Doctor of Science in Pure Mathematics - Number Theory in Cambridge United States | Massachusetts Institute of Technology

Since antiquity, integers and prime numbers have captivated human curiosity. In recent years, the discipline has experienced significant breakthroughs. Wiles' 1994 proof of Fermat's Last Theorem sparked ongoing mathematical developments, including Khare and Wintenberger's work on Serre's conjecture linking mod p Galois representations to modular forms. As one of the Clay Millennium Problems, the Riemann hypothesis belongs to analytic number theory - a field using calculus and complex analysis to study integers. Notable progress includes Green and Tao's demonstration of infinitely long arithmetic prime sequences. The expansive Langlands Program proposes deep links between number theory and representation theory. Computational applications emerge through number theory's cryptographic connections.

Our research group focuses on multiple areas: Galois representations, Shimura varieties, automorphic forms, lattice theory, computational methods, rational points on algebraic varieties, and K3 surface arithmetic.