Donald Clayton Spencer (April 25, 1912 – December 23, 2001) was an American mathematician, known for work on deformation theory of structures arising in differential geometry, and on several complex variables from the point of view of partial differential equations.
There he was involved in a series of collaborative works with Kunihiko Kodaira on the deformation of complex structures, which had some influence on the theory of complex manifolds and algebraic geometry, and the conception of moduli spaces.
He later worked on pseudogroups and their deformation theory, based on a fresh approach to overdetermined systems of PDEs (bypassing the Cartan–Kähler ideas based on differential forms by making an intensive use of jets).
Formulated at the level of various chain complexes, this gives rise to what is now called Spencer cohomology, a subtle and difficult theory both of formal and of analytical structure.
After his death, a mountain peak outside Silverton, Colorado was named in his honor.