Which Millennium Prize Problem Will Be Solved Next?

One of mathematics` biggest prediction questions has reached Kalshi: which Millennium Prize Problem will be solved next?

Traders currently favor the Hodge Conjecture, putting it ahead of the Birch and Swinnerton-Dyer Conjecture and three other famously difficult problems on prediction market sites like Kalshi.

That leaves five problems competing for the next breakthrough in Kalshi`s market.

Hodge Conjecture Leads Kalshi`s Market

The Hodge Conjecture has emerged as the favorite among Kalshi traders. Recent market tracking has put it around the mid-40% range, although prices have moved considerably since trading began.

When the market was listed on September 12, Hodge was already the frontrunner, with an ask price of 56 cents. The Birch and Swinnerton-Dyer Conjecture followed at 45 cents. The other three possibilities attracted substantially less support: Yang-Mills Existence and Mass Gap, the Riemann Hypothesis and P versus NP.

These prices are not assessments produced by mathematicians, but reflect what traders are collectively willing to pay and can change as new research emerges.

What Is the Hodge Conjecture?

The Hodge Conjecture deals with the relationship between algebra and geometry. In simplified terms, it asks how much information about the shape of certain mathematical spaces can be represented using algebraic equations.

The Clay Mathematics Institute notes that mathematicians know the conjecture holds in some special cases, but the general problem remains unresolved.

A solution would earn recognition as one of mathematics`most significant modern achievements. The Millenium Prize Problems were established by the Clay Mathematics Institute in 2000, with $1 million allocated to the solution of each problem.

Why Isn't Navier-Stokes in the Kalshi Market?

The market comes at an extraordinary time for mathematics. In September, OpenAI announced a solution to the Navier-Stokes existence and smoothness problem, but Navier-Stokes isn't an option because the Kalshi market opened after OpenAI announced its proposed resolution of September 8.

OpenAI said an experimental AI system had produced a proof showing that smooth fluid motion can develop a singularity in finite time. On September 11, Clay said the problem had “apparently been settled”, while stressing that its formal evaluation and credit process would be deliberately unhurried.

The development is particularly relevant because AI could also influence which problem falls next. Kalshi separately offers a market on when an AI lab will solve another Millennium Prize Problem.

How Will Kalshi Determine the Winner?

Kalshi`s market is scheduled to run as far as 2045, unless one of the listed problems is resolved first.

For a problem to qualify, the market rules require recognized evidence that it has been solved, rather than simply a researcher or AI company claiming a breakthrough.

That makes this an unusually long-term market, since today`s favorite could look very different after a major paper, AI breakthrough or new mathematical technique emerges.

You can follow more science and technology-related markets though our tech prediction sites coverage.