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Joseph Hillel Silverman (born March 27, 1955, New York City)[1] is a professor of mathematics at Brown University. Joseph Silverman received an Sc.B. from Brown University in 1977 and a Ph.D. from Harvard University in 1982 under the direction of John Tate. He taught at M.I.T. (1982–1986) and at Boston University (1986–1988) before taking a position at Brown in 1988.

Joseph H. Silverman
Born (1955-03-27) March 27, 1955 (age 64)
Nationality United States
Alma materHarvard University
AwardsLeroy P. Steele Prize (1998)
Scientific career
InstitutionsBrown University
Doctoral advisorJohn Tate
Doctoral studentsMichelle Manes

Silverman's work has been in number theory, arithmetic geometry, arithmetic dynamics and cryptography. He has published more than 100 research articles, written or coauthored six books, and edited three conference proceedings.

In 1996, Silverman, along with Jeffrey Hoffstein, Jill Pipher and Daniel Lieman, founded NTRU Cryptosystems, Inc. to market their cryptographic algorithms, NTRUEncrypt and NTRUSign.

In 2012 he became a fellow of the American Mathematical Society.[2]


Silverman has written two graduate texts on elliptic curves, The Arithmetic of Elliptic Curves (1986) and Advanced Topics in the Arithmetic of Elliptic Curves (1994). For these two books he received a Steele Prize for Mathematical Exposition from the American Mathematical Society, which cited them by saying that “Silverman's volumes have become standard references on one of the most exciting areas of algebraic geometry and number theory.” Silverman has also written three undergraduate texts: Rational Points on Elliptic Curves (1992, co-authored with John Tate), A Friendly Introduction to Number Theory (3rd ed. 2005), and An Introduction to Mathematical Cryptography (2008, co-authored with Jeffrey Hoffstein and Jill Pipher). Additional graduate-level texts authored by Silverman are Diophantine Geometry: An Introduction (2000, co-authored with Marc Hindry) and The Arithmetic of Dynamical Systems (2007).


  • ———; Hindry, M., Diophantine geometry: An introduction, ISBN 0-387-98981-1.[3]
  • ———; Cornell, G.; Stevens, G., Modular forms and Fermat's Last Theorem, ISBN 0-387-94609-8.[4]
  • ———; Hoffstein, J.; Pipher, J., An introduction to mathematical cryptography, ISBN 978-0-387-77993-5.
  • ———, The arithmetic of elliptic curves, ISBN 0-387-96203-4.[5][6] 2nd edition. 2009.
  • ———, Advanced topics in the arithmetic of elliptic curves, ISBN 0-387-94328-5.
  • ———, The arithmetic of dynamical systems, ISBN 978-0-387-69903-5.[7]
  • ———, A friendly introduction to number theory, ISBN 978-0-13-186137-4.
  • ———; Tate, J., Rational points on elliptic curves, ISBN 0-387-97825-9. 2nd edition. 2015.[6]


  1. ^ "Biographies of Candidates 2007" (PDF), Notices of the American Mathematical Society, 54 (8): 1043–1057, September 2007, retrieved 2009-05-25
  2. ^ List of Fellows of the American Mathematical Society, retrieved 2013-07-20.
  3. ^ Gross, Robert (2001). "Review: Diophantine geometry: an introduction, by M. Hindry and J. H. Silverman". Bull. Amer. Math. Soc. (N.S.). 38 (3): 379–381. doi:10.1090/s0273-0979-01-00907-7.
  4. ^ Buzzard, Kevin (1999). "Review: Modular forms and Fermat's Last Theorem, by G. Cornell, J. H. Silverman, and G. Stevens". Bull. Amer. Math. Soc. (N.S.). 36 (2): 261–266. doi:10.1090/s0273-0979-99-00778-8.
  5. ^ Cassels, J. W. S. (1987). "Review: The arithmetic of elliptic curves, by J. H. Silverman". Bull. Amer. Math. Soc. (N.S.). 17 (1): 148–149. doi:10.1090/s0273-0979-1987-15544-3.
  6. ^ a b Silverman, Joseph (2017). "Rational points on, and the arithmetic of, elliptic curves: A tale of two books (and an article)" (PDF). Bulletin of the American Mathematical Society (N.S.). 54 (4): 591–594.
  7. ^ Benedetto, Robert L. (January 2009). "Review of The arithmetic of dynamical systems by Joseph H. Silverman" (PDF). Bull. Amer. Math. Soc. (N.S.). 46 (1): 157–164.

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