This is a story about keeping the faith in a discipline not exactly known for its religiosity: mathematics.
The field of arithmetic statistics — the study of statistical patterns in arithmetic objects such as number fields, class groups, and elliptic curves — rests on sets of conjectures whose predictions have been only partially proven.
In 2001, mathematician Jordan Ellenberg ’93, Ph.D. ’98, and some colleagues set out on a humbling yearslong odyssey to disprove one of the field’s most famous sets of predictions, the Cohen-Lenstra conjectures.
“We were like, there’s no evidence these conjectures are true,” Ellenberg said. “People conjecture them because we can’t think of any reason to think otherwise, but there’s no real evidence that they’re true.”
The conjectures — formulated by Henri Cohen and Hendrik Lenstra in the 1980s at the dawn of computational number theory — predict that the structures of certainarithmetic objects display statistical regularities.
