Mrowka is the son of Polish mathematician Stanisław Mrówka [pl],[1] and is married to MIT mathematics professor Gigliola Staffilani.

[2] A 1983 graduate of the Massachusetts Institute of Technology, he received the PhD from the University of California, Berkeley in 1988 under the direction of Clifford Taubes and Robion Kirby.

[4] A prior Sloan fellow and Young Presidential Investigator, in 1994 he was an invited speaker at the International Congress of Mathematicians (ICM) in Zurich.

"[5] He was named a Guggenheim Fellow in 2010, and in 2011 he received the Doob Prize with Peter B. Kronheimer for their book Monopoles and Three-Manifolds (Cambridge University Press, 2007).

[14] The citation says: "The proof is a beautiful work of synthesis which draws upon advances made in the fields of gauge theory, symplectic and contact geometry, and foliations over the past 20 years.