In mid‐March, our Department of Mathematics proudly hosted Oxford-based Fields Medalist James A. Maynard for a two-day event marking the inaugural edition of the Pittsburgh Mathematical Horizons Lecture Series, made possible by the generous support of the Benter Foundation.
Day One – A Deep Dive into Prime Mysteries
On March 20, a joint Mathematical Colloquium was organized in collaboration with Carnegie Mellon University. Targeted toward a mathematical audience, the session saw over 200 math enthusiasts and experts—with such high attendance that latecomers had to stand. In his talk, “Primes and the Riemann Hypothesis,” Maynard offered an accessible exploration of one of mathematics’ greatest unsolved problems. He explained that although the Riemann Hypothesis remains unproven, many of its consequences for the distribution of prime numbers can be established under milder conditions—if any potential counterexamples are sufficiently rare. His presentation also highlighted recent collaborative breakthroughs with Larry Guth, which have significantly advanced our understanding of these exceptional cases.
Day Two – Bridging Pure Mathematics and Everyday Life
The following day, the focus shifted to engaging a wider audience at the inaugural Pittsburgh Mathematical Horizons Lecture, held in the historic Frick Fine Arts Building. This 20th-century venue, known for its elegant architecture and rich artistic heritage, provided a fitting setting for discussions on age-old number theoretic questions. The public lecture was opened by Dean Leibovich, a physicist by training, and moderated by Carl Wang-Erickson. Over 200 attendees—from undergraduates and high school students to senior community members—gathered to hear Maynard address the intriguing question: “How often do two prime numbers differ by exactly 2?” In tackling what is known as the twin prime conjecture, he eloquently connected these deep mathematical ideas to practical applications, such as the security systems that underpin modern internet communications.
Progress
A unifying theme throughout both days was the exciting, incremental progress made in addressing monumental challenges like the Riemann Hypothesis and the twin prime conjecture. While complete solutions still elude us, the advancements of the last two decades—bolstered by Maynard’s own pioneering contributions—demonstrate remarkable strides toward overcoming these obstacles. It is precisely this groundbreaking work that earned him the Fields Medal, an honor widely regarded as equivalent to winning a Nobel Prize in mathematics.
Beyond the Lectures
In addition to his presentations, James A. Maynard interacted with graduate students, postdoctoral researchers, and faculty over lunches and dinners. His approachable demeanor and readiness to engage in lively discussion left an enduring impact on all who attended. We extend our heartfelt thanks to James A. Maynard for sharing his expertise and passion, making this event an unforgettable celebration of mathematical innovation.