斯狄爾獎是在1970年由伯克霍夫（Birhoff）、奧斯古特（Osgood）及高斯坦（Graustein）創立，資金來自利萊．斯狄爾（Leroy P. Steele）遺下的145,000美元。自1970年至1976年，每年也頒發給在數學研究有卓越成就的人士。
在1977年，美國數學學會修訂了頒授獎項的條文，使得每年頒授三個斯狄爾獎，分別有三個不同的獲獎條件（一）得獎者在數學上在具影響力的貢獻，長時期作高水平的研究工作，並對某數學領域的發展作出貢獻及透過指導博士學生對數學作出影響；（二）得獎者在卓越的著作，包括：書藉、可觀的研究或發現性研究論文；（三）得獎者的著作，不管是何時的結果，證實在某數學領域中是重要的基本或遲續性的成果或是研究中的重要典範。在1993年，美國數學學會正式把這三個獎定名為（一）斯狄爾終身成就獎（Steele Prize for Lifetime Achievement）；（二）斯狄爾數學發現獎（Steele Prize for Mathematical Exposition）；（三）斯狄爾研究啟發性貢獻獎（Steele Prize for Seminal Contribution to Research）。
歷屆斯狄爾獎得主：
| 1970 | Solomon Lefschetz |
| 1971 | James B. Carrell |
| Jean A. Dieudonné | |
| Phillip A. Griffiths | |
| 1972 | Edward B. Curtis |
| William J. Ellison | |
| Lawrence F. Payne | |
| Dana S. Scott | |
| 1975 | Lipman Bers |
| Martin D. Davis | |
| Joseph L. Taylor | |
| George W. Mackey | |
| H. Blaine Lawson | |
| 1979 | Salomon Bochner |
| Hans Lewy | |
| Antoni Zygmund | |
| Robin Hartshorne | |
| Joseph J. Kohn | |
| 1980 | André Weil |
| Harold M. Edwards | |
| Gerhard P. Hochschild | |
| 1981 | Oscar Zariski |
| Eberhard Hopf | |
| Nelson Dunford and Jacob T. Schwartz | |
| 1982 | Lars V. Ahlfors |
| Tsit-Yuen Lam | |
| John W. Milnor | |
| Fritz John | |
| 1983 | Paul R. Halmos |
| Steven C. Kleene | |
| Shiing-Shen Chern | |
| 1984 | Elias M. Stein |
| Lennart Carleson | |
| Joseph L. Doob | |
| 1985 | Michael Spivak |
| Robert Steinberg | |
| Hassler Whitney | |
| 1986 | Donald E. Knuth |
| Rudolf E. Kalman | |
| Saunders Mac Lane | |
| 1987 | Martin Gardner |
| Herbert Federer and Wendell Fleming | |
| Samuel Eilenberg | |
| 1988 | Sigurdur Helgason |
| Gian-Carlo Rota | |
| Deane Montgomery | |
| 1989 | Daniel Gorenstein |
| Alberto P. Calderón | |
| Irving Kaplansky | |
| 1990 | R. D. Richtmyer |
| Bertram Kostant | |
| Raoul Bott | |
| 1991 | Jean-François Treves |
| Eugenio Calabi | |
| Armand Borel | |
| 1993 | Jacques Dixmier |
| James Glimm | |
| Peter D. Lax | |
| 1993 | Walter Rudin (Mathematical Exposition) |
| George Daniel Mostow (Seminal Contribution to Research) | |
| Eugene B. Dynkin (Lifetime Achievement) | |
| 1994 | Ingrid Daubechies (Mathematical Exposition) |
| Louis de Branges (Seminal Contribution to Research) | |
| Louis Nirenberg (Lifetime Achievement) | |
| 1995 | Jean-Pierre Serre (Mathematical Exposition) |
| Edward Nelson (Seminal Contribution to Research) | |
| John T. Tate (Lifetime Achievement) | |
| 1996 | Bruce C. Berndt (Mathematical Exposition) |
| William Fulton (Mathematical Exposition) | |
| Daniel Stroock and S.R.S. Varadhan (Seminal Contribution to Research) | |
| Goro Shimura (Lifetime Achievement) | |
| 1997 | Anthony W. Knapp (Mathematical Exposition) |
| Mikhael Gromov (Seminal Contribution to Research) | |
| Ralph S. Phillips (Lifetime Achievement) | |
| 1998 | Joseph Silverman (Mathematical Exposition) |
| Herbert Wilf and Doron Zeilberger (Seminal Contribution to Research) | |
| Nathan Jacobson (Lifetime Achievement) | |
| 1999 | Serge Lang (Mathematical Exposition) |
| Michael G. Crandall (Seminal Contribution to Research) | |
| John F. Nash (Seminal Contribution to Research) | |
| Richard V. Kadison (Lifetime Achievement) | |
| 2000 | John H. Conway (Mathematical Exposition) |
| Barry Mazur (Seminal Contribution to Research) | |
| Isadore M. Singer (Lifetime Achievement) | |
| 2001 | Richard P. Stanley (Mathematical Exposition) |
| Leslie F. Greengard and Vladimir Rokhlin (Seminal Contribution to Research) | |
| Harry Kesten (Lifetime Achievement) | |
| 2002 | Yitzhak Katznelson (Mathematical Exposition) |
| Mark Goresky and Robert MacPherson (Seminal Contribution to Research) | |
| Michael Artin and Elias Stein (Lifetime Achievement) | |
| 2003 | John B. Garnett (Mathematical Exposition) |
| Ronald Jensen and Michael Morley (Seminal Contribution to Research) | |
| Ron Graham and Victor Guillemin (Lifetime Achievement) | |
| 2004 | John W. Milnor (Mathematical Exposition) |
| Lawrence C. Evans and Nicolai V. Krylov (Seminal Contribution to Research) | |
| Cathleen Synge Morawetz (Lifetime Achievement) |