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**Tristan Needham** is a British mathematician and professor of mathematics at the University of San Francisco.

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 D.Phil. in 1987 and in 1989 took up his post at University of San Francisco.^{[1]}^{[2]}

In 1993 he published *A Visual Explanation of Jensen's inequality*.^{[3]} The following year he published *The Geometry of Harmonic Functions*, which won the Carl B. Allendoerfer Award for 1995.^{[4]}^{[5]}

Needham wrote the book *Visual Complex Analysis*, which has received positive reviews.^{[6]} Though it is described as a "radical first course in complex analysis aimed at undergraduates", writing in *Mathematical Reviews* D.H. Armitage said that "the book will be appreciated most by those who already know some complex analysis."^{[7]} 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".^{[8]} 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.

In 2021, Needham published *Visual Differential Geometry and Forms: A Mathematical Drama in Five Acts (Princeton University Press)*^{[9]}*.* (The original title was *Visual Differential Geometry*.) Much of this material was already developed in the writing of *Visual Complex Analysis*.

- Needham, Tristan.
*Visual Complex Analysis.*The Clarendon Press, Oxford University Press, New York, 1997 ISBN 0-19-853447-7.^{[10]}^{[11]}

- Needham, Tristan.
*Visual Differential Geometry and Forms: A Mathematical Drama in Five Acts.*Princeton University Press, Princeton, 2021 ISBN 9780691203706.^{[12]}^{[13]}^{[14]}

**^**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.**^**Needham, Tristan (1993). "A Visual Explanation of Jensen's Inequality".*The American Mathematical Monthly*.**100**(8): 768–771. doi:10.2307/2324783. JSTOR 2324783.**^**Needham, Tristan (1994). "The Geometry of Harmonic Functions".*Mathematics Magazine*.**67**(2): 92–108. doi:10.1080/0025570X.1994.11996195. ISSN 0025-570X.**^**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**^**Needham, Tristan (2021).*Visual Differential Geometry and Forms: A Mathematical Drama in Five Acts*. Princeton University Press. ISBN 9780691203690.**^**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.**^**Bultheel, Adhemar (2021-01-10). "Book Review: Visual Differential Geometry and Forms (T. Needham)".*MAA Publications*. Mathematical Association of America (MAA). Retrieved 2022-09-03.**^**https://www.math.colostate.edu/~clayton/research/papers/VDGF.pdf review by Clayton Shonkwiler**^**https://euromathsoc.org/magazine/articles/110 review by Frank Morgan

- Tristan Needham at the Mathematics Genealogy Project
- Author website for the book
*Visual Complex Analysis* - Princeton University Press website for the book
*Visual Differential Geometry and Forms: A Mathematical Drama in Five Acts* - Author website (including Errata) for the book
*Visual Differential Geometry and Forms: A Mathematical Drama in Five Acts*