[2] In 2005, he got his PhD in mathematics from the Massachusetts Institute of Technology, where he studied geometry of objects with random shapes under the supervision of Tomasz Mrowka.
[5] 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.
[6] In his research, Guth has strengthened Gromov's systolic inequality for essential manifolds[7] and, along with Nets Katz, found a solution to the Erdős distinct distances problem.
[15] 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.