Clay Mathematics Institute

The Clay Mathematics Institute is a private foundation from the USA that supports mathematical research with money. It was founded in 1998 by businessman Landon T. Clay and his wife Lavinia. The foundation does not operate its own laboratories and does not teach students. It awards scholarships, funds conferences, and honors outstanding work. Worldwide, however, it is known for something else: a list of seven especially difficult, unsolved mathematical problems. This list is called the Millennium Problems, and a prize of one million US dollars has been offered for each individual problem.

Seven problems, seven million dollars

In the year 2000, the institute published the seven problems it considered the most important open questions in mathematics. The idea behind this was not merely publicity. A clearly formulated question with a high prize draws attention to a field of research and motivates young talent. The model was a list by mathematician David Hilbert from the year 1900, which had shaped the field for decades.

For the tech world, one problem in particular is of interest: the question of whether P equals NP. Put simply, this concerns whether every task whose solution can be quickly verified can also be quickly solved. A Sudoku puzzle is checked in seconds but tedious to fill in. If P equaled NP, there would be fast procedures for such tasks. Among other things, this would render today’s internet encryption useless, since it relies on the fact that certain calculations practically take too long to carry out.

Other problems on the list sound more abstract, but they are likewise tied to everyday technology. The Navier-Stokes equations describe flowing liquids and air. They are used daily in weather models and aircraft simulations, even though no one can mathematically prove that their solutions always behave cleanly.

How to get the prize money

You cannot simply submit your solution to the institute and hope for it to be checked. The rules require that the work first appear in a respected specialist journal. There, other experts read it and look for errors, a process called peer review. After that, the solution must hold up in the professional community for two years.

Only then does the institute set up its own committee to give the proof a final assessment. These hurdles have a practical reason: every year, many people claim to have solved a Millennium Problem. Most submissions contain errors that only specialists can recognize. The institute therefore leaves the review to the normal scientific process.

To this day, exactly one problem is considered solved. Around 2003, the Russian mathematician Grigori Perelman proved the Poincaré conjecture, a statement about the shape of three-dimensional spaces. He published his work only on the internet, not in a journal, and the institute recognized the solution nonetheless. Perelman declined the million dollars in 2010. He considered the distribution of credit unfair, since other researchers had done important preliminary work.

Why the institute turns up in AI news

The Millennium Problems have become a benchmark by which companies want to measure the strength of their AI systems. When a company presents a new language model, the statement often comes up that it should eventually be able to do real mathematics. A Millennium Problem is then gladly named as a long-term goal. This is deliberately set high, since these tasks have resisted the best experts for decades.

So far, smaller successes are more realistic. AI programs help verify proofs, find counterexamples, or solve tasks at the level of mathematics olympiads. This is remarkable, but it falls far short of a Millennium Problem. Anyone reading such a headline should therefore check carefully which task was actually solved.

Incidentally, the institute is also an example of how private foundations steer research. Whoever offers prize money also helps decide which questions count as important. Similar models exist in the tech industry, such as announced competitions for autonomous vehicles or bug bounty programs, in which companies pay for discovered security vulnerabilities.