Szegedy earned a master's degree in 1998 and a Ph.D. in 2003 from Eötvös Loránd University in Budapest. His dissertation, supervised by Péter Pál Pálfy, was about group theory and was entitled "On the Sylow and Borel subgroups of classical groups". After temporary positions at the Alfréd Rényi Institute of Mathematics, Microsoft Research, and the Institute for Advanced Study, he joined the faculty of the University of Toronto Scarborough in 2006. He returned to the Rényi Institute in 2013.
Szegedy won the Géza Grünwald Commemorative Prize for young researchers of the János Bolyai Mathematical Society in 2002. He was one of two winners of the 2009 European Prize in Combinatorics, and in 2010 he became a Sloan Fellow. With László Lovász, he was one of the winners of the 2012 Fulkerson Prize, for their joint work on graph limits. He was the 2013 winner of the Coxeter–James Prize of the Canadian Mathematical Society.
- Curriculum vitae, Alfred Rényi Institute, retrieved 2015-03-19.
- Balázs Szegedy at the Mathematics Genealogy Project.
- EuroComb 2009: European Conference on Combinatorics, Graph Theory and Applications, University of Bordeaux 1, retrieved 2015-03-19.
- 2010 Sloan Research Fellowships, Alfred P. Sloan Foundation, February 16, 2010, retrieved 2015-03-19.
- Balázs Szegedy wins prestigious Fulkerson Prize, University of Toronto Scarborough, August 29, 2012, retrieved 2015-03-19.
- University of Toronto Professor recognized for research excellence: Balázs Szegedy to receive 2013 CMS Coxeter–James prize, Canadian Mathematical Society, April 15, 2013, retrieved 2015-03-19.