The chebfun project is based in Oxford's Numerical Analysis Group, part of the Oxford University Computing Laboratory. It started during 2002-2005 as a DPhil research investigation by Zachary Battles, a Rhodes Scholar from the USA, under the supervision of Nick Trefethen. This led to Version 1 of the system, for smooth functions on the interval [-1,1], described in the 2004 SISC paper by Battles and Trefethen and in Battles' 2006 thesis.
The second phase of the project began in the autumn of 2006 with the beginning of research funding from the UK Engineering and Physical Sciences Research Council. First to join the team was DPhil student Ricardo Pachón, from Colombia, who extended the system to piecewise continuous functions and arbitrary intervals. Automatic subdivision and edge detection were added by Pachón and further developed in collaboration with Rodrigo Platte, from Brazil, a post-doc who arrived in October 2007. Beginning in January 2008, Toby Driscoll of the University of Delaware also became heavily involved. In this period the system was completely rewritten by Pachón and Platte, and the chebop system was developed for extending the reach to differential equations. A key collaborator in the chebop work has been Folkmar Bornemann of the Technical University of Munich. Chebfun Version 2 was released in June 2008.