Brummell did his undergraduate studies at Imperial College at the University of London (UK) in Mathematics and received his B.Sc. there with first class honours. He was accepted to do a Ph.D. in the Department of Applied Mathematics at the same university, under the supervision of Dr. D.R. Moore. In 1988, Brummell received his Ph.D. for work on mathematical and numerical models of convection. In November 1988, Brummell moved to JILA and the Astrophysical and Planetary Science Department of the University of Colorado, where he worked on research problems in astrophysical and geophysical fluid dynamics, and taught mathematical and numerical methods, fluid dynamics and astrophysics. In late 2006, Brummell accepted a job in the formative Applied Mathematics and Statistics Department at the University of California, Santa Cruz, as an Associate Professor. Brummell was promoted to Full Professor in July 2009. Brummell was the Chair of the AMS department between July 2014-2017. The AMS department split in 2018 and Brummell is now part of the nascent Department of Applied Mathematics. Brummell continues to do research in solar deep interior physics, examining fundamental MHD process such dynamo theory, magnetic buoyancy instabilities and transport by convection, via a mixture of analytical methods and high performance numerical simulations.