Sam Raskin has wrapped his head around a math problem so complex it took five academic studies — and more than 900 pages — to solve. The results are a sweeping, game-changing math proof that was ...

In quantum mechanics, the geometry of quantum states has emerged as a powerful framework for understanding phenomena ranging from electrical conductivity to superconductivity. One research direction ...

Debates over how geometry is understood and learned date back at least to the days of Plato, with more recent scholars concluding that only humans possess the foundations of this understanding.

Geometric group theory and discrete mathematics intersect in the study of groups through the lens of geometric and combinatorial structures. At its core, geometric group theory probes how algebraic ...

Wei Ho, the first director of the Women and Mathematics program at the Institute for Advanced Study, combines algebra and geometry in her work on an ancient class of curves. Like many people who would ...

Dennis Gaitsgory has dedicated the past 30 years to proving the geometric Langlands conjecture. Over the decades, he and his collaborators have built an extensive body of work, forming the foundation ...