He was born into a Jewish family in Győr, Austria-Hungary and died in Budapest, Hungary.

[4] Then, Riesz was the rector and a professor at the University of Szeged, as well as a member of the Hungarian Academy of Sciences.

He established the spectral theory for bounded symmetric operators in a form very much like that now regarded as standard.

Together with Alfréd Haar, Riesz founded the Acta Scientiarum Mathematicarum journal.

[4] The corpus of his bibliography was compiled by the mathematician Pál Medgyessy.