Large language models (LLMs) increasingly excel at mathematical reasoning, but their unreliability limits their utility in mathematics research. A mitigation is using LLMs to generate formal proofs in...

A practical framework for set-theoretical development in Lean - VTrelat/ZFLean

We present ZFLean, a Lean 4 library for doing core mathematics inside a model of ZFC with the ergonomics expected of typed Mathlib developments. Building on Mathlib's ZFC model, we contribute a relati...

The computation of the vertices of a polyhedron described by a system of linear inequalities is a central problem in polyhedral computation. It is a fundamental step in the conversion between H-repres...

Proof auto-formalization translates natural-language (NL) theorems and proofs into a formal language (FL) such as Lean, enabling mechanical verification. Despite rapid progress, research-level proofs ...

Computer-assisted proofs in dynamics establish results about nonlinear systems by rigorous numerical computation. Their correctness rests on a trusted base of interval-arithmetic libraries and analyti...

Analog computing with microwave signals can perform linear transformations directly in the analog domain, as the signals propagate through a microwave network. A fundamental question is which transfor...

The Steiner Deltoid as the Tangent Envelope of Wallace--Simson Lines in Isabelle/HOL in the Archive of Formal Proofs

Steiner's Line Theorem in Isabelle/HOL in the Archive of Formal Proofs

We report on an approach to teaching logic to mixed groups of computer science, mathematics, and philosophy students, based on the logico-pluralistic LogiKEy methodology, used for more than a decade i...

This article offers an introduction to metaprogramming in Isabelle/HOL for beginners, based on a running example for working with multivariate polynomials. The example is motivated by our formalisatio...

We present an AI-assisted Lean 4 formalization of the Poincaré conjecture. The project began with limited reusable formal infrastructure for the geometric analysis behind the proof. To organize this w...

Portable Lean 4 autoformalization skills for Codex and Claude Code - scottnarmstrong/LeanAutoformalizationSkills

[latexpage] In the last six month, autoformalization of research-level mathematics has gone from possible to easy. Back in early April, when Julia Kempe and I finished formalizing De Giorgi-Nash-Moser...

En el artículo «El futuro de las matemáticas», Jeremy Avigad examina cómo la inteligencia artificial ha automatizado la resolución de problemas y advierte de un riesgo: que la obtención de resultados

[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, …

En el artículo «Cómo afrontar los riesgos de la IA en el ámbito académico», la autora sostiene que la inteligencia artificial es ya una realidad inevitable, pero advierte de que su uso indiscriminado

“We are in an age in which artificial intelligence is no longer a technological curiosity or a tool used by specialists. Generative AI can now write, summarize, translate, code, solve mathematical …

En el artículo «¿Se acabó la carrera de matemáticas o es solo la graduación?», Cristiano Szegedy sostiene que la inteligencia artificial aplicada a las matemáticas se encuentra todavía en una etapa in

En el artículo «¿La IA supone el fin de las matemáticas tal como las conocemos?», Jordana Cepelewicz reflexiona sobre las consecuencias de que la inteligencia artificial sea capaz de resolver problema

Mathematicians are facing the sudden shift with grief, anger, and a desperate search for fresh ideas: “If we don’t adapt, there’s just no more math in 50 years.”

Mathematicians and Muse Spark collaborate on six research papers

Here are the reads I shared on Mastodon this past week: 1. Lean 4 A constructive ATLAS of finite simple groups in Lean. ~ Gerald Höhn. #LeanProver #ITP #AI4Math A Lean formalization of the Hamilton-P

En el artículo «Why I became a professional mathematician», Frank Vallentin reflexiona sobre su vocación, nacida de la belleza, la profundidad y el trabajo en equipo. Aunque una IA sobrehumana mecanic

In this personal essay, I reconstruct the reasons why I chose to become a professional mathematician. In particular, I want to find out whether I would still find these reasons convincing and motiv…

En el artículo «YAPOAI (Yet Another Post on AI): AI, understanding, and mathematical work», Najib Idrissi reflexiona sobre el papel de la IA en la investigación matemática. Aunque recurre a estos mod

I use large language models quite a lot in my research. I ask them to look for references, explain unfamiliar mathematics, write code, suggest approaches, find counterexamples, and try to prove thi…

En el artículo «If math is more than proof, we need to better celebrate the rest of it», Grant Sanderson parte de una idea extendida: resolver problemas y generar demostraciones han servido siempre co

[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…

“At the moment, the mathematics community is facing an unprecedented misalignment brought on by the advent of LLMs. According to the standard telling, the basic tension is between our traditional v…

En el artículo «AIM: an invitation to explore mathematics together», Matthew Colbrook sugiere utilizar la IA para mejorar el aprendizaje matemático. Su meta es abrir camino a estudiantes y jóvenes inv