He was the Regius Professor of Mathematics at the University of St. Andrews from 2015 to 2017, and was the chief research officer at Cryptos Fund until 2019.
He was the principal of a couple of small hedge funds, and later did research for Edgestream LP, in addition to his academic work.
Rivin's PhD thesis[1][2] and a series of extensions[3][4][5] characterized hyperbolic 3-dimensional polyhedra in terms of their dihedral angles, resolving a long-standing open question of Jakob Steiner on the inscribable combinatorial types.
Rivin has also made advances in counting geodesics on surfaces,[8] the study of generic elements of discrete subgroups of Lie groups,[9] and in the theory of dynamical systems.
[10] Rivin is also active in applied areas, having written large parts of the Mathematica 2.0 kernel, and he developed a database of hypothetical zeolites in collaboration with M. M. J. Treacy.