Why do the seven million-dollar math problems stay unsolved, even in the age of AI?
AI has cracked Go and protein folding, yet seven math problems handed down from the 1900s remain. These seven are no random set but a list chosen exactly a century apart, and AI stalls because they demand proof, not computation.
AI has beaten the world champion at Go and solved a protein-folding problem that stood for decades. Yet math problems handed down from the 1900s are still untouched, even with a million dollars riding on each. Why does the cleverest tool we have come to a halt before these seven? To see the answer, we first have to see how the seven ever came to sit together.
To say "they are hard, so no one can solve them" is too flat. There is something more interesting. These seven were not gathered at random but chosen on purpose, exactly a century apart. In 1900 one mathematician announced the problems the twentieth century ought to solve, and precisely a hundred years later, in 2000, an institute took up that spirit and posted seven problems for the twenty-first century to mark the new millennium. So understanding what these problems are is the same as joining two scenes in the history of mathematics.
So these seven are not merely a collection of hard problems. They are a landmark in the history of mathematics, a direction one person drew a century ago, taken up and re-bound by successors a hundred years on. This is also where AI's halting shows itself. These problems demand not fast computation but a new proof, a leap of thought no one has yet had. Computation is walking a road quickly; proof is laying a road that was not there.
Top: the timeline of a century handed down, 1900 to 2000 to 2003. Bottom: the field and current status of each of the seven problems. Tap the nodes and cards.
In Paris in 1900, David Hilbert laid out twenty-three unsolved problems at the International Congress of Mathematicians. He believed the list would set the direction of the coming century's mathematics, and indeed twentieth-century mathematicians wrestled with them and opened new fields.
Exactly a hundred years later, on 24 May 2000, at the Collège de France in that same Paris, the Clay Mathematics Institute announced the seven Millennium Prize Problems in honor of the centenary of Hilbert's lecture. An advisory board, consulting leading experts worldwide, picked the most important classic problems that had long resisted solution. Each carries a million dollars, seven million in all, with no time limit for solving them.
Tellingly, the two lists meet at one point. One of the seven, the Riemann hypothesis (posed in 1859), is the very problem that also appeared on Hilbert's list of twenty-three a century earlier. Unsolved across a hundred years, it earned a place on both.
So why can AI not solve them? The heart of it is that these problems are not to be computed but proved. Go is a search through possibilities and protein folding is learning from vast patterns, but a mathematical proof argues, without a gap, that something must hold across infinitely many cases. No amount of checking cases ever amounts to a proof. And one of the seven, the P versus NP problem, asks, paradoxically, just how far the limit of what a machine can quickly solve actually reaches. Until that is answered, the limit of AI itself remains undecided.
These problems do not stay on the blackboard. The Riemann hypothesis is about how prime numbers are distributed, and primes are the basis of today's internet encryption. P versus NP asks about the fundamental limits of the search, logistics, and scheduling we use every day, and Navier-Stokes is the fluid equation that weather forecasting and aircraft design stand on. The problems that look most abstract are in fact holding up the bottom layer of the technology we lean on daily. So the day one of them is solved will be not merely the day a mathematician collects a million dollars, but the day some floor of the world is laid anew.