Artificial intelligence (AI) is making its mark these days in all types of fields and pursuits including tackling tough mathematical challenges. The Erdős website has chronicled exciting advances in this direction since Christmas. Fifteen problems have been successfully solved, going from the “open” category to “solved.” This transition showcases the truly profound effect that AI is having on mathematics research. Of these, 11 solutions explicitly attribute their contributions to the power of AI models.
Neel Somani, a researcher experimenting on OpenAI’s new model, recently had a surprising breakthrough while testing it. Part of what first led Dr. McKee to explore ChatGPT’s potential was his experience having AI concisely explain mathematical axioms. These proved procure Legendre’s formula, Bertrand’s postulate, and the theorem of the Star of David. This announcement is a peek into AI’s vast power to confront deep mathematical questions in ways we’ve never imagined before.
Hungarian mathematician Paul Erdős was so prolific that he’s credited with proposing over one thousand conjectures called the Erdős problems. These challenges have inspired and stumped mathematicians for decades. These problems are maintained online and have become a focal point for researchers exploring the intersection of mathematics and AI. More recently, in November, the first Gemini AI-powered model AlphaEvolve addressed multiple Erdős problems with autonomous solutions. This historic advancement foreshadows a longer term change to how mathematics will be approached in the future.
Recent experimental evidence indicates that GPT 5.2 has indeed become an extraordinarily powerful instrument for advanced mathematics. Eight challenges experienced tangible advancements due to AI’s autonomous features. We hope you’re as excited, because… six other cases demonstrated AI’s remarkable capacity to find and build on existing research, making it invaluable in solving difficult equations.
To validate a proof mainly connected to one of the original Erdős problems, Somani relied on a tool called Harmonic. The proof was eventually successful! I was especially intrigued by his idea of using the prompt-based capabilities of LLMs to generate solutions to unsolved open math problems.
“I was curious to establish a baseline for when LLMs are effectively able to solve open math problems compared to where they struggle,” – Neel Somani.
One of the biggest stars in the field, mathematician Terence Tao has written about the recent developments on his GitHub page. It was those scalable implications of AI that he said found the potential to create new mathematical theorems.
“As such, many of these easier Erdős problems are now more likely to be solved by purely AI-based methods than by human or hybrid means,” – Terence Tao.
Tao’s experiences mirror a wider movement among professors within academia, specifically math and computer science instructors, who are beginning to use more AI tools. It was an issue that Achim, another leading researcher in the field, viewed as critically important to the development.
“I care more about the fact that math and computer science professors are using [AI tools],” – Achim.
In only 15 minutes, ChatGPT provided a full proof to one of the Erdős conundrums! Nothing came close to its overall processing time. Such a rapid response time raises fascinating questions about AI’s role in mathematics, now, and in the future. Will it someday be better than humans at specialized tasks or decision-making?
Somani described AI’s performance as “anecdotally more skilled at mathematical reasoning than previous iterations.” As this observation demonstrates, AI technology has made incredible strides and can now be applied to highly complex domains such as a field like mathematics.
This synergy between AI and mathematicians may well lead to breakthrough solutions of many historic mathematical conundrums. As researchers continue to explore AI’s capabilities, the landscape of mathematical problem-solving may undergo significant changes, potentially reshaping how future mathematicians approach their craft.