The De Morgan Medal is a prize for outstanding contribution to mathematics, awarded by the London Mathematical Society (LMS). The Society's most prestigeous award, it is given in memory of Augustus De Morgan, who was the first President of the LMS.

The medal is given every third year (in years divisible by 3). The only grounds for the award of the Medal are the candidate's contributions to mathematics but it can only be awarded to a mathematician who is normally resident in the United Kingdom on 1st January of the relevant year.

Past winners of the medals are:

• 1884 Arthur Cayley
• 1887 James Joseph Sylvester
• 1890 Lord Rayleigh
• 1893 Felix Klein
• 1896 S. Roberts
• 1899 William Burnside
• 1902 A. G. Greenhill
• 1905 H. F. Baker
• 1908 J. W. L. Glaisher
• 1911 Horace Lamb
• 1914 J. Larmor
• 1917 W. H. Young
• 1920 E. W. Hobson
• 1923 P. A. MacMahon
• 1926 AEH Love
• 1929 Godfrey Harold Hardy
• 1932 Bertrand Russell
• 1935 E. T. Whittaker
• 1938 JE Littlewood
• 1941 Louis Mordell
• 1944 S. Chapman
• 1950 A. S. Besicovitch
• 1953 E C Titchmarsh
• 1956 G. I. Taylor
• 1959 W V D Hodge
• 1962 Max Newman
• 1965 Philip Hall
• 1968 Mary Cartwright
• 1971 Kurt Mahler
• 1974 Graham Higman
• 1977 C. Ambrose Rogers
• 1980 Michael Atiyah
• 1983 K. F. Roth
• 1986 J. W. S. Cassels
• 1989 D. G. Kendall
• 1992 Albrecht Fröhlich
• 1995 W. K. Hayman
• 1998 R. A. Rankin
• 2001 J. A. Green
• 2004 Roger Penrose