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OpenAI announces ten results on long-standing open problems in mathematics and theoretical computer science, achieved by an internal version of its next model Astra, with proofs formalized in Lean.
A post claims that mathematical breakthroughs can be achieved with a few prompts, linking to a ChatGPT conversation.
A new arXiv paper disproves Maxwell's 1873 conjecture by presenting a configuration of five point charges with at least 24 non-degenerate critical points, exceeding the conjectured bound. The construction was suggested by OpenAI's GPT-5.6 Sol, with the authors verifying the mathematics.
GPT-5.6 Sol reportedly found a counterexample to the Maxwell conjecture, a 100+ year old problem, with human mathematicians communicating the result.
This paper investigates how LLM-generated difficulty ratings for math items align with actual student performance, finding that LLMs systematically underestimate difficulty for items driven by learner misconceptions, a phenomenon termed the 'Easy Trap'.
A practical book introducing logic for programmers to improve software design, verification, and reasoning, covering topics from simplifying conditionals to formal verification and constraint solving.
A free 674-page PDF of the textbook 'Introduction to Machine Learning' by Laurent Younes is available, covering mathematical foundations and algorithms for machine learning.
An AI system called Theo Conjecture, leveraging a large language model, solved a 35-year-old graph theory problem originally posed by mathematician Paul Erdős, discovering an unexpected term. The system works by proposing, testing, and revising mathematical ideas in a loop.
Hillel Wayne announces the completion and 1.0 release of his book 'Logic for Programmers', a guide to using logic in software development, now available in print and as a free update for early ebook buyers.
A researcher describes a project to mathematically formalize truth, justification, and trustworthiness of AI-generated claims, seeking input on formal methods, logic, and probability theory for building a 'Trust Engine'.
This paper proves that the Burau representation of the braid group B_4 is faithful, settling the final unknown case in a long-standing problem in low-dimensional topology.
Roman Vershynin's textbook 'High-Dimensional Probability' second edition is available as a free PDF download from the author's website, targeting doctoral students and researchers in data science.
Promotion of the book 'Mathematical Methods in Data Science' which bridges theory and applications using Python, available on Amazon.
The article discusses how AI models like Anthropic's Fable and ChatGPT have been used by mathematicians to disprove famous conjectures, suggesting a new paradigm of brute intelligence in fields with verifiable answers.
A mathematician describes a spiritual crisis triggered by recent LLM-generated counterexamples to long-standing conjectures, arguing that the human experience of mathematical discovery is vital and threatened.
An educational tweet explaining that tensors are not just bigger matrices but mathematical objects representing relationships across dimensions, independent of coordinate systems, and foundational to physics, engineering, and deep learning.
A curated list of free eBooks, papers, and video lectures on mathematics for machine learning, aggregated from the dair-ai/Mathematics-for-ML GitHub repository.
A blog post shares a free PDF of 'All You Wanted to Know about Mathematics but Were Afraid to Ask: Mathematics for Science Students, Volume 2' by Louis Lyons, covering advanced mathematics topics for physics and engineering students.
A 585-page open-access PDF textbook on game theory from arXiv, containing 165 solved exercises.
A free PDF of the Linear Algebra textbook by David Cherney, Tom Denton, and Andrew Walton from UC Davis is shared, emphasizing its importance for AI and data science.