An OpenAI model has disproved the belief that the best possible solutions to simplify arrangements looked roughly like square grids. It has discovered a new family of constructions that performs better. Despite the excitement, the broader problem remains unsolved due to the AI not providing a new answer for the rise in number of pairs.
If you take a sheet of paper and add some dots, how many pairs can be the same distance apart? Company says work on Paul Erdős planar unit distance problem shows advance in AI reasoning OpenAI has claimed a further advance in AI reasoning after its technology successfully tackled an 80-year-old maths problem.
The question posed by Erdős is simple to explain. If you take a sheet of paper and add some dots, how many pairs can be the same distance apart? Erdős proposed the number would rise only slightly faster than the number of dots themselves. OpenAI’s model concluded otherwise by drawing on different branches of mathematics to uncover a family of arrangements that break the limit in Erdős’s conjecture.
While the work has excited mathematicians, the broader problem remains unsolved because the AI did not come up with a new answer for how fast the pairs of dots rise, but merely showed that the limit Erdős proposed was too low
Openai Paul Erdős Planar Unit Distance Problem AI Reasoning Mathematics Belief Square Grids Discussions Improvement
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