He received his doctorate from Harvard University in 1970, under the supervision of Andrew Gleason.

[1] He is currently (as of 2018[update]) a professor at the Courant Institute of Mathematical Sciences of New York University.

In 1963, while studying at the Massachusetts Institute of Technology, Spencer became a Putnam Fellow.

[4] He was elected as a fellow of the Society for Industrial and Applied Mathematics in 2017, "for contributions to discrete mathematics and theory of computing, particularly random graphs and networks, Ramsey theory, logic, and randomized algorithms".

[5] In 2021, he received the Leroy P. Steele Prize for Mathematical Exposition with his coauthor Noga Alon for their book The Probabilistic Method.