Transformation

“Exponential” is a widely misused term. It shows up as a synonym for “rapid,” but its precise meaning is far more remarkable. As many readers of Quanta will already know, it means to double and double and double again, the pace of change accelerating faster and faster. It’s hard to develop intuition for just how rapid this kind of growth is, not least because it rarely lasts: Changes begin to come so quickly that they run out of steam.

Computing power is an exception that has held for the better part of a century. Built atop that exponential growth, frontier artificial-intelligence models have likewise grown exponentially for the last decade and a half.

In the autumn of 2025, I began reporting a feature for Quanta about the impact artificial-intelligence algorithms were having on math research. In all candor, I expected that impact to be limited. I knew that AI had a tendency to hallucinate, and in my limited firsthand use of large language models, I’d found them unreliable. I’d been a journalist for two and a half decades, so tech industry hype was not new to me. I knew that some serious people were using AI on real problems — I expected to find that, like any other tool, it would have certain interesting niche uses. The possibility that it might transform the discipline seemed remote.

As I reported the story over the course of the last months of 2025 and the first of 2026, I was surprised by what I found. Fundamental change had not yet arrived, but it was impossible to avoid the conclusion that it was coming. My intuition for what exponential growth can do was — predictably — off.

Over this past summer, the scale of the change AI is bringing to math has become clearer. As Akshay Venkatesh of the Institute for Advanced Study wrote in a prescient essay: “Mechanical reasoning will change not only how we do mathematics, but what it is; this must be renegotiated amongst its practitioners and with society.”

These updates are intended to be a chronicle of that renegotiation, which is now underway at a rapid, sometimes frenetic, pace.

Our goals here are twofold.

First, as new results are established with the aid of artificial-intelligence algorithms, we will explain them in a timely fashion. We will put new results in mathematical context: How important do mathematicians think the latest counterexample is? How novel is a connection that AI discovered between different branches of math? What are the potential consequences of a new method of proof? Did AI reveal that a problem previously thought to be hard was simpler than it seemed, or did it solve a hard problem?

Second, we will cover the ways in which mathematicians are wrestling with the changes AI is bringing to their discipline. That response is, like the mathematical community itself, varied. Some welcomed these changes; others now call for resistance to AI or even “total opposition to the use of artificial intelligence in mathematics.” How effective is formalization as a tool for combating AI slop? Can an AI model be a co-author on a paper, or even its sole author? How do peer review and mathematical journals change when AI is used to do math?

It is my expectation that some aspects of what it is to be a mathematician will abide through the transformations brought by AI. Others will, in all likelihood, be wholly changed.

These are just some of the topics we will tackle. If you have an idea for something you think we should cover, we’d like to hear from you. Please write us at [email protected].

These are, of course, big questions. We will continue to cover them both here and in the rest of Quanta’s digital pages.

Welcome to Transformation.