For nearly 80 years, mathematicians have struggled to solve a classic geometry puzzle first posed by Paul Erdős in 1946: the planar unit distance problem. The question posed by the legendary Hungarian mathematician was, on the surface, deceptively simple.

It asks: if you take a piece of paper and add some dots, how many pairs can be exactly the same distance apart? Erdős himself proposed that the maximum number grows only slightly faster than the number of dots. Although many mathematicians agreed with him, no one could find a way to mathematically prove it.