AI contributions to Erdős problems on Terry Tao’s GitHub feels like a glimpse into the industrialisation of pure math research, with Tao the most high-profile industrial tycoon and many others hot on his heels. The recent GPTs in particular have been just killing it: ctrl+F-ing “GPT-5.x” turns up 208 instances, with 76 appearances of 5.2, 75 of 5.4 and 55 of 5.5; there are 58 “Gemini”s and 39 “Claude”s.
Tangentially, I’ve previously joked that there should be a whimsical “Erdos problems benchmark” (inspired by Tao’s Mathstodon comments) defined to be “the proportion of currently outstanding Erdos problems amenable to current AI tools operated with minimal human intervention”, with the current SOTA being his guess of 1-2% as of Jan 2026. The 1st disclaimer on Tao’s page sensibly warns against taking this joke at face value:
1. This page is not a benchmark
Erdős problems vary widely in difficulty, by several orders of magnitude, ranging from extremely difficult problems to low-hanging fruits. It is hard to tell in advance which category a given problem falls into. Moreover, a thorough literature review is not always available; see disclaimer 2.
However, a problem only stated once in the literature with scant record of followup work may very well be of the second category. In particular, we advise against direct comparison of raw counts of problems solved by different methodologies, as this could be comparing apples to oranges.
That last disclaimer seems more pertinent than ever due to frontier models’ current disproportionate competence at this very narrow slice of mathematical activity vs other parts of math. Quoting it in full:
11. Problem solving is only one component of mathematical research
The Erdős problem site and this wiki are focused on problems of Erdős. Solving mathematical problems is an important component of mathematical research, which is relatively easy to quantify. As long as problems and arguments are unambiguous, one can check whether an argument solves a problem. Hence problem solving is an attractive goal for experimentation with AI systems as it provides objective improvement criteria.
Such focus on problem solving may give the impression that this is the only, or primary, activity that mathematicians value in research. This is not the case. The complementary activity of theory building—construction of frameworks that naturally encapsulate mathematical phenomena—is no less essential but harder to quantify. For further reading, we recommend Thurston’s “On proof and progress in mathematics” and Timothy Gowers’ “The two cultures of mathematics”. Other activities include exposition, teaching, curating literature, building communities, developing software and databases, and administrative duties.
Here’s a very relevant article I wrote back then about LLM solving open problems (it references Have LLMs Generated Novel Insights) https://jimfund.com/math.html
The second half of your article made me think of Gwern’s LLM daydreaming proposal (July 2025)
Despite impressive capabilities, large language models have yet to produce a genuine breakthrough. The puzzle is why.
A reason may be that they lack some fundamental aspects of human thought: they are frozen, unable to learn from experience, and they have no “default mode” for background processing, a source of spontaneous human insight.
To illustrate the issue, I describe such insights, and give an example concrete algorithm of a day-dreaming loop (DDL): a background process that continuously samples pairs of concepts from memory. A generator model explores non-obvious links between them, and a critic model filters the results for genuinely valuable ideas. These discoveries are fed back into the system’s memory, creating a compounding feedback loop where new ideas themselves become seeds for future combinations.
The cost of this process—a “daydreaming tax”—would be substantial, given the low hit rate for truly novel connections. This expense, however, may be the necessary price for innovation. It would also create a moat against model distillation, as valuable insights emerge from the combinations no one would know to ask for.
The strategic implication is counterintuitive: to make AI cheaper and faster for end users, we might first need to build systems that spend most of their compute on this “wasteful” background search. This suggests a future where expensive, daydreaming AIs are used primarily to generate proprietary training data for the next generation of efficient models, offering a path around the looming data wall.
I don’t have a sense of whether this idea is good, I just aesthetically like it.
TT has been pretty bad at predicting or having an accurate world model of this stuff as far as I can tell. People give him a lot of deference because he’s a math genius and tbf to him he does have an open mind to a certain extent but he seems to struggle to publicly speak about the implications of current trajectories beyond 6 months
Yeah I find generalised deference strange, it’s like a weird prestige status-related Ra thing. Maybe I’ve just seen too many examples of world-class domain-specific geniuses being just not very impressive outside of their domains.
Yes it just seemed like a relevant time to bring this up, we don’t discuss TT that much here so I figured I’d say my 2 cents if people then go look him up and watch his recent interviews.
AI contributions to Erdős problems on Terry Tao’s GitHub feels like a glimpse into the industrialisation of pure math research, with Tao the most high-profile industrial tycoon and many others hot on his heels. The recent GPTs in particular have been just killing it: ctrl+F-ing “GPT-5.x” turns up 208 instances, with 76 appearances of 5.2, 75 of 5.4 and 55 of 5.5; there are 58 “Gemini”s and 39 “Claude”s.
The contributions are taxonomized like so:
Tangentially, I’ve previously joked that there should be a whimsical “Erdos problems benchmark” (inspired by Tao’s Mathstodon comments) defined to be “the proportion of currently outstanding Erdos problems amenable to current AI tools operated with minimal human intervention”, with the current SOTA being his guess of 1-2% as of Jan 2026. The 1st disclaimer on Tao’s page sensibly warns against taking this joke at face value:
All disclaimers:
That last disclaimer seems more pertinent than ever due to frontier models’ current disproportionate competence at this very narrow slice of mathematical activity vs other parts of math. Quoting it in full:
And Tao himself, this time from 2007:
Related: Have LLMs Generated Novel Insights?
Other answers are ~1 years ago, but I am actively adding examples as I encounter them in my reply
Yeah nice thanks. I track some “benchmarks” too, albeit mostly whimsical.
Here’s a very relevant article I wrote back then about LLM solving open problems (it references Have LLMs Generated Novel Insights) https://jimfund.com/math.html
The second half of your article made me think of Gwern’s LLM daydreaming proposal (July 2025)
I don’t have a sense of whether this idea is good, I just aesthetically like it.
TT has been pretty bad at predicting or having an accurate world model of this stuff as far as I can tell. People give him a lot of deference because he’s a math genius and tbf to him he does have an open mind to a certain extent but he seems to struggle to publicly speak about the implications of current trajectories beyond 6 months
Yeah I find generalised deference strange, it’s like a weird prestige status-related Ra thing. Maybe I’ve just seen too many examples of world-class domain-specific geniuses being just not very impressive outside of their domains.
What do you mean specifically? This post isn’t about the “implications of current trajectories beyond 6 months”.
Yes it just seemed like a relevant time to bring this up, we don’t discuss TT that much here so I figured I’d say my 2 cents if people then go look him up and watch his recent interviews.