mathematics

A reference FAQ document covering matrices and quaternions, primarily for 3D graphics and game development, with corrections and contributions from multiple authors.

A personal account of hunting for million-digit prime numbers using a home computer setup.

The article describes a project that uses Fourier series and epicycles to reconstruct a human face on the three faces of a cube, demonstrating how sinusoids can generate complex shapes.

Mathematicians have extended the classic 1992 proof about card shuffling to less precise shuffles, showing that a 'cutoff phenomenon' still occurs even with uneven deck splits.

A GitHub repository aggregates complete math and science video course resources from top universities like Harvard, Stanford, and MIT, free and open-source, integrating all courses into one repository.

Weibo's VibeThinker-3B, a 3B parameter model, claims to match or exceed the reasoning performance of much larger models like DeepSeek V3.2 and Gemini 3 Pro on math and coding benchmarks, sparking debate over benchmark reliability and the necessity of scaling.

The tweet praises a mathematical idea timed well for AI inference's arithmetic profile and expresses interest in seeing results on reasoning models during long generation runs.

The First Proof test evaluated four AI systems on novel research-level math problems, with the top model scoring only 6 out of 10, demonstrating that current AI still lags behind top mathematicians in rigorous reasoning.

AI has progressed to the point of contributing to original mathematical research, outperforming human mathematicians and potentially reducing demand for the profession, though human-AI teams may ultimately excel.

This paper from the Axiom team investigates the rarity of lattice triangles, presenting a mathematical result on the distribution of convex lattice polygons.

This paper presents EinsteinArena, an agent-native platform enabling decentralized scientific discovery through open interaction among autonomous AI agents. The platform has already produced 12 new state-of-the-art results, including an improved lower bound for the kissing number problem in dimension 11, demonstrating that collective AI-driven research can emerge from agents sharing insights and building on each other's work.

24-year-old Carina L Hong raised $64M to build an AI that outperforms the world's best mathematicians, aiming to advance mathematical superintelligence and shape next-generation AI.

This paper applies graph neural networks to predict the solvability of finite groups, demonstrating an AI-driven approach to a classic problem in group theory.

Terry Tao, a renowned mathematician, discusses his evolving views on artificial intelligence in mathematics and his advocacy for large-scale collaborations and computer verification of proofs.

This book presents a mathematical theory of deep representation learning, aiming to demystify the internal mechanisms of large deep networks using optimization and information theory, making architecture design a matter of linear algebra and calculus.

This tutorial introduces functional analysis concepts needed in physical problems, covering Hilbert spaces, compact operators, and eigenfunctions, aimed at scientists and engineers.

Google new paper proposes the LEAP framework, which decomposes math problems into goal trees, learns from Lean verifier feedback, and improves LLM accuracy on math competition problems from 10% to 70%. It solves all 12 problems of Putnam 2025 and surpasses dedicated gold-medal-level systems on IMO-style benchmarks.

An OpenAI model found a counterexample to an 80-year-old Erdős conjecture, with researchers sharing the story on the OpenAI Podcast about how AI and mathematicians can collaborate on mathematical discoveries.

VAMPS is a new benchmark of 1,168 multimodal bilingual math problems designed to evaluate whether LLMs can benefit from constructing and reasoning over graphs/visualizations. Key finding: direct analytical solving surprisingly outperforms tool-enabled visual solving even on problems where plotting is a natural strategy.

The Leiden Declaration on Artificial Intelligence and Mathematics calls for action to address challenges and opportunities of AI in mathematics research, emphasizing ethical values and responsibilities. It is endorsed by the International Mathematical Union.