“If you are a mathematician,” one of the world’s leading mathematicians recently wrote, “you may want to make sure you are sitting down before reading further.” And you’ll definitely need to sit down ...

Last week, OpenAI shocked the mathematical community by revealing that one of its internal artificial intelligence (AI) models had found a counterexample to a famous conjecture made by legendary ...

OpenAI claims its new reasoning model has produced an original mathematical proof disproving a famous unsolved conjecture in geometry, which was first posed by Paul Erdős in 1946. If this sounds ...

A new quantum-inspired algorithm has cracked a problem so massive that conventional supercomputers struggle to even approach it. Researchers used the method to simulate extraordinarily complex quantum ...

Penn researchers have developed a smarter AI method for solving notoriously difficult inverse equations, which help scientists uncover hidden causes behind observable effects. By introducing ...

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Liam Price just cracked a 60-year-old problem that world-class mathematicians have tried and failed to solve. He’s 23 years old and has no advanced mathematics training. What he does have is a ChatGPT ...

The original version of this story appeared in Quanta Magazine. In 1939, upon arriving late to his statistics course at UC Berkeley, George Dantzig—a first-year graduate student—copied two problems ...

Determining the least expensive path for a new subway line underneath a metropolis like New York City is a colossal planning challenge—involving thousands of potential routes through hundreds of city ...

The leading approach to the simplex method, a widely used technique for balancing complex logistical constraints, can’t get any better. In 1939, upon arriving late to his statistics course at the ...

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If you want to solve a tricky problem, it often helps to get organized. You might, for example, break the problem into pieces and tackle the easiest pieces first. But this kind of sorting has a cost.