Larry Guth

Lawrence David Guth (; born 1977) is a professor of mathematics at the Massachusetts Institute of Technology.

Education and career

Guth graduated from Yale University in 2000 with a BS in mathematics.

In 2005, he received his PhD in mathematics from the Massachusetts Institute of Technology (MIT), where he studied geometry of objects with random shapes under the supervision of Tomasz Mrowka.

In 2012, Guth moved to MIT, where he is Claude Shannon Professor of Mathematics. and, along with Nets Katz, found a solution to the Erdős distinct distances problem. His interests include the Kakeya conjecture and the systolic inequality.

Doctoral students

Guth has supervised graduate students at the University of Toronto and the Massachusetts Institute of Technology. His other doctoral students have included Dominic Dotterrer, Hannah Alpert, Ben Yang, Thao Do, Aleksandr Berdnikov, Alexey Balitskiy, Sahana Vasudevan, Yuqiu Fu, Shengwen Gan, Lingxian Zhang, and Sarah Tammen. His doctoral student Hong Wang received her PhD from MIT in 2019 under his supervision and was awarded the Fields Medal in 2026 for her work in harmonic analysis and geometric measure theory.

Recognition

Guth won an Alfred P. Sloan Fellowship in 2010. He was an invited speaker at the International Congress of Mathematicians in India in 2010, where he spoke about systolic geometry.

In 2013, the American Mathematical Society awarded Guth its annual Salem Prize, citing his "major contributions to geometry and combinatorics."

In 2014 he received a Simons Investigator Award. In 2015, he received the Clay Research Award.

He was included in the 2019 class of fellows of the American Mathematical Society "for contributions to harmonic analysis, combinatorics and geometry, and for exposition of high level mathematics".

On February 20, 2020, the National Academy of Sciences announced that Guth is the first winner of their new $20,000 Maryam Mirzakhani Prize in Mathematics for mid-career mathematicians. The citation states that his award is "for developing surprising, original, and deep connections between geometry, analysis, topology, and combinatorics, which have led to the solution of, or major advances on, many outstanding problems in these fields." He was one of three recipients of the 2020 Bôcher Memorial Prize. In 2021, he was elected member of the US National Academy of Sciences .

Personal He is the son of Alan Guth, a theoretical physicist known for the theory of inflation in cosmology.

Work Metaphors in systolic geometry: the video . . . . . . .