**Peter McMullen** (born 11 May 1942) is a British mathematician, a professor emeritus of mathematics at University College London.

McMullen earned bachelor's and master's degrees from Trinity College, Cambridge, and taught at Western Washington University from 1968 to 1969.

He is known for his work in polyhedral combinatorics and discrete geometry, and in particular for proving what was then called the upper bound conjecture and now is the upper bound theorem. This result states that cyclic polytopes have the maximum possible number of faces among all polytopes with a given dimension and number of vertices. McMullen also formulated the g-conjecture, later the g-theorem of Billera, Lee, and Stanley, characterizing the *f*-vectors of simplicial spheres.

McMullen was invited to speak at the 1974 International Congress of Mathematicians; his contribution there had the title *Metrical and combinatorial properties of convex polytopes*.

He was elected as a foreign member of the Austrian Academy of Sciences in 2006.

In 2012 he became an inaugural fellow of the American Mathematical Society.

Research papers
McMullen, P. (1970), "The maximum numbers of faces of a convex polytope", *Mathematika*, **17**: 179–184, MR 0283691, doi:10.1112/s0025579300002850 .
—— (1975), "Non-linear angle-sum relations for polyhedral cones and polytopes", *Mathematical Proceedings of the Cambridge Philosophical Society*, **78** (2): 247–261, MR 0394436, doi:10.1017/s0305004100051665 .
—— (1993), "On simple polytopes", *Inventiones Mathematicae*, **113** (2): 419–444, MR 1228132, doi:10.1007/BF01244313 .
Survey articles
——; Schneider, Rolf (1983), "Valuations on convex bodies", *Convexity and its applications*, Basel: Birkhäuser, pp. 170–247, MR 731112 . Updated as "Valuations and dissections" (by McMullen alone) in *Handbook of convex geometry* (1993), MR1243000.
Books
——; Shephard, G. C. (1971), *Convex Polytopes and the Upper Bound Conjecture*, Cambridge University Press .
——; Schulte, Egon (2002), *Abstract regular polytopes*, Encyclopedia of Mathematics and its Applications, **92**, Cambridge: Cambridge University Press, ISBN 0-521-81496-0, MR 1965665, doi:10.1017/CBO9780511546686 .