In April 2013, Yitang Zhang, an adjunct professor at the University of New Hampshire at the time, emailed a proof titled “Bounded gaps between primes” to Annals of Mathematics, a journal published by both Princeton and the Institute for Advanced Study. The proof is related to the Twin Prime Conjecture, a long-standing mathematical problem that aims to prove that there exists an infinite amount of twin primes – prime numbers that differ by exactly two – like 5 and 7, 11 and 13, and so on. Zhang’s submission did not prove this for all primes, yet he established an upper bound of 70 million. Just days after his submission, Zhang became a national sensation.
In September 2026, OpenAI, an A.I. research and deployment company, released an article titled “On the Navier-Stokes Millennium Prize Problem”, in which they announced a solution to the Navier-Stokes existence and smoothness problem, part of a designated list of seven mathematical problems deemed so difficult that the reward for solving one is a staggering one million dollars. The Navier-Stokes equations describe and predict how fluids, like liquids and gas particles, change throughout time. The reason why solving this would be a big deal is because these equations have existed for centuries yet mathematicians have gained relatively minimal information about how they behave up to this point.
But to me, these two stories are more different than they are similar. Both share remarkable breakthroughs in the field. So, what sets them apart? I believe there is an apt word: humanity.
Zhang did not merely wake up one day and decide to submit revolutionary mathematical findings, nor was he motivated by any monetary benefit. His story is far more interesting, and it captures the true essence of pursuing mathematical research – one of genuine human curiosity, grit, and humility.
For OpenAI, its idea for writing the proof came about rather suddenly; according to their article announcing the proof, it was after they got word that two Millennium Prize problems had been solved earlier that month. Inspired by these rumors and what they described as a “step size change” in the performance of their internal model, they quickly launched an effort into trying to solve one of the other problems using a system of coordinating agents. They published the results of their solution just a week later.
OpenAI’s motive stands in stark contrast to the human-driven pursuit embodied by mathematicians like Zhang. For people like him, the project blossoms out of a question they have about the world, and what steps they will take to answer it, even if that means years of stagnance or setback. For a corporation like OpenAI, their goals become a little different. Sure, you could point out that it’s obvious why a for-profit company would want to involve itself in something like this. After all, I had mentioned earlier that the stake in the game is a million dollars. But Dr. Elijah Fender, a Bellevue College mathematics professor whose own research spans Hamiltonian mechanics and dynamical systems, pointed out a different perspective to their incentives.
“The money isn’t the Millennium Prize. It’s the press,” Fender said. “Math is treated as this high ivory-tower discipline, and it looks very good if their product can do a thing most of society cannot. You don’t need to prove the Navier-Stokes equation if your product is already self-evidently useful.”
So it seems as though this is another one of OpenAI’s ways of asserting dominance in the A.I. sphere, which is not something we aren’t already familiar with. Ever since A.I. took the world by storm, it has been a consistent rat race over which company releases the next frontier model. And Fender implies that it seems as though these companies can get a little insecure at times, feeling the need to prove that their products are indeed winning the race.
Yet there is also a deeper issue than what the incentive is for a proof like this to come out, and that concerns what a proof is actually supposed to achieve.
Sure, a group of 10,000 or so agentic robots have the ability to make logical connections at a much more efficient rate than what the human mind is capable of, but the point of solving a long-standing problem like this does not solely lie in the final output. It is an act of the translation of gained knowledge, to cement human achievement for centuries to come via deliberation, contestation, and amendment. It’s easy to imagine that conjuring up a proof within days using a machine could potentially distance the researcher from the crux of the findings in a way that doing it naturally, over a much longer time span, wouldn’t. As Fender notes, math functions quite like art.
“The point of any art is relating to another human being and the pursuit of truth. You could prove the most beautiful thing in the world, but if you do it in a way that you couldn’t explain it to somebody else, that thing dies with you. That’s not human knowledge if nobody understands it.”
While it’s true I may have gripes with the growing role A.I. is playing in the field of mathematics research, I will admit that this feat is nothing short of impressive. After all, the math that created this intelligence to begin with was discovered by humans. And it is becoming clear that this technology will only get better, allowing us to discover more insights into the entrenched language of our universe that we have cherished since its discovery. So it may be that working with it in part will come to be inevitable. But we must not forget the very reason we humans invented research in the first place: to have a genuine curiosity for why the world works as it does – or as we may prove, it doesn’t.
