In 1912, Srinivasa Ramanujan mailed pages of unproven formulas to mathematicians in England. Two of them, now called the Rogers-Ramanujan identities, say that two very different ways of counting partitions always give the same answer.
Try it with 6. Using parts that differ by at least 2, you get 1+5, 2+4 and 6: three ways. Using only parts ending in 1, 4, 6 or 9, you get 1+1+1+1+1+1, 1+1+4 and 6: also three. The identities say the two counts match for every number.
Yifeng Huang, now a postdoc at Emory University, noticed that counting matrices on the pinched curve y² = x³ reproduced one side of these identities. With Ruofan Jiang and Alexei Oblomkov, he linked the identities to a trefoil knot and conjectured infinitely many new families, one for each curve x^a = y^b. Huang, Ken Ono and Kenny Lau proved the conjecture in September 2026, helped by the AI system AxiomProver.
Source: Scientific American, October 29, 2026 — https://www.scientificamerican.com/article/mathematicians-find-an-infinite-number-of-ramanujan-equations/
