A.I. VERSES MATHEMATICS

DR. ZEYNEP TUFEKCI HAS BECOME MY GO-TO on lofty matters: See “How Zeynep Tufekci Keeps Getting the Big Things Right,” Ben Smith, The New York Times, August 23, 2020. See also my “Plato, The Internet, Education, and A.I.,” December 17, 2022; “Grok Goes Bonkers,” May 23, 2025; and “Dr. Zeynep Tufekci Clarifies A.I.,” July 5, 2026.

This time she focuses on a matter close to my heart, mathematics: “This is a Rare Arena in Which People Think A.I. Is Helping. It’s Making Things Worse,” a Guest Essay, The New York Times, September 22, 2026. 

The Navier-Stokes Equations in Fluid Dynamics. Wikipedia observes that “The Navier-Stokes equations describe the motion of viscous fluids.” They are a system of partial differential equations, the sort of mathematics I have in mind when I say my Ph.D. in math is in “dynamical systems theory, sorta differential equations without the dirty bits.” 

Wikipedia is rather more specific in noting, “The Navier–Stokes equations are also of great interest to pure mathematics. The Navier–Stokes existence and smoothness problem concerns whether they have smooth (meaning infinitely differentiable) or bounded solutions in three-dimensional Euclidean space, as opposed to a breakdown with unbounded solutions. This is one of seven Millennium Prize Problems, notable open mathematics problems for which the Clay Mathematics Institute offered $1 million prizes in 2000 for correct solutions. In September 2026, OpenAI announced a claimed counterexample to the existence and smoothness problem. The announcement was followed by a priority dispute, and the claimed counterexample has yet to be independently verified.”

Talk about “dirty bits.” But let’s accept this as the starting point for the Tufekci article.

Good News? No, Bad. She recounts, “The proof hasn’t been independently verified yet, but amid all the debate about artificial intelligence and the companies that develop it, it looked like something everyone could feel good about, an example of A.I. truly advancing human knowledge rather than trying to sell us something or control our lives.”

“In truth,” Dr. Tufekci says, “it was precisely the opposite: the clearest evidence yet that generative A.I., rather than aiding scientific progress, may be thwarting it.”

LLM Basics. Recall the underlying idea of A.I.’s Large Language Models: They scrape data from everywhere, good and bad, relevant and irrelevant, and then play probabilistic games of conceptual next words: “To be _____”? Ah, an easy one: “or not to be.” 

But what about “determined at a later date”? Or “ ‘Hero X’ Season 2”? Or “absent from the body is to be present with the lord 2 Corinthians 5:8.” 

Remember, I’m leaving out the dirty bits.

The Matter of Intellectual Property. How would Apostle Paul feel if A.I. agents latched onto this last one? Or, as Dr. Tufekci observes, “For starters, two mathematicians who had been trying for months to reach their own solution to the famous problem say the new proof appears to have ripped off their unpublished work, which also used an OpenAI model. The company, after first equivocating, quickly changed its tune: It said the model it used for the solution had not looked at any of the prompts that the lead mathematician had entered into the OpenAI model within the last two months. Whatever the case, to get to the finish line in so little time, OpenAI had deployed an advanced model not available to the public, using computing power that would have cost an outsider an estimated $15 million. How could regular researchers compete with a secret tool that has the power to steal your work and mint its own money?”

And Cui Bono? As lawyers inherited from Cicero, “Who profits?” Dr. Tufekci observes, “Flashy finishes like this don’t necessarily contribute to mathematical knowledge. Terence Tao, perhaps the most prominent mathematician of his generation, is generally positive about A.I. and math—so positive that he was featured in one of OpenAI’s ads. But contemplating the possibility of Navier-Stokes being solved by A.I., he wrote a long post explaining that ‘in most cases in pure mathematics, the problems are posed not because we desperately want the solution to these problems in and of themselves.’ Instead, mathematicians want to see all the work that goes into achieving the solution—all the not-quite-right hypotheses that got adjusted this way or that, all the seemingly dead ends that ‘in fact end up being highly instructive in the nature of their failure.’ ”

Cui bono? In the mathematical sense, only the A.I.’s public-relations departments (and company stockholders).

What of Academic Research? Dr. Tufekci recounts, “OpenAI rushed to undertake this challenge because a rumor was circulating that Anthropic, its chief rival, had solved one or two famously daunting math problems. Why would mathematicians present at conferences or publish early work — why would they even talk to colleagues — if the rumor of a solution to a big problem causes an A.I. company to swoop down and spend huge amounts of money to steal the thunder?”

Plus, hitherto, academic research has the tradition of peer-review. By contrast, even the A.I. companies admit that they don’t quite understand what their agents are doing. As Dr. Tufekci notes, “What’s slop and what’s not? Is there an actual gem amid the gazillion new hypotheses? It’s becoming increasingly impossible to tell.”

Thanks, Dr. Tufekci. And, by the way, this only confirms the idiocy of Trump’s guardrails comment about “a STRONG AND SMART (High IQ) PRESIDENT, and the U.S.A. has that, in spades!” ds

© Dennis Simanaitis, SimanaitisSays.com, 2026