Peter McMullen

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Peter McMullen (born May 11, 1942 in Hillingdon , England ) is a British mathematician who deals with geometry.

life and work

McMullen is the son of a mathematician and studied from 1960 at Trinity College in Cambridge and at the University of Birmingham , where he received his doctorate in 1968. He then worked at universities in London , Siegen , the University of British Columbia ( Vancouver ), the University of Freiburg and from 1991 professor at University College London . In 1978 he received the D. Sc. at University College. Today he is professor emeritus there.

McMullen is a leading scientist in combinatorial geometry, especially the polyhedron theory , which he treats with abstract algebraic methods and where he works e.g. B. set up the G-conjecture proven by Richard P. Stanley .

In 1970 he proved the Upper Bound Conjecture (established by Theodore Motzkin in 1957) over the maximum number of 1, 2, 3, .., (d-1) dimensional surfaces of a d-dimensional convex polyhedron with a given number of vertices. In 1993 he proved a theorem on the number of faces of simple polyhedra ("On simple polytopes", Inventiones Mathematicae, Vol. 113, 1993, pp. 419-444) using methods of algebraic geometry.

In 1974 he was invited speaker at the International Congress of Mathematicians in Vancouver ( Metrical and combinatorial properties of convex polytopes ). He is a fellow of the American Mathematical Society .


  • with Egon Schulte: Abstract Regular Polytopes , Encyclopedia of Mathematics and its Applications, Cambridge University Press 2002, ISBN 0-521-81496-0
  • with GCShephard : Convex Polytopes and the upper bound conjecture , Cambridge University Press, London Mathematical Society Lecture Notes, 1971
  • The numbers of faces of simplicial polytopes , Israel J. Math., Volume 9, 1971, pp. 559-570
  • On simple polytopes , Inventiones Mathematicae, Volume 113, 1993, pp. 419-444


  • Peter Gruber "On the history of convex geometry and the geometry of numbers", in G. Fischer u. a. (Editor) “100 Years of Mathematics”, Vieweg 1990

Web links


  1. The inequalities given by him characterize the so-called f-vectors, which count the area numbers according to dimension, but they do not determine them. McMullen The numbers of faces of simplicial polytopes , Israel Journal Mathematics, Vol. 9, 1971, pp. 559-570
  2. ^ A conjecture about the minimal number, the minimally bound conjecture, was proven by David Barnette from 1971 to 1973.