Robion Cromwell Kirby (born February 25, 1938) is a Professor of Mathematics at the University of California, Berkeley who specializes in low-dimensional topology.

He also proved the fundamental result on the Kirby calculus, a method for describing 3-manifolds and smooth 4-manifolds by surgery on framed links.

[1] He received his Ph.D. from the University of Chicago in 1965, with thesis "Smoothing Locally Flat Imbeddings" written under the direction of Eldon Dyer [de].

While there he developed his "torus trick" which enabled him to solve, in dimensions greater than four (with additional joint work with Siebenmann), four of John Milnor's seven most important problems in geometric topology.

In 1995 he became the first mathematician to receive the NAS Award for Scientific Reviewing from the National Academy of Sciences for his problem list in low-dimensional topology.