Jonathan Webster

Jonathan Webster is a Professor in the Department of Mathematical Sciences at Butler University. He holds a Ph.D. from the University of Calgary and has a dual background in Mathematics and Computer Engineering from Rose-Hulman Institute of Technology, along with a Master's in Mathematics from the University of Illinois at Urbana-Champaign. His academic work bridges mathematics and computer science with a strong emphasis on undergraduate research mentorship.

Education

• Ph.D., University of Calgary, 2010
• M.S. in Mathematics, University of Illinois at Urbana-Champaign, 2004
• B.S. in Mathematics, Rose-Hulman Institute of Technology, 2001
• B.S. in Computer Engineering, Rose-Hulman Institute of Technology, 2001

Jonathan Webster's research focuses on algorithmic and computational number theory, particularly in areas such as Carmichael numbers, pseudoprimes, Legendre's conjecture, and the multiplication table problem. He develops and implements algorithms to explore deep number-theoretic questions, often pushing computational limits. His work is highly collaborative, frequently involving undergraduate students and established researchers like Andrew Shallue and Jonathan Sorenson.

His recent publications (2024–2025) highlight a consistent trend in computational number theory, with several papers accepted to the prestigious Algorithmic Number Theory Symposium (ANTS) and journals like INTEGERS and Mathematics of Computation. These works involve extensive data generation, algorithm design, and verification, often accompanied by publicly released source code and datasets. In parallel, he contributes to mathematics education, particularly in designing and promoting undergraduate research experiences.

His scientific contributions include:

• Tabulation of all Carmichael numbers below 10^22
• Verification of Legendre’s conjecture up to 7·10^13
• Advancing the understanding of absolute Lucas pseudoprimes
• Developing efficient algorithms for the multiplication table problem
• Historical research on inessential discriminant divisors with Fernando Gouvêa

Webster actively mentors undergraduate researchers, with students like Chloe Helmreich, Nick Sorenson, and David Purdum co-authoring peer-reviewed publications. He has secured research support through collaborative grants and institutional funding, enabling student participation in conferences and computational projects. His pedagogical work, including publications in MAA Focus and PRIMUS, emphasizes creating accessible research opportunities for undergraduates. While not explicitly mentioning a lab, his research group functions as a computational number theory team, producing open-source tools and large-scale datasets. Future work likely includes extending computational bounds, exploring new pseudoprime families, and expanding undergraduate research models.