SMRTR Science & EngineeringSep 28, 2025Quanta Magazine

New Math Revives Geometry’s Oldest Problems

SMRTR summary

Ancient mathematicians posed counting problems in geometry that took centuries to solve, like finding how many circles can touch three given circles (answer: eight after 1,800 years). Now mathematicians Kirsten Wickelgren and Jesse Kass have revived this field by using motivic homotopy theory to solve these problems across many different number systems simultaneously, providing new insights into both geometry and various mathematical structures.

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