He comes from a noted academic family: his father, Zsigmond Pál Pach [hu] (1919–2001) was a well-known historian, and his mother Klára (née Sós, 1925–2020) was a university mathematics teacher;[3] his maternal aunt Vera T. Sós and her husband Pál Turán are two of the best-known Hungarian mathematicians.

[4] Pach received his Candidate degree from the Hungarian Academy of Sciences, in 1983, where his advisor was Miklós Simonovits.

[11] In the early 90s[12] together with Micha Perles, he initiated the systematic study of extremal problems on topological and geometric graphs.

Some of Pach's most-cited research work[13] concerns the combinatorial complexity of families of curves in the plane and their applications to motion planning problems[14][15] the maximum number of k-sets and halving lines that a planar point set may have,[16] crossing numbers of graphs,[17][18] embedding of planar graphs onto fixed sets of points,[19][20] and lower bounds for epsilon-nets.

[26] In 2014 he was elected as a member of Academia Europaea,[25] and in 2015 as a fellow of the American Mathematical Society "for contributions to discrete and combinatorial geometry and to convexity and combinatorics.