Terry Tao is the most famous and award-laden mathematician working today. He is known for his groundbreaking work in many areas of mathematics and when he speaks, people listen. A few weeks ago he took to the stage at the International Congress of Mathematics, held every four years, to give his lecture, “Mathematics in the Age of AI.” He voiced concern about what he called an unprecedented threat. “AI has created a crisis in our mathematical values and practices,” he said, and his words resonated because, just days before, Anthropic’s Claude Fable AI program had solved the so-called Jacobian conjecture which has puzzled mathematicians since 1939. It was a devastating achievement, all the more so because the solution fitted into a single tweet.
But the Jacobian conjecture is far from the only high-level math problem toppled by AI this year. In May, OpenAI announced that it had cracked the “unit distance” problem. Eighty years of struggle by mathematicians was ended by a simple inquiry to a chatbot. Experts praised the solution as elegant and clever. Daniel Litt of the University of Toronto, who was asked by OpenAI to verify the proof, said: “This is the unique interesting result produced autonomously by AI so far.”
Math is at a watershed because AI is producing solutions faster than mathematicians can read them
Then, last month, OpenAI announced that it had solved ten major problems in mathematics and theoretical computer science, some of which mathematicians didn’t expect to be figured out in their lifetimes. Just last week, an OpenAI model reportedly solved a so-called Millennium Prize Problem, the first in 20 years. This million-dollar-prize puzzle involved the equations that govern the motion of fluids, the Navier-Stokes equations, which describe the flow of water from a bathtub, the swirl of hurricanes and the development of an El Niño. Thanks to AI, we now know this important equation is fundamentally flawed.
But what will AI’s achievements do to the practice of mathematics, and the humans pursuing math? The Fields Medal is math’s highest prize, and now 24 Fields medalists, including Tao, have written an open letter of objection entitled “A Severe Misalignment of AI in Mathematics,” posing the question: is AI ruining math? It’s the question of the moment. The letter says that solving sometimes age-old problems that have foxed generations is only part of what math is all about. AI does not bring understanding, it says, and is poor at explaining what it has done. What’s more, it is disillusioning students who now think of math as a subject with no future for them. “The issues the mathematical community faces… [involve] how to make sure that, as AI changes the way work is done, we do not lose sight of what that work was meant to achieve in the first place,” read the letter.
Bryna Kra, of Northwestern University, goes further. She says AI has broken all aspects of math. She says that for generations, the production of theorems – mathematical statements that can be demonstrated to be true – was the primary measure of mathematical success and progress. Sometimes they took a lifetime or more to produce and positions and prizes were based on them. A good theorem opened the door to a deeper understanding.
But, she adds, because AI will lower the cost and shorten the time of producing these proofs, fabled mathematical conjectures will fall with increasing rapidity. In fact, AI is producing solutions faster than mathematicians can read them. Because of this, math is at a watershed, she says.
The ever-growing power of AI is forcing the mathematical community to confront some profound issues – after which math as we know it will be history. Humans have a new tool, some would even say partner, in exploring numbers and their properties. Whatever happens, math will never be the same. This is, literally, year zero.
Built up over thousands of years of human thinking, this intellectual edifice, which is perhaps the closest humanity comes to touching the infinite and the eternal, could collapse. Fundamentally, people study pure math for many reasons – but chiefly a passion for beauty and truth. The quest could be snatched away from us and taken into new dimensions in ways we might not understand. What if AI produces a major proof and no human can appreciate how it was arrived at? What then do mathematicians do, aside from write letters? What happens to math when a machine can do it better?
We are at the start of a new age in math, and perhaps even a new era in human intellectual growth. The industrial revolution scaled labor and changed the world; now the AI revolution is scaling knowledge and the world will change much more. The hope of mathematicians such as Tao is that AI will pause and do the grunt work, mining what we already know and leaving the high concepts free for humans to imagine new mathematical universes and seek eternal truth and beauty.
For now there is a temporary symbiosis. Large language models will be better when there is a trial-and-error approach to finding a proof, the ability to try a lot of ideas which are not particularly novel until the LLM eventually gets lucky. Humans will, for the moment, provide the conceptual leaps that logic alone cannot explain.
But perhaps AI will also take that away from us. Scientists are testing AI’s capacity for ingenuity by feeding pre-Einstein science into an LLM to see if it will come up with Einstein’s revolutionary ideas all on its own. At the moment LLMs can’t make this leap of creativity, but no one is sure if that will always be the case.
When he found an elegant proof, the great mathematician Paul Erdős used to say: “That’s one for ‘the book,’” thinking of a book in heaven where all the mathematical proofs could be found. Who – or what – will be the author of that book now?
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