He was nonetheless accepted for graduate studies at Princeton University, where he received his PhD in mathematics in 1959 after completing a doctoral dissertation titled On embeddings of spheres.

In an elementary fashion, he proved the generalized Schoenflies conjecture (his complete proof required an additional result by Marston Morse), around the same time as Morton Brown.

Mazur's first proof of this theorem depended upon a complete analysis of the rational points on certain modular curves.

The ideas of this paper and Mazur's notion of Galois deformations were among the key ingredients in Wiles's proof of Fermat's Last Theorem.

"He expanded his thoughts in the 2003 book Imagining Numbers[7] and Circles Disturbed, a collection of essays on mathematics and narrative that he edited with writer Apostolos Doxiadis.