Ronald Graham

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Ronald graham (1987)

Ronald Lewis "Ron" Graham (born October 31, 1935 in Taft , California - † July 6, 2020 in La Jolla , San Diego , California) was an American mathematician . He did pioneering work in the field of discrete mathematics , particularly Ramsey theory .


Graham received his Doctor of Philosophy in Mathematics from the University of California, Berkeley (On Finite Sums of Rational Numbers) in 1962 . He was a professor at the University of California at San Diego . In 1972 he developed the Graham scan algorithm for calculating the convex hull of a simple polygon.

In a 1977 paper, Graham gave an upper bound for solving a problem in Ramsey theory , known as Graham's number . This was considered to be the largest number used in a mathematical proof to date and was also included in the Guinness Book of Records .

Ronald Graham as a juggler

Graham published more than 300 essays and five books. In particular, he wrote the book Concrete Mathematics with Donald E. Knuth and Oren Patashnik .

With Jeffrey Lagarias and others he investigated the number theory of Apollonian circular packings in the 2000s .

In 2003 he received the Leroy P. Steele Prize of the American Mathematical Society , of which he was a fellow; In 1993/94 he was its president. In 1983 he was invited speaker at the International Congress of Mathematicians in Warsaw (Recent developments in Ramsey theory). In 1985 he was elected to the National Academy of Sciences and in 1986 to the American Academy of Arts and Sciences . In 1993 he and Claude Berge were the first to receive the Euler Medal . Graham was also President of the International Jugglers' Association and teacher of juggler Steve Mills , inventor of the Mills Mess juggling trick .

Graham was friends with Paul Erdős and supported the idea of ​​assigning Erdős numbers . His own Erdős number was 1.

Graham was married to the mathematician Fan Chung . He died in California in July 2020 at the age of 84.


Ronald graham (1998)
  • With Paul Erdős : Old and New Problems and Results in Combinatorial Number Theory. L'Enseignement Mathématique, 1980.
  • With Fan Chung: Erdős on Graphs: His Legacy of Unsolved Problems. AK Peters, 1998.
  • With Jaroslav Nešetřil (ed.): The Mathematics of Paul Erdős. Two volumes. Springer, 1997.
  • Rudiments of Ramsey Theory. American Mathematical Society, 1981.
  • With Donald E. Knuth & Oren Patashnik: Concrete Mathematics: A Foundation for Computer Science. Addison-Wesley, 1989; 1994.
  • With Joel H. Spencer & Bruce L. Rothschild : Ramsey Theory. Wiley, 1980; 1990.
  • With Martin Grötschel & László Lovász (eds.): Handbook of Combinatorics. MIT Press, 1995.
  • With Persi Diaconis : Magical Mathematics: The Mathematical Ideas That Animate Great Magic Tricks. Princeton University Press, 2011 (received the Euler Book Prize ).


  • Donald J. Albers, GL Alexanderson: Mathematical People - Profiles and Interviews. Birkhäuser, 1985.

Web links

Commons : Ronald Graham  - Collection of pictures, videos and audio files


  1. Ronald Graham in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / id used
  2. ^ Publications by Ron Graham on
  3. Ronald L. Graham, Jeffrey Lagarias, Colin L. Mallows, Allan R. Wilks, Catherine H. Yan: Apollonian circle packings: number theory. J. Number Theory. Volume 100, 2003, pp. 1-45.
  4. Ronald L. Graham, Jeffrey Lagarias, Colin L. Mallows, Allan R. Wilks, Catherine H. Yan: Apollonian circle packings: geometry and group theory. I. The Apollonian group, Discrete Comput. Geom. Volume 34, 2005, pp. 547-585.
  5. ICA Medals. List of Euler Medal Winners. Institute of Combinatorics and its Applications, accessed July 8, 2020 .
  6. Bruce Landman, Melvyn B. Nathanson, Jaroslav Nesetril, Richard J. Nowakowski, Carl Pomerance: Combinatorial Number Theory: Proceedings of the 'Integers Conference 2005' in Celebration of the 70th Birthday of Ronald Graham, Carrollton, Georgia, October 27-30 , 2005 . De Gruyter, Berlin / Boston 2007, ISBN 978-3-11-092509-8 ( [accessed July 8, 2020]).
  7. Legend Stage: Steve Mills. In: European Juggling Convention Ireland 2014, archived from the original on July 17, 2014 ; accessed on July 8, 2020 (English).
  8. Ronald Lewis Graham. In: MacTutor History of Mathematics Archive. University of St Andrews, accessed July 8, 2020.