Much of mathematics is driven by intuition, by a deep-rooted sense of what should be true. But sometimes instinct can lead a mathematician astray. Early evidence might not represent the bigger picture ...

DeepMind’s AlphaEvolve helps solve a math puzzle with Terence Tao, showing how AI can now invent new ideas—and prove old ones ...

The Collatz conjecture is also known as the “3n + 1” problem. It’s an easy problem to explain and check, and has been tested up into the nineteen figure range. But it’s only now that anyone has come ...

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Mathematicians have proved a key building block of the Langlands programme, sometimes referred to as a “grand unified theory” of maths due to the deep links it proposes between seemingly distant ...

Consider a pencil lying on your desk. Try to spin it around so that it points once in every direction, but make sure it sweeps over as little of the desk’s surface as possible. You might twirl the ...

The artificial intelligence (AI) program DeepMind has gotten closer to proving a math conjecture that's bedeviled mathematicians for decades and revealed another new conjecture that may unravel how ...

The last dimension of Keller's conjecture has been proven using a computer algorithm. The conjecture involves the way hypercubes in different dimensions share sides when tiled. The proof is ...

This summer, as part of the Department's Summer Research Experience for Undegraduates and First-Year Graduate Students, graduate student Summer Haag, undergraduate Clyde Kertzer, postdoc James ...