| 1865 | A. De Morgan, FRAS |
1939 | G.H. Hardy |
| 1866 | J.J. Sylvester | 1941 | J.E. Littlewood |
| 1868 | A. Cayley | 1943 | L.J. Mordell |
| 1870 | W. Spottiswoode | 1945 | E.C. Titchmarsh |
| 1872 | T.A. Hirst | 1947 | W.V.D. Hodge |
| 1874 | H.J.S. Smith | 1949 | M.H.A. Newman |
| 1876 | Lord Rayleigh | 1951 | G. Temple |
| 1878 | C.W. Merrifield | 1953 | J.H.C. Whitehead |
| 1880 | S. Roberts |
1955 | P. Hall |
| 1882 | O. Henrici | 1957 | H. Davenport |
| 1884 | J.W.L. Glaisher | 1959 | H.A. Heilbronn |
| 1886 | J. Cockle, Kt | 1961 | M.L. Cartwright |
| 1888 | J.J. Walker | 1963 | A.G. Walker |
| 1890 | A.G. Greenhill | 1965 | G. Higman |
| 1892 | A.B. Kempe | 1967 | J.A. Todd |
| 1894 | P.A. MacMahon, RA | 1969 | E. Collingwood, CBE |
| 1896 | E.B. Elliott | 1970 | C.A. Rogers |
| 1898 | Lord Kelvin, GCVO | 1972 | D.G. Kendall |
| 1900 | E.W. Hobson | 1974 | M.F. Atiyah |
| 1902 | H. Lamb | 1976 | J.W.S. Cassels |
| 1904 | A.R. Forsyth | 1978 | C.T.C. Wall |
| 1906 | W. Burnside |
1980 | B.E. Johnson |
| 1908 | W.D. Niven, KCB | 1982 | P.M. Cohn |
| 1910 | H.F. Baker | 1984 | I.M. James |
| 1912 | A.E.H. Love | 1986 | E.C. Zeeman |
| 1914 | J. Larmor, Kt, MP | 1988 | J.H. Coates |
| 1916 | H.M. Macdonald | 1990 | J.F.C. Kingman |
| 1918 | J.E. Campbell | 1992 | J.R. Ringrose |
| 1920 | H.W. Richmond | 1994 | N.J. Hitchin |
| 1922 | W.H. Young | 1996 | J.M. Ball |
| 1924 | A.L. Dixon | 1998 | M.J. Taylor |
| 1926 | G.H. Hardy | 2000 | J.T. Stuart |
| 1928 | E.T. Whittaker |
2002 | P. Goddard |
| 1929 | S. Chapman | 2003 | F.C. Kirwan |
| 1931 | A.C. Dixon | 2005 | J.F. Toland |
| 1933 | G.N. Watson |
2007 | E.B. Davies |
| 1935 | G.B. Jeffery | 2009 | A.J. Macintyre |
| 1937 | E.A. Milne |
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