Pyber received his Ph.D. from the Hungarian Academy of Sciences in 1989 under the direction of László Lovász and Gyula O.H.
[4] In 1986, he proved the conjecture of Paul Erdős that a graph with n vertices and its complement can be covered with n2/4+2 cliques.
[6] Together with Tomasz Łuczak, Pyber proved the conjecture of McKay that for every ε>0, there is a constant C such that C randomly chosen elements invariably generate the symmetric group Sn with probability greater than 1-ε.
Pyber has made fundamental contributions in enumerating finite groups of a given order n. In 1993, he proved[8] that if the prime power decomposition of n is n=p1g1 ⋯ pkgk and μ=max(g1,...,gk), then the number of groups of order n is at mostIn 2004, Pyber settled several questions in subgroup growth by completing the investigation of the spectrum of possible subgroup growth types.
In 2011, Pyber and Andrei Jaikin-Zapirain obtained a surprisingly explicit formula for the number of random elements needed to generate a finite d-generator group with high probability.