Who's Who in abc Conjecture Research

The abc conjecture, formulated independently by David Masser and Joseph Oesterle in 1985, is a central open problem in number theory. For any three coprime positive integers a, b, c with a + b = c, it asserts that c is bounded above by a fixed power of the radical rad(abc) (the product of the distinct prime factors of abc). The conjecture is open. It implies a striking range of consequences in Diophantine equations, including an asymptotic form of Fermat's last theorem, bounds on Wieferich primes, and the Szpiro conjecture for elliptic curves. Shinichi Mochizuki announced a claimed proof via Inter-universal Teichmuller theory in 2012; as of 2025 the proof has not been accepted by the broader mathematical community.

This site is a reference directory of the researchers most active on the abc conjecture and the surrounding circle of problems: the Szpiro and Vojta conjectures, S-unit and Thue equations, height inequalities, Belyi maps, and arithmetic analogues of Nevanlinna theory. It catalogs the Top 100 researchers ranked from arXiv preprint output and OpenAlex citation data, and gives their institutions.