Richard Burt Melrose is an Australian mathematician and emeritus professor at the Massachusetts Institute of Technology who works on geometric analysis, partial differential equations, and differential geometry.

[1] Melrose received in 1974 his Ph.D. from Cambridge University under F. Gerard Friedlander with thesis Initial and Initial-Boundary Value Problems.

His doctoral students include Mark S. Joshi, John M. Lee, Rafe Mazzeo, András Vasy, and Maciej Zworski.

In 1984 Melrose received the Bôcher Memorial Prize for his work on scattering theory.

He was in 1978 an invited speaker (Singularities of solutions of boundary value problems) at the ICM in Helsinki and in 1990 a plenary speaker (Pseudodifferential operators, corners and singular limits) at the ICM in Kyoto.