SC Connecticut News

Yale University mathematics professor Sam Raskin has achieved a significant breakthrough in the field of mathematics by solving a major portion of the Langlands Conjectures, often referred to as a "Rosetta Stone" of math. This accomplishment, completed in collaboration with Dennis Gaitsgory from the Max Planck Institute and a team of mathematicians, was detailed in five academic studies totaling over 900 pages.

The Langlands Conjectures, introduced in the 1960s by Canadian mathematician Robert Langlands, propose deep connections between number theory, harmonic analysis, and geometry. These areas have traditionally been considered separate domains within mathematics. The solution led by Raskin and Gaitsgory focuses on the geometric aspect of these conjectures.

"There’s definitely something buzzy about this one," said Raskin. He expressed that people are generally excited to see long-standing problems resolved. Alexander Goncharov, another professor at Yale, described the solution as a "landmark" achievement and highlighted its significance as one of the most fundamental problems in mathematics.

David Ben-Zvi from the University of Texas at Austin commented on the importance of this development: “It’s the first time we have a really complete understanding of one corner of the Langlands program, and that’s inspiring.”

Beyond pure mathematics, Raskin's work has drawn interest from theoretical physicists due to its potential implications for understanding particle physics and natural phenomena like electricity and magnetism.

Raskin's journey toward solving this complex problem began during his undergraduate years at the University of Chicago and continued through his graduate studies under Gaitsgory at Harvard. His career path was influenced by early exposure to geometric Langlands research.

Reflecting on his mathematical approach, Raskin said: “I think about mathematics as a part of nature, with interesting things to be discovered along the way.” This philosophy has guided him through decades-long research culminating in what he describes as "the satisfaction of a proof."

The team's comprehensive solution includes developing new mathematical tools necessary for tackling such intricate problems. Their work represents not only an academic triumph but also a testament to collaborative efforts across years and institutions.