In this web content, a team of mathematicians discovered a pattern in circle packings that defied the local-global conjecture. By analyzing graphs of pairs of remainders, the team noticed a continual pattern that challenged their initial expectations. The team eventually realized that the pattern disproved the conjecture, which had previously held for virtually all cases. The discovery also raised doubts about other conjectures in number theory. The team’s work demonstrates the power of data analysis in revealing new mathematical concepts. This surprising finding was made possible by a low-stakes summer project and an attitude of playful exploration. The discovery has exciting implications for the future of number theory.
https://www.quantamagazine.org/two-students-shoot-down-a-widely-believed-math-conjecture-20230810/