OpenAI's unreleased Astra model has produced what its October 2025 announcement only pretended to: genuine solutions to ten long-standing open problems in mathematics and theoretical computer science, ...

A deep technical guide to how modern AI really works—from neural networks and transformers to RAG, embeddings, reasoning ...

Predictive AI develops human-aligned AI systems for advanced image and video enhancement. Artificial intelligence is almost universally described through optimization. Ask why Layer Normalization ...

OpenAI’s Astra generates machine‑checkable proofs for ten decades‑old math problems, showing how verified AI can cut ...

Sebastien Bubeck of OpenAI says “yes, nonsofic groups exist”—as an example of “many new beautiful results” from Astra, next major OpenAI model. OpenAI published a page and PDF detailing ten advances ...

To use a spreadsheet with all its power you need to understand how to use symbols to represent cells and how to use formulas ...

But from the perspective of research mathematicians, and especially young people who are pursuing a Ph.D. in mathematics, ...

Alpöge’s discovery is the latest in a string of high-profile mathematical breakthroughs made by large language models. Recent examples include OpenAI’s disproof of the unit distance conjecture, and ...

Al-Khwarzmi: Father of Algebra and the Algorithm is a free educational AI-animated docudrama chronicling Al-Khwarizmi's ...

AI is increasingly being used as collaborators in mathematical research rather than simply as computational tools.

Recently, a technique called equality saturation adapted e-graphs for program optimization. Equality saturation can ...

Explore our campus, meet lecturers and current students, and learn more about what it's like to study at Manchester. We place social responsibility at the heart of your learning which means you can ...