Mathematicians Debate a World Without Infinity

A conference at Columbia University in April 2025 gathered mathematicians, physicists, and philosophers to explore ultrafinitism, the radical view that infinity does not exist. Led by Doron Zeilberger, a Rutgers professor, ultrafinitists argue that numbers are finite and that concepts like infinite sets are unnecessary. The movement traces back to Soviet dissident Alexander Esenin-Volpin in the 1960s-70s and later Edward Nelson, who attempted to rebuild arithmetic without infinity. Physicists like Nicolas Gisin and Sean Carroll have shown interest, as finitist models may resolve quantum paradoxes. However, most mathematicians reject ultrafinitism as quackery, and the movement lacks a coherent formal theory. Organizer Justin Clarke-Doane sees the conference as a sign of growing curiosity, but progress remains halting.