Tristan is the son of social anthropologist Rodney Needham of Oxford, England. He attended the Dragon School. Later Needham attended the University of Oxford and 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.
Needham wrote the 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 fact Douglas Hofstadter wrote "Needham's work of art with its hundreds and hundreds of beautiful figures á la Latta, brings complex analysis alive in an unprecedented manner". Hofstadter had studied complex analysis at Stanford with Gordon Latta, and he recalled "Latta's amazingly precise and elegant blackboard diagrams". In 2001 a German language version, translated by Norbert Herrmann and Ina Paschen, was published by R. Oldenbourg Verlag, Munich.
He is currently completing a new book, originally titled, Visual Differential Geometry, but ultimately titled, Visual Differential Geometry and Forms: A Mathematical Drama in Five Acts [Princeton University Press, 2020 (forthcoming)].
- Faculty profile Archived 2012-06-07 at the Wayback Machine from University of San Francisco
- University of San Francisco website – History of the Sciences: Changing Course.
- American Mathematical Monthly 100(8):768–71
- Mathematics Magazine 67(2):92–108
- Allendoerfer Award from Mathematics Association of America
- 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
- Preface page xvi of Chris Pritchard (2003) Changing Shape of Geometry, Cambridge University Press ISBN 0521531624
- Rossella Lupacchini and Annarita Angelini. The Art of Science, p. 73. (Google Books)
- Farris, Frank A. (1998-01-01). "Review of Visual Complex Analysis". The American Mathematical Monthly. 105 (6): 570–576. doi:10.2307/2589427. JSTOR 2589427.
- Shiu, P. (1999-01-01). "Review of Visual Complex Analysis". The Mathematical Gazette. 83 (496): 182–183. doi:10.2307/3618747. JSTOR 3618747.