There are many ways in which AI is generating uncertainty in mathematics. We are not sure how it will impact our jobs, it is raising questions about how it might affect academic training, and it is…

We provide a proposed set of guidelines for PhD students and their supervisors. Given that PhD students are the most affected, both professionally and psychologically, by the advent of AI in mathem…

“Over the past year, many people have written eloquently and at length on the continuously improving power of generative AI (Large Language Models or LLMs) for research mathematics. Opinions range …

Continuamos con nuestra travesía sobre los números reales. Ya mencionamos en la primera entrada que nuestra intención es construir los números reales, es decir, nuestro cuerpo ordenado Dedekind-com…

The set \(P_{n}\) consists of the characteristic vectors of pedigrees, which are combinatorial encodings in one-to-one correspondence with Hamiltonian cycles. For \(n \geq 4\) and \(τ_{n} = \binom{n}{...

We describe Redhill, a Lean formalisation of the major results in Hölzl, Kleine and Stephan's "Improved Lower Bounds for Strong $n$-Conjectures" (arXiv:2409.13439). Design decisions regarding types an...

(This is a guest post, written by Jeremy Avigad, Kevin Buzzard, Johan Commelin, Rémy Degenne, Kim Morrison, Oliver Nash and Adam Topaz.) Mathematicians’ reactions to last week’s big OpenAI release …

We prove that the cyclic sum $\sum_{i=0}^{10}(x_i-x_{i+1})/(x_{i+1}+x_{i+2})$ is nonnegative for every strictly positive real eleven-tuple, with indices taken modulo eleven. Clearing denominators redu...

We consider the future of mathematics as a profession in a world where artificial intelligence may surpass human mathematicians in essentially every technical task. Through an informal dialogue, we…

Razborov's flag algebra method is one of the most successful tools for proving asymptotic density inequalities in extremal graph theory. It reduces an inequality about all large graphs avoiding a forb...

Introduction Who it is for. This guide is aimed at teachers who want to introduce Lean 4 to mathematics students who are used to writing proofs on paper but have no previous programming experience. No

El reto de esta semana consiste en demostrar en Lean 4 que la sucesión constante (a_{n} = L) converge a (L). Para ello, completar la siguiente teoría: import Mathlib.Tactic def LimSuc (a : ℕ → ℝ) (L

El reto consiste en demostrar en Lean 4 que si una sucesión tiene dos subsucesiones con límites distintos, entonces la sucesión no es convergente. Para ello, completar la siguiente teoría: import Math

“I am a mathematician and a (theoretical) computer scientist. AI affects both vocations deeply. On the back of the recent AI-driven Navier-Stokes result, computer science colleagues joked that I am…

“I believe that the development of AI tools will lead to a transformation of mathematics, both professionally and culturally. However, it will be a tragic missed opportunity if the massive shifts i…

“Free inquiry is a good in itself. The freedom to wonder, to play with an idea, and to follow a question belongs among the goods of a human life. It needs neither the endorsement of a corporation n…

Here are the 38 reads I shared on Mastodon this past week. This week's main thread is the impact of AI on mathematics. Terence Tao ("Math 2.0"), Jeremy Avigad, Christian Szegedy and Quanta Magazine ea

“Much of the discussion about AI and mathematics concerns what we might lose: understanding, creativity, professional identity, or employment. These concerns deserve attention. But I also see a pos…

[This is a guest post by Thomas Hales. This blog post was initially written in a different file format and converted using AI. — T.] Mathematicians have been weighing in on what they value ab…

I am uploading my slides to my public lecture “Math 2.0” that I gave yesterday evening at Caltech. (The talk was planned over a year ago, and was initially titled “Machine Assiste…

Presentación A quién va dirigida. Esta guía está dirigida a profesores que deseen presentar Lean 4 a estudiantes de Matemáticas acostumbrados a demostrar en papel pero sin experiencia previa en progra

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...