Spivak received his PhD in mathematics from UC Berkeley in 2007 under the supervision of Peter Teichner and Jacob Lurie.

[2] His thesis was on derived manifolds,[3] Spivak worked as a postdoc at the University of Oregon and Massachusetts Institute of Technology.

[4] Spivak and Robert Kent developed a human-readable categorical system of knowledge representation called ologs.

[9] The goal of ologs, and of Spivak's book, was to show that category theory can be made relatively easy and thus be understood by a wider audience.

[14] The two, together with Rémy Tuyeras, wrote the first article using category theory to understand the structure of deep learning, called "Backprop as functor".