Herrera-Revilla is one of the most outstanding scholars of Mexican Science. He studied engineering (civil and chemical), physics and mathematics at the National University of Mexico (UNAM) and obtained his PhD from Brown University (Division of Applied Mathematics), where he received the Graduate School Alumnus Award and two Professorship offers, the second one with tenure, three years after graduation. He is a very active Emeritus Professor at UNAM and also at SNI (the National Research System) where he held a Chair of Excellence (2003-2018). His pioneering work in many areas of applied mathematics and science has been recognized both nationally and internationally. At his country, he has won the three most important science prizes offered there: The National Award, the Academy of Sciences' and the "Luis Elizondo" award.
Very early in his career, he was selected to serve as a member of the National Institute for Scientific Research (1968-71), body in which other nine of the most distinguished scientists of Mexico participated, the latter consecrated. He proposed and Professor Herrera-Revilla was founder of the International Journal for Numerical Methods of Partial Differential Equations in Engineering
, and remained as Editor from 1985 to 2015, when he became Emeritus Editor. He also was Editor-in-Chief of Geofisica Internacional