Wataru Takeda has completely solved the polynomial analogue of the long-standing Brocard–Ramanujan problem, a breakthrough 150 years after its original proposal. The study resolves the problem for polynomials over finite fields and was published in the journal Finite Fields and Their Applications.
Researchers have developed big algebras, a new mathematical tool that connects abstract algebra and geometry, enabling unprecedented insights into symmetry groups. This breakthrough has the potential to strengthen the connection between quantum physics and number theory.
Johan Torkel Håstad of KTH Royal Institute of Technology is awarded the 2018 Donald E. Knuth Prize for his significant contributions to computer science, including optimization and cryptography. The prize recognizes his transformative techniques that have influenced subsequent work in these areas.
Elliptic curves are mathematically doughnut-shaped objects with specific configurations of rational points that determine their properties. Mathematicians have found a new form of moonshine that reveals deep information about these curves, including infinitely many and their general behavior.
Ivan Corwin, a recent Ph.D. from NYU, and Jack Thorne, a Harvard University PhD candidate, were selected for their research achievements in probability, algebraic number theory, and representation theory. They will receive funding for one to five years to support their mathematical research.
John Tate has made significant contributions to the field of algebraic number theory and arithmetic geometry. His work has resulted in the creation of fundamental concepts and the development of lasting impact on modern mathematics.
The American Mathematical Society awarded prizes in various categories including lifetime achievement, seminal contributions, mathematical exposition, and outstanding research by an undergraduate student. Notable winners include George Lusztig, Endre Szemerédi, Neil Trudinger, Alberto Bressan, and Hiroshi Ooguri.
Gregory Margulis has been recognized for his monumental contributions to algebra and its applications in various fields. He will share this year's Wolf Prize with Sergei Novikov at the University of Maryland.