How Emmy Noether's theorem uses the Lagrangian to provide a formula for calculating the quantity of symmetries in a system—like the orbit of planets.

Noether discovered that for every continuous symmetry of a system, there is a conserved quantity—that is, a quantity that ...

When the Leiden Declaration on Artificial Intelligence and Mathematics went live on 2 June 2026, things moved quickly. The ...

In the mid-noughties, when music by the Killers and Franz Ferdinand blared out of every pub and nightclub I passed, I spent ...

Decades ago, Paul Erdős used randomness to illuminate the vast and weird world of networks. Now mathematicians are making his ...

Consumers are rethinking beauty spending as value becomes more important than prestige. From magnetic lashes and press-on ...

Trading squishable toys might impact your kids more than you’d think.

Large language models can write essays, summarize legal clauses, explain ancient history, draft emails, and produce code that ...

With Midsummer Classic approaching, a look at some players who deserve a nod.

ChatGPT's breakthrough is not what it seems.

Last week, I introduced Emmy Noether, an extraordinary figure in the fields of mathematics and physics. To understand Noether ...

Below is a list of the main sub-projects in this repository. Each folder contains documents, code, or both, related to a specific mathematical or machine learning topic.