Smith's Prize was the name of each of two prizes awarded annually to two research students in mathematics and theoretical physics at the University of Cambridge from 1769.^[1] Following the reorganization in 1998, they are now awarded under the names Smith-Knight Prize and Rayleigh-Knight Prize.

The Smith Prize fund was founded by bequest of Robert Smith upon his death in 1768, having by his will left £3,500 of South Sea Company stock to the University. Every year two or more junior Bachelor of Arts students who had made the greatest progress in mathematics and natural philosophy were to be awarded a prize from the fund. The prize was awarded every year from 1769 to 1998 except 1917.

From 1769 to 1885, the prize was awarded for the best performance in a series of examinations. In 1854 George Stokes included an examination question on a particular theorem that William Thomson had written to him about, which is now known as Stokes' theorem.^[2] T. W. Körner notes

Only a small number of students took the Smith's prize examination in the nineteenth century. When Karl Pearson took the examination in 1879, the examiners were Stokes, Maxwell, Cayley, and Todhunter and the examinees went on each occasion to an examiner's dwelling, did a morning paper, had lunch there and continued their work on the paper in the afternoon.^[3]

In 1885, the examination was renamed Part III, (now known as the Master of Advanced Study in Mathematics for students who studied outside of Cambridge before taking it) and the prize was awarded for the best submitted essay rather than examination performance. According to Barrow-Green

By fostering an interest in the study of applied mathematics, the competition contributed towards the success in mathematical physics that was to become the hallmark of Cambridge mathematics during the second half of the nineteenth century.^[1]

In the twentieth century, the competition stimulated postgraduate research in mathematics in Cambridge and the competition has played a significant role by providing a springboard for graduates considering an academic career. The majority of prize-winners have gone on to become professional mathematicians or physicists.

The Rayleigh Prize was an additional prize, which was awarded for the first time in 1911.

The Smith's and Rayleigh prizes were only available to Cambridge graduate students who had been undergraduates at Cambridge. The J.T. Knight Prize was established in 1974 for Cambridge graduates who had been undergraduates at other universities. The prize commemorates J.T. Knight (1942–1970), who had been an undergraduate student at Glasgow and a graduate student at Cambridge. He was killed in a motor car accident in Ireland in April 1970.

Originally, in 1769, the prizes were worth £25 each and remained at that level for 100 years. In 1867, they fell to £23 and in 1915 were still reported to be worth that amount.^{[citation needed]} By 1930, the value had risen to about £30, and by 1940, the value had risen by a further one pound to £31. By 1998, a Smith's Prize was worth around £250.^[1]

In 2007, the value of the three prize funds was roughly £175,000.^[4]

In 1998 the Smith Prize, Rayleigh Prize and J. T. Knight Prize were replaced by the Smith-Knight Prize and Rayleigh-Knight Prize,^[5] the standard for the former being higher than that required for the latter.

For the period up to 1940 a complete list is given in Barrow-Green (1999) including titles of prize essays from 1889 to 1940. The following includes a selection from this list.

A more complete list of Rayleigh prize recipients is given in Appendix 1 ("List of Prize Winners and their Essays 1885–1940") of^[1]

• 1913 Ralph H. Fowler^[41]
• 1923 Edward Collingwood
• 1927 William McCrea^[42]
• 1930 Harold Davenport^[43]
• 1937 David Stanley Evans^[44]
• 1951 Gabriel Andrew Dirac^[45]
• 1980 David Benson^[46]
• 1982 Susan Stepney^[47]
• 1994 Group 4: J.D. King, A.P. Martin. Group 5: K.M. Croudace, J.R. Elliot.
• 1998 P. Bolchover, O. T. Johnson, R. W. Verrill, R. Bhattacharyya, U. A. Salam, S. A. Wright and T. J. Hunt

• 1974 Cameron Leigh Stewart^[48] Allan J. Clarke
• 1975 Frank Kelly^[49] and Ian Sobey
• 1976 Trevor McDougall
• 1977 Gerard Murphy
• 1981 Bruce Allen and Philip K. Pollett
• 1983 Ya-xiang Yuan
• 1985 Reinhard Diestel
• 1987 Qin Sheng (mathematician)
• 1988 Somak Raychaudhury
• 1990 Darryn W. Waugh
• 1991 Renzo L. Ricca
• 1992 Grant Lythe, Christophe Pichon, Henrik O. Rasmussen
• 1993 Anastasios Christou Petkou
• 1994 Group 1: M. Gaberdiel, Y. Liu. Group 3: H.A. Chamblin. Group 4: P.P. Avelino, S.G. Lack, A.L. Sydenham. Group 5: S. Keras, U. Meyer, G.M. Pritchard, H. Ramanathan, K. Strobl. Group 6: A.O. Bender, V. Toledano Laredo.
• 1996 Conor Houghton, Thomas Manke
• 1997 Arno Schindlmayr
• 1998 A. Bejancu, G. M. Keith, J. Sawon, D. R. Brecher, T. S. H. Leinster, S. Slijepcevic, K. K. Damodaran, A. R. Mohebalhojeh, C. T. Snydal, F. De Rooij, O. Pikhurko, David K. H. Tan, P. R. Hiemer, T. Prestidge, F. Wagner, Viet Ha Hoàng, A. W. Rempel and Jium-Huei Proty Wu

• 1999 D. W. Essex, H. S. Reall, A. Saikia, A. C. Faul, Duncan C. Richer, M. J. Vartiainen, T. A. Fisher, J. Rosenzweig, J. Wierzba and J. B. Gutowski^[50][51]
• 2001 B. J. Green, T A. Mennim, A. Mijatovic, F. A. Dolan, Paul D. Metcalfe and S. R. Tod
• 2002 Konstantin Ardakov,^[52] Edward Crane^[53] and Simon Wadsley^[54]
• 2004 Neil Roxburgh^[55]
• 2005 David Conlon^[56]
• 2008 Miguel Paulos
• 2009 Olga Goulko
• 2010 Miguel Custódio
• 2011 Ioan Manolescu
• 2014 Bhargav P. Narayanan^[57]
• 2018 Theodor Bjorkmo, Muntazir Abidi, Amelia Drew, Leong Khim Wong
• 2020 Jef Laga, Kasia Warburton, Daniel Zhang, Shayan Iranipour
• 2021 David Gwilym Baker, Hannah Banks, Jason Joykutty, Andreas Schachner, Mohammed Rifath Khan Shafi ^[58]

• 1999 C. D. Bloor, R. Oeckl, J. Y. Whiston, Y-C. Chen, P. L. Rendon, C. Wunderer, J. H. P. Dawes, D. M. Rodgers, H-M. Gutmann and A. N. Ross
• 2001 A. F. R. Bain, S. Khan, S. Schafer-Nameki, N. R. Farr, J. Niesen, J. H. Siggers, M. Fayers, D. Oriti, M. J. Tildesley, J. R. Gair, M. R. E. H. Pickles, A. J. Tolley, S. R. Hodges, R. Portugues, C. Voll, M. Kampp, P. J. P. Roche and B. M. J. B. Walker^[59]
• 2004 Oliver Rinne
• 2005 Guillaume Pierre Bascoul and Giuseppe Di Graziano
• 2007 Anders Hansen^[60] and Vladimir Lazić

• List of mathematics awards