AI and the World's Hard Problems · Mathematics · arXiv · 2026-10-26
The space of equators has infinite Hofer's diameter
The paper settles several questions about Hofer's geometry of the two-sphere. It proves that the space of equators has infinite Hofer diameter, constructs simple commutators of arbitrarily large Hofer norm, and exhibits a Hamiltonian diffeomorphism whose iterates escape to infinity from autonomous diffeomorphisms. It also embeds the free group of rank two into the Hamiltonian group with Hofer's metric via a bi-Lipschitz monomorphism, and the paper was written with substantial AI assistance.