Gear studied at the University of Cambridge with a bachelor"s degree in 1957 and an Master of Arts in 1960 and at the University of Illinois, Urbana-Champaign with an Master of Surgery in 1957 and a Doctor of Philosophy in 1960 under Abraham H. Taub with thesis Singular Shock Intersections in Plane Flow.
From 1960 to 1962 he worked as an engineer for International Business Machines Corporation. From 1962 to 1990 he was a professor of computer science at the University of Illinois, Urbana-Champaign, where he was from 1985 to 1990 chair of the mathematics department. From 1992 to 2000 he was president of the Nippon Electric Corporation Research Institute in Princeton. From 1966 to 1971 he was a consultant at Argonne National Laboratory.
Gear works on numerical analysis, computer graphics, and software development.
He is known for the development of BDF methods (originally introduced by the chemists Charles Francis Curtiss und Joseph Oakland Hirschfelder in 1952), a multi-step method for solving stiff systems of differential equations. Gear first published on BDF methods in 1966.
He worked on computer applications to nonlinear systems and biology (such as chemotaxis of bacteria) and has continued this research after his retirement from Princeton University as professor emeritus. Gear is an American citizen.
In 1987 he received an honorary doctorate from the Royal Institute of Technology in Stockholm.
Institute of Electrical and Electronics Engineers. Association for Computing Machinery. Society for Industrial and Applied Mathematics.
