The 2018 Steele Prize for Seminal Contribution to Research in Discrete Mathematics/Logic will be awarded to Sergey Fomin and Andrei Zelevinsky (posthumously) for their paper “Cluster algebras I: Foundations,” published in 2002 in the Journal of the American Mathematical Society.

The paper is a modern exemplar of how combinatorial imagination can influence mathematics at large. In the fifteen years since their introduction, cluster algebras have been shown to be important in many seemingly different areas of mathematics, including root systems, Poisson geometry, Teichmüller theory, quiver representations,integrable systems, and quantum affine algebras. This paper is a work of lasting importance, both for its varied applications and for the intrinsic beauty of the theory.