Maths news

The subject is alive.

School maths can feel like a finished object — a fixed body of rules handed down from somewhere. It is not. Here is what has actually been happening, in plain English, with a note on why each one might matter if you are learning the subject.

4 September 2026 · Formal verification

Fermat’s Last Theorem has been checked by machine, end to end

Pierre de Fermat claimed in about 1637 that an + bn = cn has no whole-number solutions for n > 2, and that he had a proof too large for his margin. It took until 1995, and Andrew Wiles, to produce one — 129 pages that only a handful of people on earth could check.

In 2024 Kevin Buzzard at Imperial College London began a community project to translate that proof into Lean, a proof assistant that verifies every logical step by machine. In August 2026, Anthropic’s Claude completed an end-to-end formalisation in eleven days, writing around 13 million lines of Lean and proving some 29,500 intermediate theorems. Buzzard reviewed the result.

Why it matters to you A proof assistant will not accept “it is obvious that”. Every step has to be justified from things already established. That is exactly the standard your teacher is reaching for when they ask you to show your working — and it is what STEP and the Oxbridge interview are really testing.

Anthropic’s write-up · Buzzard and Taylor’s blueprint

8 September 2026 · Millennium Prize

A Millennium Prize problem appears to have fallen

The Navier–Stokes equations describe how fluids move — water in a pipe, air over a wing, blood in an artery. The open question, one of the seven Clay Millennium Prize problems, was whether their solutions always stay well-behaved in three dimensions, or whether they can blow up to infinity in finite time.

In September 2026 two efforts announced results on the singularity question within a day of each other, both machine-verified in Lean. The work builds substantially on techniques developed by Diego Córdoba and Luis Martínez-Zoroa.

Read this carefully A Lean proof guarantees the argument follows from the stated assumptions. It does not guarantee that the statement formalised is the one mathematicians meant to prove — that check is still human, and it is still going on. There is also an active dispute about priority. Watching a claim of this size get scrutinised in public is a much better education in how mathematics works than any textbook account.

Quanta Magazine’s report

2026 admissions round · University entry

Oxford has retired the MAT

From the 2026 admissions round, the Mathematics Admissions Test is no longer run. Every applicant to Oxford Maths, Computer Science and their joint courses now sits the TMUA: two 75-minute papers, twenty multiple-choice questions each, no calculator, at a Pearson VUE test centre in mid-October.

The second paper is the interesting one. It tests mathematical reasoning — proof, logic, and whether you can tell a valid argument from a persuasive one — which school syllabuses barely touch.

Why it matters to you If you are applying to Oxford for maths, a lot of the free preparation material you will find is written for a test that no longer exists. Work from Oxford’s own page, and see what this changes.
September 2026 · The bigger picture

“What is mathematics for in the age of AI?”

The International Congress of Mathematicians — the discipline’s largest gathering, held every four years — spent a good deal of 2026 on exactly this question. The honest answer from the room was that nobody is sure yet, and that the interesting part is not whether machines can produce proofs but what mathematicians should now spend their attention on.

My take Every wave of automation in mathematics — log tables, the calculator, computer algebra — has raised the value of judgement rather than lowered it. Knowing which question to ask, whether an answer is plausible, and what a model is quietly assuming has never been automatable, and it is precisely what teaching principles rather than procedures builds.

Quanta, live from ICM 2026

Curious about any of this?

These are exactly the conversations I most enjoy having with students. They also happen to be the ones that make people better at the exam.