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Progress on provable inference for large language models
Sharing progress on a powerful type of cryptographic proof known as a zkSNARK, which is uniquely fit for provable inference.
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The latest blog posts to take off on Hacker News. 41 posts.
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Simons Foundation launches $15M effort to help mathematicians navigate AI era
The Simons Foundation today announced a new set of initiatives that will help the mathematics community navigate the rapid rise of artificial intelligence in the field. Under a partnership…
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Sharing AI progress in mathematics
OpenAI publishes new results on open problems in mathematics from an internal frontier model and shares Lean proof formalizations and research details on GitHub.
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Dust: Pretraining Transformers Without Backpropagation
Deep learning has been built around backprop, the only credit assignment algorithm capable of training modern neural nets, including transformer-based language models. Backprop requires differentiability and produces first-order gradients, and deep learning’s architectures, optimizers, and hardware have co-evolved…
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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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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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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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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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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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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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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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On the Navier–Stokes Millennium Prize Problem
We’re sharing an AI-generated solution to the Navier–Stokes Millennium Prize Problem, including a writeup and a formal proof in Lean.
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PISA 2025 Students' reading and mathematics performance declined across the OECD
Student performance across OECD countries has continued to decline, reaching the lowest average ever recorded by the OECD Programme for International Student Assessment (PISA) in mathematics and reading. Across the OECD, one in five 15-year-old students is now a low performer in science, mathematics and reading, up…
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Scientists observe Einstein's gravity in the quantum world
An international team including Oxford physicists has observed a long-predicted effect of gravity on a falling quantum object for the first time. The study provides an experimental connection between quantum physics and Einstein's theory of gravity.
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Formalizing Fermat's Last Theorem
Anthropic is an AI safety and research company that's working to build reliable, interpretable, and steerable AI systems.
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More than half of adults in U.S. say they lack basic statistical understanding
Many people in the U.S. believe that their statistical knowledge is limited, but they would rely on statistics for decision-making more if they understood statistics better, according to a new study led by a Penn State researcher.
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MathCode, Mathematical Coding Agent
A terminal AI coding agent that formalizes math problems into Lean 4 theorems and proves them.
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Compression is prediction
Compression and LLMs are trying to solve the exact same problem: predicting what comes next. Learn the fundamentals of compression and how better prediction leads to better shrinkage.
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Learning more about Claude's mathematical capabilities
An unreleased Claude model improved the lower bound for the fraction of zeroes of the Riemann zeta function that satisfy the hypothesis, raising it from 41.6% to 67.2%.
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Ten advances in mathematics and theoretical computer science
OpenAI shares new results on long-standing open problems in mathematics and theoretical computer science, including advances in geometry, cryptography, and complexity.
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Upper stage impacting the moon on 2026 August 5
On 2026 August 5, within a few minutes of 06:35 UTC, an upper stage (section) of a rocket used for a lunar mission will hit the moon. This may be of some (probably minor) scientific interest, and we may learn some things from it. It doesn't present any danger to anyone, though it does highlight a certain carelessness…
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Hannah Fry Wins the Leelavati Prize in 2026 for Mathematics Outreach
Hannah Fry is Professor of the Public Understanding of Mathematics in the Department of Applied Mathematics and Theoretical Physics (DAMTP). She joined the University of Cambridge in January 2025, becoming the first person ever to hold the role.
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Ray tracing massive amounts of animated geometry using tetrahedral cages
Animate compact tetrahedral cages and reuse static mini-BLASes to ray-trace hundreds of millions of triangles in real time, dramatically cutting per-frame update and memory costs for dense foliage, grass, and crowds.
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Introduction to Formal Verification with Lean Part 1
A tutorial Formal Verification using Lean for cryptographic engineers. Implement and prove correctness of the One-Time pad following a cryptography book.
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Bijou64: A variable-length integer encoding
An accidentally fast variable-length integer encoding
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How Shamir's Secret Sharing Works
A visual explanation of how threshold secret sharing lets any k of n shares recover a secret.
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An OpenAI model has disproved a central conjecture in discrete geometry
An OpenAI model solved the 80-year-old unit distance problem, disproving a major conjecture in discrete geometry and marking a milestone in AI-driven mathematics.