James Ritchie Norris (born 29 August 1960) is a mathematician working in probability theory and stochastic analysis.

[1] He is the Professor of Stochastic Analysis in the Statistical Laboratory, University of Cambridge.

Norris was an undergraduate at Hertford College, Oxford where he graduated in 1981.

He completed his D.Phil in 1985 at Wolfson College, Oxford under the supervision of David Edwards.

[4] He is the director of the Statistical Laboratory, a trustee of the Rollo Davidson Trust[5] and co-Director of the Cambridge Centre for Analysis.