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..

After MIT, Guth went to Stanford as a postdoc and later to the University of Toronto as an assistant professor on a tenure track.

In 2011, New York University's Courant Institute of Mathematical Sciences hired Guth as a professor, listing his areas of interest as "metric geometry, harmonic analysis, and geometric combinatorics."

In 2012, Guth moved to MIT, where he is Claude Shannon Professor of Mathematics.

Research In his research, Guth has strengthened Gromov's systolic inequality for essential manifoldsGuth's approach to Gromov's systolic inequality, Shmuel Weinberger, July 18, 2009. 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.Fall newsletter 2010, Univ. of Toronto mathematics department, retrieved May 26, 2011.ICM listing of invited speakers , retrieved May 26, 2011.

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.Clay Research Award 2015

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 . . . . . . .

References