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The Future of Mathematics
[This is a guest post by Jeremy Avigad. This blog post was initially written in a different file format and converted using AI. — T.] “Mathematics underwent, in the nineteenth century, …
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The latest blog posts to take off on Hacker News. 2,851 posts.
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Anatomy of a Lean proof for software engineers
Intro I recently worked through a problem from a theory of computation textbook that asked me to prove a property of a language using finite automata. The informal proof is a simple constructive proof where you build an automaton and show that it recognizes the language. This is kind of similar to program…
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What TLA+ can and can't check
Let's chill just a little bit on the "TLA+ will save AI from itself" narrative
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Responsible Release of AI-Generated Mathematics
Responsible Release of AI-Generated Mathematics September 29, 2026 Back to main page Download PDF At present, some frontier AI labs are testing advanced mathematical problems on proprietary models …
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Nicholas Polson has authored 258 academic papers in 2026 so far
Nicholas Polson has, by my count using his SSRN page, already written 258 working papers in 2026 alone. He’s already written (or at least published to SSRN), six papers today, August 26, 2026.
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Burning Man death rates – A short lesson in statistics
What statistics can teach us about observing 3 deaths at Burning Man in 2026.
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Reverse-engineering the Intel 8087's tangent algorithm: more than CORDIC
I hope you're not tired of the 8087, because I have another article about Intel's floating-point chip. 1 In 1980, Intel introduced the 8087...
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We're gonna need a lot more mathematicians
[This is a guest post by Amit Sahai. This blog post was initially written in a different file format and converted using AI. — T.] When I was an undergraduate student, I remember talking with…
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Side-stepping the Secretary Problem, unwittingly
Having played both parts in the kabuki play that is employee-employer matchmaking, I feel the way we play it is a zero-sum game. I wish it were not so. When this post started life in 2024, as a wall of text chat message, it was brutal out there, on both sides of the software industry interview table. The ZIRP had…
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The Advisory Group on Mathematics and Artificial Intelligence
[This is a guest post by the Advisory Group on Mathematics and Artificial Intelligence. This blog post was initially written in a different file format and converted using AI. — T.] We would …
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Why do we need human mathematicians anymore?
[This is a guest post by Po-Shen Loh, crossposted from his blog, where an illustrated version appears. This blog post was initially written in a different file format and converted using AI. —…
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RSA-896
A post about RSA-896.
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If math is more than proof, we need to better celebrate the rest of it
[This is a guest post by Grant Sanderson. This blog post was initially written in a different file format and converted using AI. — T.] A sentiment echoing throughout the mathematics communit…
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Two parallel neural ectoderm progenitors contribute to the developing brain
Stanford Health Care delivers the highest levels of care and compassion. SHC treats cancer, heart disease, brain disorders, primary care issues, and many more.
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I vibed a proof of Conway's conjecture
You can just prove things, apparently.
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Why I didn’t sign the Fields medallists’ letter
[This post has been cross-posted to Terence Tao’s blog.] When I was around 11 I heard for the first time about Fermat’s Last Theorem. I was immediately captivated by the problem stateme…
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Saving Jet Fuel
Benchmarks & Tips for Big Data, Hadoop, AWS, Google Cloud, PostgreSQL, Spark, Python & More...
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Jean-Pierre Serre turns 100
Jean-Pierre Serre is a French mathematician who has made important contributions to algebraic topology, algebraic geometry, and algebraic number theory. He was a member of Bourbaki.
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Learning to solve hard problems in RL for LLMs by never giving up
This is a blog post for my recent paper on RL post-training of LLMs: introducing the Matthew Effect and proposing to solve it with Never Give Up. It is presented interactively and less formally, more like how I give the talk. For a deeper, more technical dive, check out the paper on arxiv and code on github. The…
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Backprop Alternative: Augmented Lagrangian Predictive Coding
A local alternative to backpropagation. PC-ALM trains residual MLPs up to 1000 layers, nearly matching backprop's performance despite using only layer-local dynamics. PC-ALM equips each layer with a feedback control dynamical system that distributes and propagates supervision credit throughout a network.
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Why don't machine learning research agents overfit?
New research indicates that AI agents learn compressible models of data, which don’t have enough space to enable memorization.
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A beginning for mathematics
A positive vision for the future of mathematics: how our institutions can deepen human understanding as AI transforms mathematical research.
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Fable 5.1 Solves the Cyphral Distich, a 370-year-old cipher
Explore Claude Fable 5.1's proposed solution to Sir Thomas Urquhart's Cyphral Distich, a centuries-old cipher, with the reasoning behind the result.
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After Math
[This is a guest post by Silvia De Toffoli and Eamon Duede. This blog post was initially written in a different file format and converted using AI. — T.] Silvia De Toffoli (University School …
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Compressing a flag to 11 bits
I recently saw an interesting YouTube video by “Physics for the Birds”. The main video is about matrixes, but he used flags to explain some of the operations on matrixes:
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A Mathematical Framework for Transformer Circuits (2021)
Transformer language models are an emerging technology that is gaining increasingly broad real-world use, for example in systems like GPT-3 , LaMDA , Codex , Meena , Gopher , and similar models. However, as these models scale, their open-endedness and high capacity creates an increasing scope for unexpected and…
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Navier-Stokes Announcement
The Millennium Prize Problems were unveiled by the Clay Mathematics Institute (CMI) at a meeting in Paris in 2000 to celebrate “The Universality of Mathematical Thought”. These problems encapsulate some of the most difficult challenges that mathematicians were grappling with at the turn of the millennium. CMI’s…
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A Misalignment of AI in Mathematics
I am proud to be among the list of 25 initial signatories — all Fields Medallists — to the declaration below, which grew out of discussions between ourselves over the last week. We have…
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Factoring RSA 260
How Devin and a Cognition researcher built the world’s highest-performance GPU lattice siever, to make factoring numbers 10x cheaper than the previous…
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The Navier–Stokes Millennium Prize Problem
On the Navier–Stokes Millennium Prize Problem introduces an impressive result from OpenAI, who used an unreleased model to produce a resolution to the Navier–Stokes existence and smoothness problem, one of …