Russel Edward Caflisch was born in Charleston, West Virginia.

[2] His dissertation was titled "The Fluid Dynamic Limit and Shocks for a Model Boltzmann Equation."

[4] Until August 2017, Caflisch was the director of the Institute for Pure & Applied Mathematics (IPAM) and a professor in the Mathematics department, where he also held a joint appointment in the department of Materials Science and Engineering.

Caflisch's expertise includes topics in the field of applied mathematics, including partial differential equations, fluid dynamics, plasma physics, materials science, Monte Carlo methods, and computational finance.

[10] Caflisch was an invited speaker at International Congress of Mathematicians in Madrid in 2006,[11] and at the conference Dynamics, Equations and Applications in Kraków in 2019.