Harbater was born in New York City and attended Stuyvesant High School, where he was on the math team. After graduating in 1970, he entered Harvard University.

After graduating summa cum laude in 1974, Harbater earned a master's degree from Brandeis University and then a Ph.D. in 1978 from MIT, where he wrote a dissertation (Deformation Theory and the Fundamental Group in Algebraic Geometry) under the direction of Michael Artin.

He solved the inverse Galois problem over ${\displaystyle \mathbb {Q} _{p}(t)}$ , and made many other significant contributions to the field of Galois theory.

Harbater's recent work on patching over fields, together with Julia Hartmann and Daniel Krashen, has had applications in such varied fields as quadratic forms, central simple algebras and local-global principles.

In 1995, Harbater was awarded the Cole Prize for his solution, with Michel Raynaud, of the long outstanding Abhyankar conjecture.

In 2012, he became a fellow of the American Mathematical Society.^[1]

• Harbater, D. (1994). "Abhyankar's Conjecture on Galois Groups Over Curves". Invent. Math. 117 (1): 1–25. Bibcode:1994InMat.117....1H. doi:10.1007/BF01232232. S2CID 121690794.

• Recollections of Arthur Rothstein, (Math Teammate of Harbater)
• Cole Prize citation for David Harbater
• David Harbater at the Mathematics Genealogy Project
• Harbater's home page at Penn