Among the 377 results that OpenAI announced on October 6, 2026, one stood out. It claimed to settle the “quasi-Riemann hypothesis” — a weaker version of the Riemann hypothesis, which is arguably the biggest open question in math. The new proof is, as Jared Duker Lichtman of Stanford University put it, “the most significant AI-for-math achievement so far, by quite a margin.” The Riemann hypothesis has been an open problem for over 160 years.
Resolving it would enable mathematicians to better understand the nature of prime numbers, one of math’s most crucial building blocks. And that’s just for starters. The implications of even the more limited “quasi-RH” result are “staggering,” said Maksym Radziwiłł of New York University.
The result relied in part on techniques pioneered by Radziwiłł and Dunn. Alongside other number theorists, they have been working to understand the proof and what it could mean. Now they’re starting to get answers.
To understand what the quasi-Riemann hypothesis says, you first have to understand the Riemann hypothesis. When the Clay Mathematics Institute announced seven Millennium Prize Problems at the turn of the century, the Riemann hypothesis loomed above the other six. It was the only one carried over from the celebrated agenda-setting list of problems that David Hilbert had announced a century earlier.
On its surface, the conjecture concerns the behavior of a particular function. Start with the sum $latex 1 + \frac + \frac + \frac + \cdots $. Now use that sum (together with a special mathematical trick to extend its scope) to build a more general function, called the Riemann zeta (ζ) function: $latex \zeta (s) = 1 + \frac + \frac + \frac + \cdots$ Here, the input s is a complex number.
Complex numbers have two parts — a “real” part and an “imaginary” part, which is a multiple of the square root of −1 (written as i). Any complex number can be thought of as a point on a plane: The Riemann hypothesis is about which values of s will make the zeta function equal zero. But it is also about far more than how this particular function behaves.
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