## A Breakthrough in Mathematics: Liam Price’s Historic Discovery
Liam Price, a 23-year-old with no advanced mathematical training, recently made headlines for solving an Erdös problem—specifically, problem #1196—after it remained unresolved for 60 years. What makes this story even more captivating is that he accomplished this feat in just 80 minutes using ChatGPT, specifically the GPT-5.4 model.
### The Problem at Hand
The conjecture at the center of this breakthrough pertains to the behavior of particular mathematical sums related to primitive sets of integers—subsets of integers where no number divides another. While Jared Lichtman, a Stanford mathematician, had made partial progress on this problem over the years, it seemed that everyone working on the problem had been following a traditional pathway that didn’t yield definitive results.
### An Unconventional Approach
What set Price and ChatGPT apart was their unconventional starting point. The model employed a special function known as the von Mangoldt function, a tool from number theory intimately connected with prime numbers and the Riemann zeta function. This approach had not been considered by others tackling the problem. As Lichtman noted, “The LLM took a completely different route.”
### The Nature of the Achievement
Though the proposed solution has garnered praise, it is crucial to recognize that the initial output from ChatGPT was deemed “pretty poor” by experts like Lichtman. Further interpretation and detailing were required to distill the underlying idea that eventually led to solving the conjecture. Price himself wasn’t aware that they had found the solution until a friend, studying mathematics, recognized it—and it wasn’t until Terence Tao, a leading mathematician, confirmed their findings that their discovery gained traction.
### Controversy in the AI Community
Recent events have called attention to the capabilities of AI in mathematical problem solving. Notably, Sebastien Bubeck, a researcher at OpenAI, had claimed that GPT-5 solved multiple Erdös problems, a statement widely criticized by the mathematical community. Demis Hassabis, CEO of DeepMind, labeled it “shameful” when it was revealed that the model had only returned solutions to already solved problems available online. This incident raised skepticism regarding the authenticity of AI-assisted problem solving.
### AI’s Success Rate in Math
On GitHub, Terence Tao and Nat Sothanaphan maintain a repository tracking AI contributions to Erdös problems. Solutions are categorized using a traffic light system: green indicates complete solutions, yellow points to partial progress, and red signifies failure. So far, the ledger shows three complete AI-generated solutions, fourteen partial solutions, and eight failures. However, it’s suggested that many failed attempts won’t be reported, which may skew the perceived effectiveness of AI.
### The Future of AI in Mathematics
An initiative called “First Proof,” established by eleven mathematicians in February 2026, seeks to evaluate AI models by presenting them with ten novel mathematical problems derived from their own research. So far, preliminary results indicate that current AI systems struggle to produce autonomous solutions to challenges absent from their training datasets.
### A New Paradigm in Problem-Solving?
Terence Tao posits that the reason GPT-5.4 succeeded where many had failed was due to a “collective blockage” within the mathematical community, as everyone had been starting from the same traditional origins. The AI’s lack of awareness of established paths allowed it to explore novel avenues. Whether this method of tackling problems will stand the test of time remains to be seen. For now, Liam Price’s achievement might just signal a shift in how we approach complex mathematical questions.