Tag
Mathematicians, via the Leiden Declaration endorsed by the International Mathematical Union, warn that AI threatens core values of mathematical research, including correctness, transparency, and citation practices, while also raising concerns about industry influence and the erosion of traditional standards.
Recommend 'The Little Book of Generative AI Foundations', a generative AI math fundamentals book covering core threads like PCA, SVD, VAE, diffusion models, targeted at agentic engineering practitioners.
OpenAI's AI model disproved the Erdős unit distance conjecture, a famous problem in discrete geometry that had stumped mathematicians for 80 years, marking a milestone in AI mathematics.
Thomas Bloom provides an expository blog post on recent counterexamples to the Erdős unit distance conjecture and sum-product conjecture over the reals, including an OpenAI-assisted disproof of the unit distance conjecture and a collaborative disproof of the sum-product conjecture, sketching the constructions and intuition behind them.
Greg Brockman highlights how AI gives researchers like mathematician Terence Tao the freedom to explore bolder, more creative ideas in their work.
Terence Tao and Mark Chen discuss how AI is changing mathematical research, from literature search to code generation, and the need to adapt workflows.
The article explores extending rock-paper-scissors to more than three options by allowing ties, revealing richer game dynamics and strategies through graph theory.
ATLAS is a large-scale Lean 4 library of textbook mathematics autoformalized by LLMs, covering 26 books with over 46,000 declarations. It provides reusable formal building blocks for human and machine-driven formalization.
A curated GitHub collection (Mathematics for Machine Learning) that organizes books, papers, video lectures, and math basics for learning the math behind machine learning, covering linear algebra, calculus, probability, statistics, and more.
Since the start of 2026, AI has completely solved at least 10 Erdős problems at an overwhelming speed, and if new solutions are included, it reaches 19, which is regarded as the 'Spinning Jenny' of mathematical research.
Google DeepMind's AI agent autonomously solved 9 of 353 open Erdős problems in mathematics at a cost of a few hundred dollars per problem.
A webpage presenting known optimal packings of unit squares into a larger square, with interactive SVG diagrams for various numbers of squares.
A thread explaining the mathematical foundations behind key transformer concepts including attention, scaling factor, backpropagation, gradient descent, cross-entropy loss, RoPE, and RMSNorm.
Alexander Grothendieck revolutionized 20th-century mathematics through his work in algebraic geometry, focusing on hidden geometric structures and relationships between objects rather than the objects themselves.
A digital reproduction of Oliver Byrne's 1847 colorful edition of Euclid's Elements, featuring interactive diagrams, posters, and puzzles.
Discusses that the mathematics used by AI is mainly linear algebra, calculus, etc., from before the 19th century, but emerging phenomena such as Scaling Law, emergent abilities, double descent, in-context learning, and representation geometry lack mathematical explanation. Analogizes to the clouds in physics in 1900, suggesting it may drive the development of 21st-century mathematics.
A tweet shares a lecture at MIT by David Shirokoff covering the fundamentals of Markov Chains, including transition probabilities, Markov matrices, eigenvalues, and long-term steady state.
Daniel Lemire explores what fraction of 64-bit integers can be expressed as the product of two 32-bit integers, finding that only about 17% are, with implications for hash function design.
An open-source book that builds the mathematical foundations of large language models, covering linear algebra, calculus, probability, and transformer architectures, with over 1000 pages of clear explanations and practical examples.
OpenAI claims its unreleased reasoning model has solved the 80-year-old planar unit distance problem in mathematics, producing an original proof that outperforms traditional grid-based arrangements.