Humans and AI race to ‘blow up’ math’s toughest equations

The million-dollar race to ‘blow up’ math’s hardest equations

New results challenge AI’s promise for solving how fluids swirl—and suggest a more human path forward

Whenever I get coffee with a mathematician, I always ask which of the seven Millennium Problems they think will be next to fall. These are math’s most famous open questions . Solve one, and you’ll win a $1-million prize—but it’s only happened once since the Clay Mathematics Institute announced the list in 2000.

Mathematicians often use the Millennium Problems as a kind of yardstick, lending prestige to their own work by counting how many degrees separate it from a million-dollar payout. I think of them as a way to sense movement in a discipline where breakthroughs often take decades to unfold.

And I’ve recently begun hearing a totally new answer to my query on which will fall first. Lately mathematicians have been flagging one of the seven problems which experts previously told me was centuries beyond their grasp. It concerns mathematicians’ attempts to understand something far more familiar than imaginary numbers or string theory: the perplexing movements of fluids.

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We’ve all been enthralled by a crashing wave or cascading waterfall . These intricate flows bely deep mathematical challenges—the ones that keep us from comprehending exactly how planes fly or from perfectly predicting next week’s weather. Mathematicians have been wrestling with the equations that rule over these flows for centuries. All the while, a single basic question about these equations has eluded them, despite the addition of a million-dollar bounty.

A sustained run of recent breakthroughs, however—some trumpeted for their use of artificial intelligence—has now convinced some prominent mathematicians that victory is close at hand. Meanwhile, others still question how far the AIs can carry us—and whether a deeper, more worldly understanding might be the more viable path.