Every now and then, a math problem sticks around for decades, teasing the brightest minds and defying solution. But what if the breakthrough came not from a seasoned mathematician, but from a curious amateur armed with artificial intelligence? I recently came across a fascinating story where a 23-year-old without formal advanced training solved a 60-year-old conjecture—thanks to ChatGPT Pro and its latest large language model.
This isn’t just any problem. It’s one that stumped top mathematicians and has been part of the infamous “Erdős problems” — a collection of challenging questions left by the legendary mathematician Paul Erdős. While AI has recently made waves tackling some of these problems, many solutions were less groundbreaking upon closer inspection. But this case is different. The AI didn’t just regurgitate known methods—it proposed a genuinely novel approach to the problem.
This isn’t your average AI math success story—it’s a fresh angle on a problem that had everyone else stuck.
The problem deals with primitive sets—special collections of whole numbers where no number divides any other. Erdős coined this concept to generalize the idea of prime numbers from individuals to sets. If you think about prime numbers as the building blocks of integers, primitive sets extend that idea to groups that maintain a kind of indivisibility among themselves.
One famous attribute of these sets is the Erdős sum, a calculated score that measures certain properties of the set. Erdős had conjectured bounds on this sum, including a limit it approaches for infinite sets of primes. While parts of these conjectures were proven over the years, others — including key limits and behaviors — remained out of reach, causing many mathematicians to hit a proverbial wall.
The amateur in question, Liam Price, stumbled upon this problem without knowing all its history or difficulty. Simply experimenting with AI on a casual Monday, he queried ChatGPT 5.4 Pro, which came back with a solution that looked valid. After reviewing it together with a peer from the University of Cambridge, experts quickly noticed that the AI had bypassed the usual starting points and taken an unexpected route to the solution.
As one knowledgeable mathematician shared, the problem had a sort of “mental block”—everyone before had started with the same flawed assumption or approach. The AI, however, leveraged a known formula from related mathematical fields but never before applied to this question. That “cognitive leap” is what makes the solution stand out.
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“We have discovered a new way to think about large numbers and their anatomy,” says an expert following the breakthrough.
Of course, AI’s initial proof wasn’t perfect. Experts needed to sift through the raw output and distill the core insight into a clearer, tighter proof. This collaborative refinement shows the synergy between human expertise and AI’s generative power. More importantly, this new method could have broader implications in number theory and beyond, opening doors to problem-solving techniques previously unexplored.
What’s exciting here isn’t just the solution itself, but the glimpse it offers into how AI might help break centuries-old mental patterns and inspire novel thinking. It validates a hopeful feeling among researchers that some mathematical problems might be waiting for fresh approaches only now possible by combining human intuition with AI’s outsider creativity.
Key takeaways from this AI-assisted breakthrough
- An amateur harnessed ChatGPT 5.4 Pro to solve a long-standing math conjecture without advanced formal training.
- The AI proposed a totally new technique, avoiding the typical missteps humans made for decades.
- Experts had to refine the AI’s output, illustrating human-AI collaboration as the future of complex problem solving.
- This novel approach might unlock fresh avenues for research into primitive sets and large number theory.
Reflecting on this, the story reinforces how AI can act as a second brain or creative partner in complex intellectual pursuits—not by replacing experts but by pushing beyond habitual thinking. It’s a reminder that sometimes solutions come from unexpected places and that bringing diverse tools to a problem can reveal hidden paths.
Whether this sparks a new era in mathematics or remains a fascinating milestone awaits time and further research. But for now, it’s compelling proof that 21st-century AI isn’t just crunching numbers—it’s reshaping how we conceive problems and craft solutions.
It also serves as inspiration for all of us who love math or curious puzzles: sometimes, a fresh perspective and the right tech can break a six-decade-old wall down on a casual afternoon.
