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On 24 May 2000, a group of mathematicians took to a stage in Paris to set some problems. These were the seven Millennium Problems, the hardest mathematical puzzles then known. The exercise was organised by the Clay Mathematics Institute, a nonprofit that promised anyone who could solve one would be rewarded with a ＄1 million prize.

Twenty-five years later, how have mathematicians got on? Grigori Perelman proved the Poincaré conjecture, the only Millennium Problem to fall so far. A conjecture in maths is a statement thought to be true but not yet proven. But what about the six that remain?

In fact, tools are everything for mathematicians. That is why Isaac Newton and Gottfried Wilhelm Leibniz each developed calculus ( 微积分) in the late 17th century. Back then, there was no technique for describing properties that change over time or space. But once the right tool is in the right hands, progress is almost inevitable: with calculus, Newton performed mathematical miracles such as describing the motion of the planets under gravity.

Now there is a new tool that might make quite a difference. " Machine learning is quickly developing as another tool in the toolbox," says Dan Freed at Harvard University. But, he adds, " Some of the Millennium Problems might be less amenable to using machine learning. " That is because AI relies on being fed lots of data. In many fields, large volumes of useful data simply don't exist.

Even in the absence of large datasets, there might still be scope for AI to dig into complicated mathematical arguments. " One of the interesting things about these millennium challenges is that the problems can be simple enough for us to pose, but might have a complexity to the proof that is beyond the human mind to navigate," says Marcus du Sautoy at the University of Oxford. AI might have the required potential to find buried links, which mathematicians can then pick up and work with. " Over the next decade, we might see some interesting new conjectures emerging that we wouldn't have been able to see without the use of this tool," he says. Just as Galileo was able to see more of the heavens using a telescope, AI could give a deeper view of numbers.

Whether the Clay Mathematics Institute would accept an AI-led solution to one of its problems depends on mathematicians' willingness to see it as solved. In 2000, when the prizes were announced, Alain Connes at the College de Francein Paris, said the seven problems were "totally inaccessible to computers". But with mathematicians now open to working with AI, that seems like one more conjecture that might fall.