William Stein

William Stein is an American mathematician and computational scientist known for his work in computational number theory, algebraic number theory, and the development of open-source mathematical software. He has combined research in modular forms, elliptic curves, and L-functions with large-scale software engineering, contributing to projects that bridge academic research and practical computation. Stein's career interweaves mathematical research, software development, teaching, and service to mathematical communities.

Early life and education

Stein completed undergraduate studies at Harvard University, where exposure to research problems in algebra and number theory connected him with faculty involved in elliptic curves and modular forms. He pursued graduate study at Princeton University under the supervision of Benedict H. Gross, focusing on analytic and algebraic aspects of modular symbols and L-functions. His doctoral work engaged with conjectures and computational questions tied to the Birch and Swinnerton-Dyer conjecture, the arithmetic of elliptic curves, and algorithms for explicit class field theory. During his formative years he interacted with researchers at institutions such as Institute for Advanced Study, Harvard College Observatory, and collaborators from computational projects at Massachusetts Institute of Technology.

Mathematical research and publications

Stein's research spans analytic number theory, algorithmic aspects of modular forms, and computational approaches to L-functions and arithmetic geometry. He has published on computational methods for modular symbols, algorithms for computing spaces of modular forms, and explicit computations concerning Hecke operators and eigenforms. His work addresses questions related to the arithmetic of elliptic curves, explicit class field theory for number fields, and effective computations of special values of L-functions. Collaborations and citations link his contributions to researchers at Princeton University, University of Michigan, Columbia University, and research centers including Mathematical Sciences Research Institute and Simons Foundation. Stein's publications engage classical themes like the Modularity theorem and modern computational inquiries tied to projects such as databases of arithmetic objects spearheaded by organizations like National Science Foundation-funded initiatives.

Software development and computer algebra (SageMath and SAGE-related projects)

Stein is best known as the founder and lead developer of the open-source project SageMath (originally SAGE), a comprehensive computer algebra system integrating packages such as PARI/GP, GAP, Singular, NumPy, and SciPy. He organized communities of contributors across universities, research labs, and companies, enabling SageMath to serve researchers working on modular forms, elliptic curves, algebraic number theory, and computational projects requiring large-scale symbolic and numerical capability. Stein authored or coauthored implementations of algorithms for modular symbols, modular forms over number fields, and routines for explicit L-function computations, interfacing with libraries like FLINT and LinBox. The SageMath ecosystem fostered collaborations with projects such as the L-functions and Modular Forms Database and computational infrastructure at institutions like National Institute of Standards and Technology and cloud services used by academic consortia. Stein's emphasis on reproducible research and pedagogical tools influenced software engineering practices in computational mathematics and encouraged open licensing models in academic software.

Academic career and teaching

Stein has held academic appointments at institutions including the University of Washington, where he taught courses on number theory, computational algebra, and algorithmic aspects of arithmetic geometry. His teaching integrated software like SageMath into curricula for undergraduate and graduate courses, promoting hands-on exploration of modular forms, elliptic curves, and explicit computations with rings of integers in number fields. He has supervised graduate students who pursued research in computational aspects of automorphic forms, L-functions, and symbolic computation, with connections to research groups at University of Illinois at Urbana–Champaign and Brown University. Stein has also presented lectures and workshops at conferences organized by entities such as the American Mathematical Society, Mathematical Association of America, and summer schools hosted by Institute for Computational and Experimental Research in Mathematics.

Awards, honors, and professional service

Stein's contributions to computational mathematics and open-source software have been recognized by professional service roles and invited talks at venues like the International Congress of Mathematicians satellite conferences and workshops supported by the National Science Foundation. He has served on committees and editorial boards connected to journals and databases documenting arithmetic objects, collaborating with organizations including the American Mathematical Society, European Mathematical Society, and foundations supporting open scientific software. Stein's leadership in software development, community building around SageMath, and integration of computational tools into research and teaching have had lasting influence on computational practices in number theory and algebraic geometry.

Category:American mathematicians Category:Computational mathematicians Category:University of Washington faculty