Rota

Continually return to what you love. What is beautiful and good and true

Lots still to figure out about how we integrate with the thought processes of human mathematicians, to better capture the pedagogical purposes of proofs, not merely the epistemological ones. But I'm excited to be a part of this journey with the rest of the @mathematics_inc team.

Today my colleagues and I released a paper on the formalization of d=4 Quantum Field Theory in Lean. We believe that formal verification has the potential not only to radically reshape how mathematical research is conducted, but also to transform research in theoretical physics.

LLMs are injective and invertible. In our new paper, we show that different prompts always map to different embeddings, and this property can be used to recover input tokens from individual embeddings in latent space. (1/6)

I moved to San Francisco btw

What did I miss

@fordoglunk I hear you’ve been good

@pli_cachete Husband

Some time in the last 3 months Sarah stopped being “Tripp’s girlfriend” and I became “Sarah’s boyfriend”

So I guess I should tweet more

[Podcast] Moral realism, Kantian ethics and veganism In this episode I talk with @morallawwithin about God, secular morality, moral realism, reasons, intuitions, Kantian ethics, and more. Florence Bachus is a PhD student at Harvard studying Kantian ethics. 1:49 — God and religion 5:39 — What is truth? 8:15 — Morality without God 10:39 — Obligation 11:50 — Reasons 20:05 — Morality grounded in consciousness (Valence realism) 27:33 — Morality without God cont. 30:00 — Kantian ethics 36:44 — Why universalize? 42:18 — Kantian Contractualism 43:10 — 4 categories of moral theories 46:36 — Logic as bedrock 47:25 — Is everything intuition? 50:44 — What is philosophy? 52:53 — Are there objective moral facts? 56:29 — The Kantian argument for veganism 1:02:53 — Applying to grad school

Today we release our open-source tool designed to help physicists use AI for research-level discovery. Physical Superintelligence PBC is a company whose sole mission is to solve physics using AI. We are releasing Get Physics Done (GPD) as a tool to support practicing physicists in their research.

Excited to launch the first stage of this competition with Terry and the @sairfoundation! If a student works through a math textbook and solves all exercises correctly, you’d expect that they’ve understood something. But what? They’ve likely learned a few major results, a few techniques, and they’ve gotten good at combining results and techniques in nontrivial ways. We then test their understanding with an exam. Often we even allow them to distill what they’ve learned into a single page ‘cheat sheet’ and bring it to the exam. Years later, a student might return to the material and feel every problem is now straightforward because theyunderstand the basic ‘algorithm’ for finding a solution. Today frontier LLMs perform very well on problems from undergraduate textbooks in, e.g., linear algebra, analysis, or topology. They can even answer nontrivial extensions of such problems. But what algorithm are they applying? And can we distill that algorithm into a short human readable `cheat sheet’ that we can use to teach other weaker LLMs? This is the motivation for the first stage of our competition: to boost the performance of weak LLMs via a short human readable cheat sheet. Rather than work with a textbook, we start with closed world experiment: the equational theories project. This project was a large-scale ‘polymath’ style project that Terry ran a few years ago. The goal of that project was to take a large list of ‘equational identities’ (think associativity or commutativity) and determine the entire ‘implication graph’ (e.g., does associativity imply commutativity). They succeeded and largely without any llm help at the time. In the present competition, we want to test the ability of LLMs to correctly classify whether one identity implies another. In our initial tests, frontier LLMs already do pretty well on this task. But we’re more interested in the performance of weak LLMs, which score closer to 50% accuracy. So the challenge is design a <= 10KB cheat sheet that improves the classification accuracy of weak open source LLMs as much as possible. The sair foundation is generously hosting this competition and providing model credits (fairly limited in stage 1). We are currently planning the second stage. Please read Terry’s post below for his thoughts and more information on the resources available to participants.

New work: Do transformers actually do Bayesian inference? We built “Bayesian wind tunnels” where the true posterior is known exactly. Result: transformers track Bayes with 10⁻³-bit precision.
And we now know why. I: arxiv.org/abs/2512.22471 II: arxiv.org/abs/2512.22473
🧵

Software agents can self-improve via self-play RL Introducing Self-play SWE-RL (SSR): training a single LLM agent to self-play between bug-injection and bug-repair, grounded in real-world repositories, no human-labeled issues or tests. 🧵

Merry Christmas from our house to yours

@dioscuri don’t waste your life reading fiction and watching movies

I object to putting videogames in the same category as doomscrolling TikTok, as this video does. If someone said “don’t waste your life reading fiction and watching movies” we’d say “well it depends what fiction and what movies”. We should give the same answer for videogames.

@AcerFur This is the fault of the site

Guhhh I feel so embarrassed now. Twitter please be easy on me it wasn’t recorded as having a previous solution on the site prior to me posting the solution GPT-5.2 Pro gave okay lol

The first time I spoke to Sarah was through text. She lived in Massachusetts and I lived Texas. I pushed her to jump on a Zoom call with me that same night. In those hours I took screenshots of the video call without her knowing. I knew I would want to save them for our children.

@DeepDishEnjoyer Who among us

so the reason i'm pescetarian instead of vegan or whatever is that on a 2019 trip to the galapagos, while snorkeling, i saw tortoises float in place in the water, open their mouth, and then fish would swim inside their mouths just to get eaten

My Christmas present to the AI for maths community: The first case of an Erdős problem (not previously resolved by a human) fully autonomously resolved by an LLM and autoformalised in Lean 4 😉 Stay tuned :) Yes, checked by myself, and with full confidence can say it’s right.

New YouTube video uploaded on connections between Riemann zeta and Brownian motion! What does Riemann Zeta have to do with Brownian Motion? link below