Lenore Blum

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Lenore Blum
Lenore Blum, Berkeley, California, 1998
Born (1942-12-18) December 18, 1942 (age 80)
New York City
Alma mater
Known for
SpouseManuel Blum
ChildrenAvrim Blum
Scientific career
Fieldsmathematics, computer science
ThesisGeneralized Algebraic Theories: A Model Theoretic Approach (1968)
Doctoral advisorGerald Sacks
Doctoral studentsCarol Frieze

Lenore Carol Blum (née Epstein,[2] born December 18, 1942) is an American computer scientist and mathematician who has made contributions to the theories of real number computation, cryptography, and pseudorandom number generation. She was a distinguished career professor of computer science at Carnegie Mellon University until 2019 and is currently a professor in residence at the University of California, Berkeley.[1] She is also known for her efforts to increase diversity in mathematics and computer science.

Early life and education[edit]

Blum was born to a Jewish family in New York City, where her mother was a science teacher.[3] They moved to Venezuela when Blum was nine. After graduating from her Venezuelan high school at age 16, she studied architecture at Carnegie Institute of Technology (now Carnegie Mellon University) beginning in 1959.[4][5] With the assistance of Alan Perlis, she shifted fields to mathematics in 1960.[6] She married Manuel Blum, then a student at the Massachusetts Institute of Technology, and transferred in 1961 to Simmons College, a private women's liberal arts college in Boston.[4][5] Simmons did not have a strong mathematics program but she was eventually able to take Isadore Singer's mathematics classes at MIT,[7] graduating from Simmons with a B.S. in mathematics in 1963.[8][9]

She received her Ph.D. in mathematics from the Massachusetts Institute of Technology in 1968. Her dissertation, Generalized Algebraic Theories: A Model Theoretic Approach, was supervised by Gerald Sacks.[10] She had switched to being advised by Sacks after being unable to follow an earlier advisor in his move to Princeton University because, at the time, Princeton did not accept female graduate students.[4]


After completing her doctorate, Blum went to the University of California at Berkeley to work with Julia Robinson[11] as a postdoctoral fellow and lecturer in mathematics. However, the department had no permanent positions for women, and after two years, her position as lecturer was not renewed. In 1971 she became one of the founders of the Association for Women in Mathematics.[4][5][AWM] In 1973 she joined the faculty of Mills College, a women's college in the Oakland hills near Berkeley. In 1974 she founded the mathematics and computer science department at Mills, at that time the only computer science program at a women's college. She served as the head or co-head of the department for 13 years.[12] From 1975 to 1978 she served as the third president of the Association for Women in Mathematics.[5][AWM] Following this, Blum was elected as a Member at Large on the council of the AMS, serving from 1978 to 1980.[13] In 1979 she was awarded an endowed professorship, the first Letts-Villard Chair at Mills.[5]

In 1983 Blum won a National Science Foundation Visiting Professorship for Women award to work with Michael Shub for two years at the CUNY Graduate Center. In 1987 she spent a year at IBM. In 1992 Blum became the deputy director of the Mathematical Sciences Research Institute (MSRI), working there with its director William Thurston. After visiting the City University of Hong Kong in 1996–1998 to work on her book Complexity and Real Computation (during Hong Kong's handover from British to Chinese rule), she became a Distinguished Career Professor of Computer Science at Carnegie Mellon University (CMU) in 1999.[5][9]

At CMU, she took the philosophy that the low numbers of women majoring in computer science were in part caused by a vicious cycle: because there were few women, the women in computer science had fewer support networks (such as friends in the same major to help them with coursework) than men. And because these factors made being a computer scientist less pleasant and more difficult for the women, fewer women chose to major in computer science. Instead of the then-popular approach of changing the curriculum to be more application-centric in the hope of attracting women, she pushed to maintain a traditional computer science program but to change the culture surrounding the program to be more welcoming. In support of this goal, she founded the Women@SCS program at CMU, which provided both mentoring and outreach opportunities for women in computer science.[14] Through this program, which came to be directed by Blum's student Carol Frieze, CMU was able to increase the proportion of women in the undergraduate computer science program to nearly 50%.[15]

Blum also founded Project Olympus at CMU, a business incubator program that led to many startups in Pittsburgh associated with CMU and its computer program. She resigned from CMU in 2018 (effective August 2019) after a change in management structure of Project Olympus led to sexist treatment of her and the exclusion of other women from project activities.[14]


The Blum Blum Shub pseudorandom number generator, published jointly by Blum, Manuel Blum, and Michael Shub, is based on the operation of squaring numbers modulo the products of two large primes. Its security can be reduced to the computational hardness assumption that integer factorization is infeasible.[BBS]

Blum is also known for the Blum–Shub–Smale machine, a theoretical model of computation over the real numbers. Blum and her co-authors, Michael Shub and Stephen Smale, showed that (analogously to the theory of Turing machines) one can define analogues of NP-completeness, undecidability, and universality for this model. For instance, in this model it is undecidable to determine whether a given point belongs to the Mandelbrot set.[5][BSS] She published a book on the subject,[16][CRC] and in 1990 she gave an address at the International Congress of Mathematicians on computational complexity theory and real computation.[12][5]


In 2002, Blum was selected to be an Association for Women in Mathematics Noether Lecturer.[17]

In 2005, Blum was a recipient of the Presidential Award for Excellence in Science, Mathematics, and Engineering Mentoring, given by president George W. Bush "for her efforts to mentor girls and women in technology fields where traditionally they are underrepresented".[18] She was given the Simmons University 2018 Distinguished Alumnae Lifetime Achievement Award in 2018.[2]

Blum was elected as a Fellow of the American Association for the Advancement of Science in 1979.[5] In 2012, Blum became a fellow of the American Mathematical Society.[19] In 2017 she was selected as a fellow of the Association for Women in Mathematics in the inaugural class.[20]

She is included in a deck of playing cards featuring notable women mathematicians published by the Association of Women in Mathematics.[21]

Personal life[edit]

Lenore Blum is married to Manuel Blum and is the mother of Avrim Blum.[5] All three are MIT alumni and have been professors of Computer Science at Carnegie Mellon.[11]

Selected publications[edit]

Blum, Lenore; Blum, Manuel (1975), "Toward a mathematical theory of inductive inference", Information and Computation, 28 (2): 125–155, doi:10.1016/S0019-9958(75)90261-2, MR 0395312
Blum, L.; Blum, M.; Shub, M. (1986), "A simple unpredictable pseudorandom number generator", SIAM Journal on Computing, 15 (2): 364–383, doi:10.1137/0215025, MR 0837589
Blum, Lenore (1988), "A new simple homotopy algorithm for linear programming. I", Journal of Complexity, 4 (2): 124–136, doi:10.1016/0885-064X(88)90025-8, MR 0938440
Blum, Lenore; Shub, Mike; Smale, Steve (1989), "On a theory of computation and complexity over the real numbers: NP-completeness, recursive functions and universal machines", Bulletin of the American Mathematical Society, New Series, 21 (1): 1–46, doi:10.1090/S0273-0979-1989-15750-9, MR 0974426
Blum, Lenore; Cucker, Felipe; Shub, Michael; Smale, Steve (1998), Complexity and Real Computation, New York: Springer-Verlag, doi:10.1007/978-1-4612-0701-6, ISBN 0-387-98281-7, S2CID 12510680[16]


  1. ^ a b "Lenore Blum | EECS at UC Berkeley". www2.eecs.berkeley.edu. Retrieved 2021-11-13.
  2. ^ a b "Alumnae/i Award Recipients", Simmons University, archived from the original on 2019-04-19, retrieved 2019-01-22
  3. ^ O'Connor, John J.; Robertson, Edmund F., "Lenore Blum", MacTutor History of Mathematics Archive, University of St Andrews
  4. ^ a b c d Tabachnik, Toby (December 8, 2017), "Accidental activist Lenore Blum changes formula for women in math", Jewish Chronicle, Times of Israel
  5. ^ a b c d e f g h i j O'Connor, John J.; Robertson, Edmund F., "Lenore Blum", MacTutor History of Mathematics Archive, University of St Andrews
  6. ^ Blum, Lenore (February 13, 2019), "Girl On The Move: My time with computer pioneer Alan Perlis", Pittsburgh Quarterly
  7. ^ Perl, Teri (1993), Women and Numbers: Lives of Women Mathematicians, Wide World Publishing/Tetra, p. 84
  8. ^ "Class of 1963 News: Professor tries to instill passion for math, science", Simmons College Class of 1963 News. Originally written by Joyce Gannon and published Sunday, August 21, 2005 in the Pittsburgh Post-Gazette
  9. ^ a b "Short Vita: Lenore Blum", Carnegie Mellon University website
  10. ^ Lenore Blum at the Mathematics Genealogy Project
  11. ^ a b Spice, Byron (October 21, 2001), "Dad, mom join son to form a potent computer science team at CMU", Pittsburgh Post-Gazette
  12. ^ a b "Lenore Blum", Biographies of Women Mathematicians, Agnes Scott College
  13. ^ "AMS Committees". American Mathematical Society. Retrieved 2023-03-28.
  14. ^ a b Certo, Tracy (September 6, 2018), "Lenore Blum shocked the community with her sudden resignation from CMU. Here she tells us why.", Next Pittsburgh
  15. ^ Andersen, Nick (September 16, 2016), "Carnegie Mellon pushes for more women in engineering and computer science", Washington Post
  16. ^ a b Reviews of Complexity and Real Computation:
  17. ^ "Lenore Blum", Noether Lectures, Association for Women in Mathematics, retrieved 9 January 2021
  18. ^ Bails, Jennifer (May 17, 2005), "CMU professor honored for mentoring", Pittsburgh Tribune-Review
  19. ^ List of Fellows of the American Mathematical Society, retrieved 2012-11-10.
  20. ^ "2018 Inaugural Class of AWM Fellows". Association for Women in Mathematics. Retrieved 8 January 2019.
  21. ^ "Mathematicians of EvenQuads Deck 1". awm-math.org. Retrieved 2022-06-18.

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