He also holds a professor emeritus status at the Alfréd Rényi Institute of Mathematics of the Hungarian Academy of Sciences.

Since his parents wished him to become a doctor, Szemerédi enrolled at a college of medicine, but he dropped out after six months (in an interview[2] he explained it: "I was not sure I could do work bearing such responsibility.").

He is best known for his proof from 1975 of an old conjecture of Paul Erdős and Pál Turán: if a sequence of natural numbers has positive upper density then it contains arbitrarily long arithmetic progressions.

With Ajtai and János Komlós he proved the ct2/log t upper bound for the Ramsey number R(3,t), and constructed a sorting network of optimal depth.

In 2012, Szemerédi was awarded the Abel Prize "for his fundamental contributions to discrete mathematics and theoretical computer science, and in recognition of the profound and lasting impact of these contributions on additive number theory and ergodic theory"[22] The Abel Prize citation also credited Szemerédi with bringing combinatorics to the centre-stage of mathematics and noted his place in the tradition of Hungarian mathematicians such as George Pólya who emphasized a problem-solving approach to mathematics.

[23] Szemerédi reacted to the announcement by saying that "It is not my own personal achievement, but recognition for this field of mathematics and Hungarian mathematicians," that gave him the most pleasure.

[25] Prior to the conference a volume of the Bolyai Society Mathematical Studies Series, An Irregular Mind, a collection of papers edited by Imre Bárány and József Solymosi, was published to celebrate Szemerédi's achievements on the occasion of his 70th birthday.