OpenAI makes a breakthrough on an 80-year-old Geometrical Conjecture

OpenAI, the company behind ChatGPT, shared that their unreleased model has made a breakthrough on a long-standing math problem.

The Planar Unit Distance Problem, first proposed by Paul Erdos in 1946, has had mathematicians stuck for 80 years, being one of the best-known questions in combinatorial geometry.

This question proposed by the Hungarian mathematician is known for being simple to explain but difficult to solve. The Planar Unit Distance Problem essentially asks:  if points are placed on a flat two-dimensional plane, how many pairs of those points can be exactly one unit apart from each other?

"Since Erdos’ original work, the prevailing belief has been that the 'square grid' constructions depicted further below were essentially optimal for maximizing the number of unit-distance pairs. An internal OpenAI model has disproved this longstanding conjecture, providing an infinite family of examples that yield a polynomial improvemen," stated OpenAI in a blog post.

OpenAI's breakthrough becomes even more of a monumental accomplishment as the proof for this mathematical conjecture does not come from any model or system that is specifically trained for mathematics, rather it came from a general-purpose reasoning model.

This also marks a significant moment in history as it; "...would be the first time AI has autonomously solved a prominent open problem central to a field of mathematics", OpenAI shared on X.

With this accomplishment OpenAI expresses the depth of reasoning these systems now support having independently solved this problem that has stood unsolved for decades.

To support and review the proof of this new breakthrough, OpenAI published comments from renowned mathematicians including Noga Alon, Tim Gowers, Arul Shankar, Jacob Tsimerman verifying the proof and being impressed by the work produced by this model.

Reactions to this achievement remain mixed as there were people marveling and people expressing concern and criticism at OpenAI.

"I think this is the real AI milestone people should be paying attention to. Not better summaries. Not faster chat. A model found a new construction in a problem mathematicians had been circling since 1946. That shifts AI from “tool that explains knowledge” to “system that can expand the frontier,” an X user commented.

Another user expressed their concern commenting, "When AI is surpassing the top human intelligence that soon, what's the meaning left for human scientists to still working on those problems?"

Nevertheless, this breakthrough has spread a lot of excitement in both mathematical communities as well as AI communities, as it remains a new proof to understand a puzzling, age old mathematical problem.