Our best equations for describing the way fluids move were first written down two hundred years ago and ever since nobody has been able to answer a simple question about them – do they sometimes blow up? This explosive phrase has a precise mathematical meaning describing where apparently out of nowhere, part of the fluid starts to move infinitely fast. It would be like an infinite whirlpool forming in your bathtub in response to a flick of your toes.
Understanding the Navier-Stokes equations – named after the pair who discovered them – has been a long running quest for mathematicians. So much so that the blow-up question sits on the list of prestigious Millennium Prize Problems, each of which comes with a $1 million reward for solving. This week, OpenAI stunned the world of mathematics with its announcement that its AI agents have finally found the answer: the equations do sometimes blow-up.
The implication is not that fluids will start misbehaving but instead that the equations are not perfect. This is good news for your bathtub. Mathematics, however, may never be the same again.
Terence Tao: AI companies are harming mathematics The reason for this is not the result itself. The Navier-Stokes equations have already proven themselves many times over to be incredibly useful in applications ranging from making better airplane wings to modelling the flow of fluids through artificial hearts. Mathematicians had a suspicion that blow-ups were possible, now they know for sure.
That’s not to underplay the discovery, it is one of the biggest mathematical breakthroughs in decades. But the way it has happened, and the resulting fall out, is what will have the most dramatic effect on mathematics for years to come. OpenAI began working on the problem after they got wind that a pair of mathematicians had made some progress, which hadn’t yet been published.
Researchers at the tech company decided to set thousands of their AI agents on solving the problem. Just 88 hours later, they were done. OpenAI has solved the Navier-Stokes Millennium problem using $15m of AI effort Over the last few months, AI has made breakthrough after breakthrough in mathematics with this most recent development being by far the most impressive.
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