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

Papers and videos explaining open problems in the AIM GitHub repository, their mathematics and applications.

AI for Mathematical Problems: An Invitation for Mathematicians - MColbrook/AIM

[This is a guest post by Matthew Colbrook. This blog post was initially written in a different file format and converted using AI. — T.] (Disclosure: ChatGPT helped me write and refine this p…

125 free math textbooks professors publish on their own pages: algebra, calculus, analysis, probability and statistics, sorted by subject, level and format.

En el artículo «To grieve, or not to grieve? (Mathematics and AI)» Kevin Buzzard explora la crisis existencial que atraviesan los matemáticos ante el avance de la IA, comparando su reacción con el pro

Recent events in the field of AI for mathematics have shown us beyond all reasonable doubt that the field is currently undergoing a rapid transformation, unlike anything that we have ever seen befo…

We formalise in Lean 4, on top of Mathlib, the solvability of the Dirichlet problem for second-order linear elliptic operators in divergence form. The machine-verified results, with no sorry in the de...

We formalize the smooth three-dimensional Poincaré conjecture, together with the Moise smoothing theorem, yielding the topological three-dimensional Poincaré conjecture. The smooth proof follows the H...

arXiv papers that use Lean, the interactive theorem prover. Updated daily.

The AI-generated Lean proof of Fermat's Last Theorem follows the broad classical strategy, but its intermediate results vary in scope and formulation. Comparing selected declarations with their source...

Two years ago I argued that we needed an autoformalizer. Since then an industry has formed around the idea, and in September 2026 an AI system formalized Fermat's Last Theorem. Autoformalization now w...

LLMs can solve standard Haskell exercises. We explain why this challenges functional programming course design and why our new course will allow their use.

El artículo «AI solves a ‘holy grail’ problem from probability theory» explora el misterio de la teoría de la percolación y la búsqueda de su «umbral crítico». En esencia, este campo estudia cómo el c

The Odlyzko-Poonen conjecture states that a monic polynomial of constant coefficient $1$ and with remaining coefficients chosen independently and uniformly from $\{0,1 \}$ is irreducible over the rati...

El artículo Can AI truly prove anything? sostiene que la capacidad de la IA para generar pruebas formales (como en código Lean) no equivale a "hacer matemáticas". Propone distinguir entre resultados "

“About a hundred years ago, David Hilbert gave a rigorous definition of a mathematical proof: […] I will not recall here the definition of the set of axioms of logic, which was, of course, the main…

We present new proofs of weak normalization for intuitionistic and classical propositional logics (with the full set of operators -- falsum, implication, conjunction and disjunction). These proofs wor...

While neural theorem provers have achieved impressive milestones in formal mathematics, they largely operate on the assumption that faithful Lean 4 formal statements are already provided. Translating ...

We present a constructive atlas of finite simple groups with proofs of their orders, simplicity, and structural properties. The eight completed families are cyclic groups of prime order, alternating g...

The shallow embedding of higher-order modal logic in classical higher-order logic, used in Benzmüller and Scott's Notes on Gödel's and Scott's variants of the ontological argument (2025), reaches beyo...

El artículo Responsible release of AI-generated mathematics, del Advisory group on mathematics and artificial intelligence, analiza la tensión entre los avances de la inteligencia artificial en matemá

El artículo Applied mathematics has met the machine before sostiene que la IA no afecta por igual a las matemáticas puras y a las aplicadas. Las puras se identifican con grandes conjeturas, sus «faros

Why does AI worry applied mathematicians less? We have met the machine before: human computers moved up to designing algorithms, and a computer run led to the solution. Driven by problems rather th…