In May 2026, OpenAI released a new math result that sent shock waves throughout the world of mathematical research. A major unsolved problem called the “unit distance conjecture” had just been resolved by generative AI.
Since then, there has been a steady drumbeat of new results that either partially or completely leverage artificial intelligence to solve research-level mathematics problems. However, most new math results published in any given month are still generated by humans.
So where is this going? How good, and how quickly, will AI capabilities grow? Will most mathematical research be predominantly artificial intelligence? Or, as some mathematicians suggest, will AI combine with human ingenuity and other computer tools to create a golden age of mathematics?
A list of unsolvable problems
One of the most prolific mathematicians of the 20th century was Hungarian Paul Erdős, known for the breadth of his collaborations with mathematicians across many sub-fields.
Throughout his career, he proposed hundreds of unsolved problems that today are known as Erdős problems. This list is a tempting place to start for any AI company wishing to show it can solve problems in mathematics.
Over the decades, human researchers have steadily resolved many of the Erdős problems, but a large number remain unsolved. One was the unit distance problem from the field of geometric graph theory.
Humans on the shoulders of AI
This wasn’t the first mathematical problem to be solved by AI — it wasn’t even the first Erdős problem to be solved by AI — but it was the most significant. The unit distance problem is a prominent one that many researchers have attempted to solve since 1946, when it was proposed.
It was particularly noteworthy that, having read the proof of the unit distance problem by AI, it was human researchers who managed to adapt the central technique of the proof to solve — only a week later — another significant conjecture called the “sum-product conjecture.”
Much as the AI result rested on the shoulders of many mathematicians before it, humans were able to climb one step higher due to advances by AI.
A combination of technologies
Computer-based tools have been helping humans with mathematics for as long as there have been computers. These tools have become increasingly sophisticated and might run on the world’s largest supercomputers, modelling climate change or pandemics.
Even within pure mathematics, preliminary research shows that proof of some theoretical results can grow to petabytes in size — that is equal to one million gigabytes.
Computational tools aren’t the only way computers are aiding humans. How can you be convinced about the validity of an argument too large or technical to be easily verified even by experts? Using a computer language created for proof verification, mathematicians can make extremely precise versions of every component of an argument. Then the proof-verification system checks that every step logically follows from the underlying axioms, or starting points, of the proof.
In a recent pre-print paper, mathematicians combined each of these technologies — computational tools, proof verification and artificial intelligence — together with their own human ingenuity to achieve a new result in a field of math called Ramsey theory.
After exhaustive and rather clever computational searches, AI was able to conjecture a general pattern for a particular phenomenon, prove that the pattern did indeed hold and help the authors convert the argument for proof verification.
This combination of technologies led them to believe that we are now entering a “golden age” of mathematics.
Million-dollar math problems
Today the capabilities of AI are mixed. Some mathematical fields, notably graph theory, have been particularly amenable to AI-based proofs, but others seem quite resistant.
For every math problem AI does solve, there are huge numbers of problems that AI has failed to solve when prompted. For the most famous unsolved problems — such as the six remaining Millennium Prize problems where the Clay Mathematics Institute will pay you a million dollars if you can solve one of them — the problems seem as completely out of reach for AI as they do for us humans.
As to the future, we don’t know how far and how fast AI’s capabilities will grow. If progress is substantial, what will mathematical research look like for humans in five or 10 years? These early examples where humans built on AI results or leveraged AI along with existing tools to achieve new mathematical heights could give a glimpse of one possible future.
On the flip side, student anxiety about spending years of their lives honing their mathematical skills is understandable. There are natural fears about AI replacing humans in research mathematics. Thankfully, we’re not close to that yet.
- is an Associate Teaching Professor, Mathematics, University of Victoria
- This article first appeared in The Conversation
