Marcel Riesz (Hungarian: Riesz Marcell [ˈriːs ˈmɒrt͡sɛll]; 16 November 1886 – 4 September 1969) was a Hungarian mathematician, known for work on summation methods, potential theory, and other parts of analysis, as well as number theory, partial differential equations, and Clifford algebras.

According to Lars Gårding, Riesz arrived in Lund as a renowned star of mathematics, and for a time his appointment may have seemed like an exile.

[1] His results on summability of trigonometric series include a generalisation of Fejér's theorem to Cesàro means of arbitrary order.

[4] He also studied the summability of power and Dirichlet series, and coauthored a book Hardy & Riesz (1915) on the latter with G.H.

[1] In 1916, he introduced the Riesz interpolation formula for trigonometric polynomials, which allowed him to give a new proof of Bernstein's inequality.

[2][10] Riesz also established, independently of Andrey Kolmogorov, what is now called the Kolmogorov–Riesz compactness criterion in Lp: a subset K ⊂Lp(Rn) is precompact if and only if the following three conditions hold: (a) K is bounded; (b) for every ε > 0 there exists R > 0 so that for every f ∈ K; (c) for every ε > 0 there exists ρ > 0 so that for every y ∈ Rn with |y| < ρ, and every f ∈ K.[11] After 1930, the interests of Riesz shifted to potential theory and partial differential equations.

His 1958 lecture notes, the complete version of which was only published in 1993 (Riesz (1993)), were dubbed by the physicist David Hestenes "the midwife of the rebirth" of Clifford algebras.

[12] Riesz's doctoral students in Stockholm include Harald Cramér and Einar Carl Hille.