Tristan is the son of social anthropologist Rodney Needham of Oxford, England. He attended the Dragon School where his classmates included Hugh Laurie and Stephen Wolfram. Later Needham studied physics at Merton College, and then transferred to the Mathematical Institute where he studied under Roger Penrose. He obtained his Ph.D. in 1987 and in 1989 took up his post at University of San Francisco.
In 1993 he wrote "A Visual Explanation of Jensen's inequality". The following year he produced "The Geometry of Harmonic Functions". Needham is best known for his book Visual Complex Analysis which has received positive reviews. Though it is described as a "radical first course in complex analysis aimed at undergraduates", writing in Mathematical Reviews D.H. Armitage opined that "the book will be appreciated most by those who already know some complex analysis." In 2001 a German language version, translated by Norbert Herrmann and Ina Paschen, was published by R. Olderbourg Verlag, Munich.
- Needham, Tristan. Visual Complex Analysis. The Clarendon Press, Oxford University Press, New York, 1997 ISBN 0-19-853447-7.
- Faculty profile from University of San Francisco
- American Mathematical Monthly 100(8):768–71
- Mathematics Magazine 67(2):92–108
- Frank A. Farris (1998) American Mathematical Monthly, 105(6):570: "Visual Complex Analysis will show you the field of complex analysis in a way you almost certainly have not seen it before".
- Review of Visual Complex Analysis from Mathematical Reviews