Vacuum decay, a process that could end the universe as we know it, may happen 10,000 times sooner than expected. Fortunately, it still won’t happen for a very, very long time. When physicists speak of […]
Vacuum decay, a process that could end the universe as we know it, may happen 10,000 times sooner than expected. Fortunately, it still won’t happen for a very, very long time. When physicists speak of […]
A group of nine mathematicians has proved the geometric Langlands conjecture, a key component of one of the most sweeping paradigms in modern mathematics. The proof represents the culmination of three decades of effort, said […]
In 1940, the French mathematician and artillery officer Jean Leray was taken prisoner by the Germans. He told his captors that he was a topologist, fearful that if they discovered his true area of expertise, […]
Ask a question of ChatGPT and other, similar chatbots and there’s a good chance you’ll be impressed at how adeptly it comes up with a good answer — unless it spits out unrealistic nonsense instead. […]
Nitrogen is fundamental to all life on Earth. Organisms use it to make amino acids and nucleic acids — the building blocks of proteins and DNA — among other vital molecules. Luckily, four-fifths of the […]
Sometimes mathematicians try to tackle a problem head on, and sometimes they come at it sideways. That’s especially true when the mathematical stakes are high, as with the Riemann hypothesis, whose solution comes with a […]
Deep in the Caucasus Mountains, on the border between Russia and Georgia, an unusual experiment is taking place. In an underground lab shielded by a mountain of rock, highly radioactive material sits inside a vat […]
In the fall of 2014, Andrew Wilson took a front-row seat in Ken Ono’s number theory class at Emory University in Atlanta. Wilson was not only double majoring in applied math and physics, he was […]
By now, many people think they know what machine learning is: You “feed” computers a bunch of “training data” so that they “learn” to do things without our having to specify exactly how. But computers […]
In the tiling of wallpaper and bathroom floors, collective repeated patterns often emerge. Mathematicians have long tried to find a tiling shape that never repeats in this way. In 2023, they lauded an unexpected amateur […]
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