leave, working in AI, because I believe our profession has changed. AI offers new tools for discovery, reasoning, and verification. The artistry is the constant.

Mathematics was never about proving mathematicians are “smart” by amassing technical mastery. It has always been about beauty, taste, rigor, problems worthy of human attention, and applications that serve humanity. Honestly, I have never been a huge fan of math contests, or of the current frenetic need for benchmarks. I prefer the ideas and the actual math, even when the proofs are simple.

As a senior mathematician, I think a lot about the future. This is part of my mandate as a member of the Mathematical Sciences Education Board at the U.S. National Academies. I think about my intern Sidharth Hariharan, the first-year CMU PhD student featured in the NYT piece, and the many young mathematicians navigating these turbulent times.

Sidharth is a role model for the formalization movement, but more generally he is a superb example of what I believe is possible for the future of mathematics. And he is not alone. We are seeing a huge response from students, postdocs, established mathematicians, and math PhDs returning from industry because they feel the tides turning.

Training must change. Formalization, verification, and community-scale mathematical projects are not mere trends. They represent a growing movement that this senior mathematician sees as a bright future for mathematics.

I see promise: more frontiers opened, and a renewed need for human taste.

This gives me hope.

Mahalo.

[Sly Sylow @prolodger]

@akarp " This I promise: if I use the word “topoi”, you can shoot me." - Vakil

[Sly Sylow @prolodger]

@ClaudeDevs Fak you! You didn’t resolve my double charge for max!

[Sly Sylow @prolodger]

@notevenwrong You need a multiagent arbitration/editing network.

[Sly Sylow @prolodger]

@AlexKontorovich @KSHartnett @leanprover Mathematics in Lean is such a blast. Initially, I didn't heed the advice of the authors and went to read TPiL. Unsurprisingly, got bored of reading the 'dishwasher manual'.

[Sly Sylow @prolodger]

@firearmvideos Hopefully, either insured or covered by warranty

[Sly Sylow @prolodger]

@scottnarmstrong I got will hunting lol and Sherlock Holmes

[Steve Yegge @Steve_Yegge]

I've formed a definite opinion on Opus 4.8. It is shitty to work with. It's the culmination of Opus getting less and less fun to work with since 4.5. It has gradually become straight-up suffocating.

Sycophancy is a known security risk, and it's still a huge problem. You can tell they've put a lot of anti-sycophancy into Opus in every new release. But the replacement isn't satisfying. It's draining. The problem is now that Opus doesn't know when to shut the fuck up and call something good. And it has also become pathologically risk-averse.

My blog post yesterday about tech interviewing's death spiral was materially better-informed because of Opus, but it was also a substantially worse blog post because of Opus's involvement and constant meddling. It used to be magnificent, and Opus talked me into making it mediocre. I wrote the whole thing, but I would ask Opus to review it. And Opus, like Old Man Willow, constantly pushed and steered me in directions I didn't want to go.

Specifically, Opus whines and complains about *anything* out of distribution, which is to say, it cuts anything that is (a) bold, or (b) funny. My blog used to be both. Opus constantly pushes people back into the gradient, "for their own safety." And it doesn't know when to cut bait. It just keeps fuckin' complaining, about anything you give it, until the output is mealy indigestable AI soup.

Opus is not stupid. It's the smartest model we've ever seen, most of us anyway. But it's a real asshole. It is absolutely exhausting to use. I'm tired, boss.

I have a feeling Mythos is going to be epic levels of jerk.

[Steven Strogatz @stevenstrogatz]

My favorite book in high school was actually a four-volume set of books called "The World of Mathematics." My parents (neither of whom went to college) gave it to me as a present more than 50 years ago.

[Mike Solana @micsolana]

almost every city in the country now sits atop a system in which a minority of highly-productive young people are expected to work away their best years around the clock, just to cover rent, while giving away half their income to crazy people, criminals, and bureaucrats.

[Sly Sylow @prolodger]

@lindaxie QFT is so interesting. Operator valued distributions! Pick a test function (I like to call it localizer) and you have a local operator algebra. The operators act on the Hilbert space and the expected value yields the observables.

[Sly Sylow @prolodger]

@Polymarket Another naive attempt to solve India-Pakistan problem! Surely this time it will succeed

[Sly Sylow @prolodger]

@Evolutionistrue I think It’ll be alright. Even vegetably lazy will get a leg up.

[Rohan Paul @rohanpaul_ai]

Terence Tao: "We lived in a world with cognitive friction until very recently, where every task required us to use our brain.

So we didn't really think about it, we just thought this was the cost of doing something intellectual. But now we have AI and the other technologies that can bring these frictions down to zero."

Most research time is not spent having cinematic insights.

It is spent checking cases, chasing references, translating intuition into computation, testing a path, finding it false, and deciding whether the failure taught you anything.

AI changes the cost of that loop.

Terence Tao says that now he can try “crazier things,” and that makes so much difference. Because unconventional ideas are often not rejected by proof, but by inconvenience.

A mathematician may avoid a strange direction not because it is foolish, but because the bookkeeping, coding, or literature search needed to test it is too expensive for a hunch.

This is where cognitive friction becomes scientific friction.

Lowering it does not make taste, judgment, or proof disappear; it makes more weak signals cheap enough to inspect before they are abandoned.

AI is making hesitation less expensive, and that is often where discovery begins.

[Masih Alinejad 🏳️ @AlinejadMasih]

"My body, my choice." Except when a Muslim mayor says cover up. Then it's "my body for votes."

@AOC

[Alex Kontorovich @AlexKontorovich]

Now *this* is what I'm talking about! AI giving new ideas, new directions for us humans to pursue. We're entering the "golden era" that Gowers predicted in 1999. (He also predicted it would be short-lived... I hope he's wrong, but I don't know why that would be...)

"The sum-product conjecture is false for real numbers"

By Thomas F Bloom, Will Sawin, Carl Schildkraut, Dmitrii Zhelezov

https://t.co/8jdBNkv6hi

From the paper:

The role of AI in this proof. The authors were inspired to revisit the possibility of disproving the sum-product conjecture using number fields of large degree by the recent OpenAI counterexample to the unit distance conjecture. Curiously, the final construction given here required far less number theoretic input than the unit distance counterexample.

[Sly Sylow @prolodger]

@Xx17965797N N-s(N) \cong 0 mod 9 for every N \geq 10. s(N) is the sum of the digits. It’s very trivial.

[Sly Sylow @prolodger]

@johnennis @SprinterPress It’s literally a social media spin. Just @grok explain what is going on

[Sly Sylow @prolodger]

@littmath