Blum, Lenore
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Lenore Carol Blum (née Epstein, born December 18, 1942) is an American computer scientist and mathematician who has made contributions to the theories of real number computation,
cryptography Cryptography, or cryptology (from "hidden, secret"; and ''graphein'', "to write", or ''-logy, -logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of Adversary (cryptography), ...
, and pseudorandom number generation. She was a distinguished career professor of computer science at
Carnegie Mellon University Carnegie Mellon University (CMU) is a private research university in Pittsburgh, Pennsylvania, United States. The institution was established in 1900 by Andrew Carnegie as the Carnegie Technical Schools. In 1912, it became the Carnegie Institu ...
until 2019 and is currently a professor in residence at the
University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California), is a Public university, public Land-grant university, land-grant research university in Berkeley, California, United States. Founded in 1868 and named after t ...
. She is also known for her efforts to increase
diversity Diversity, diversify, or diverse may refer to: Business *Diversity (business), the inclusion of people of different identities (ethnicity, gender, age) in the workforce *Diversity marketing, marketing communication targeting diverse customers * ...
in mathematics and computer science.


Early life and education

Blum was born to a Jewish family in New York City, where her mother was a science teacher. They moved to
Venezuela Venezuela, officially the Bolivarian Republic of Venezuela, is a country on the northern coast of South America, consisting of a continental landmass and many Federal Dependencies of Venezuela, islands and islets in the Caribbean Sea. It com ...
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. With the assistance of Alan Perlis, she shifted fields to mathematics in 1960. She married
Manuel Blum Manuel Blum (born 26 April 1938) is a Venezuelan-born American computer scientist who received the Turing Award in 1995 "In recognition of his contributions to the foundations of computational complexity theory and its application to cryptography ...
, then a student at the
Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a Private university, private research university in Cambridge, Massachusetts, United States. Established in 1861, MIT has played a significant role in the development of many areas of moder ...
, and transferred in 1961 to Simmons College, a private women's liberal arts college in Boston. Simmons did not have a strong mathematics program but she was eventually able to take Isadore Singer's mathematics classes at MIT, graduating from Simmons with a B.S. in mathematics in 1963. She received her Ph.D. in mathematics from the
Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a Private university, private research university in Cambridge, Massachusetts, United States. Established in 1861, MIT has played a significant role in the development of many areas of moder ...
in 1968. Her dissertation, ''Generalized Algebraic Theories: A Model Theoretic Approach'', showed deep connections between model theory (a branch of mathematical logic) and differential algebra. She was supervised by Gerald Sacks (after being unable to follow an earlier advisor, Kenkichi Iwasawa, in his move to
Princeton University Princeton University is a private university, private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial ...
because, at the time, Princeton did not accept female graduate students).


Career

After completing her doctorate, Blum went to the
University of California at Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California), is a public land-grant research university in Berkeley, California, United States. Founded in 1868 and named after the Anglo-Irish philosopher George Berkele ...
to work with Julia Robinson as a postdoctoral fellow and lecturer in mathematics. (Robinson did not have a regular position in the Berkeley Mathematics Department. It was not until 1976, when she was elected as the first woman in the mathematics section of the
National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, NGO, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the ...
, did Robinson receive a permanent offer from Berkeley.) At that time, the department had no permanent positions for women, and after two years, Blum's position as lecturer was not renewed. In 1971 she became one of the founders of the Association for Women in Mathematics. In 1973 she joined the faculty of
Mills College Mills College at Northeastern University in Oakland, California is part of Northeastern University's global university system. Mills College was founded as the Young Ladies Seminary in 1852 in Benicia, California; it was relocated to Oakland in ...
, 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. From 1975 to 1978 she served as the third president of the Association for Women in Mathematics. Following this, Blum was elected as a Member at Large on the council of the AMS, serving from 1978 to 1980 and later as vice-President of the AMS (1990-1993). In 1979 she was awarded an endowed professorship, the first Letts-Villard Chair at Mills. In 1983 Blum won a
National Science Foundation The U.S. National Science Foundation (NSF) is an Independent agencies of the United States government#Examples of independent agencies, independent agency of the Federal government of the United States, United States federal government that su ...
(NSF) 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 International Business Machines Corporation (using the trademark IBM), nicknamed Big Blue, is an American Multinational corporation, multinational technology company headquartered in Armonk, New York, and present in over 175 countries. It is ...
. In 1992 Blum became the deputy director of the Mathematical Sciences Research Institute (MSRI), working there with its director
William Thurston William Paul Thurston (October 30, 1946August 21, 2012) was an American mathematician. He was a pioneer in the field of low-dimensional topology and was awarded the Fields Medal in 1982 for his contributions to the study of 3-manifolds. Thurst ...
. After visiting the
City University of Hong Kong The City University of Hong Kong (CityUHK) is a public research university in Kowloon Tong, Kowloon, Hong Kong. It was founded in 1984 as the City Polytechnic of Hong Kong and formally established as the City University of Hong Kong in 1994 ...
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 Carnegie Mellon University (CMU) is a private research university in Pittsburgh, Pennsylvania, United States. The institution was established in 1900 by Andrew Carnegie as the Carnegie Technical Schools. In 1912, it became the Carnegie Institu ...
(CMU) in 1999. 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. 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%. At CMU, Blum co-directed the NSF seeded ALADDIN Center which promoted the synergy between algorithm theory and practice. She also founded Project Olympus at CMU, an 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 the CMU Center for Innovation and Entrepreneurship, which she also co-founded, led to sexist treatment of her and the exclusion of other women from project activities.


Research

The Blum Blum Shub
pseudorandom number generator A pseudorandom number generator (PRNG), also known as a deterministic random bit generator (DRBG), is an algorithm for generating a sequence of numbers whose properties approximate the properties of sequences of random number generation, random n ...
, 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 In computational complexity theory, a computational hardness assumption is the hypothesis that a particular problem cannot be solved efficiently (where ''efficiently'' typically means "in polynomial time"). It is not known how to prove (unconditi ...
that
integer factorization In mathematics, integer factorization is the decomposition of a positive integer into a product of integers. Every positive integer greater than 1 is either the product of two or more integer factors greater than 1, in which case it is a comp ...
is infeasible. Blum is also known for the Blum–Shub–Smale machine, a theoretical model of computation over the
real number In mathematics, a real number is a number that can be used to measure a continuous one- dimensional quantity such as a duration or temperature. Here, ''continuous'' means that pairs of values can have arbitrarily small differences. Every re ...
s. Blum and her co-authors, Michael Shub and Stephen Smale, showed that (analogously to the theory of
Turing machine A Turing machine is a mathematical model of computation describing an abstract machine that manipulates symbols on a strip of tape according to a table of rules. Despite the model's simplicity, it is capable of implementing any computer algori ...
s) 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 The Mandelbrot set () is a two-dimensional set (mathematics), set that is defined in the complex plane as the complex numbers c for which the function f_c(z)=z^2+c does not Stability theory, diverge to infinity when Iteration, iterated starting ...
. In this model, over any field F, the problem of deciding whether or not a finite system of polynomial equations over F has a common zero is NP-complete over F. (F could be the reals or complex numbers or the integers mod 2.) Along with Felipe Cucker, Mike Shub and Steve Smale, she published a book on the subject, and in 1990 she gave an address at the
International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the IMU Abacus Medal (known before ...
on
computational complexity theory In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and explores the relationships between these classifications. A computational problem ...
and real computation.. In 2012, on the eve of
Alan Turing Alan Mathison Turing (; 23 June 1912 – 7 June 1954) was an English mathematician, computer scientist, logician, cryptanalyst, philosopher and theoretical biologist. He was highly influential in the development of theoretical computer ...
's 100th birthday she gave an invited address at the Turing Centenary Conference at the
University of Cambridge The University of Cambridge is a Public university, public collegiate university, collegiate research university in Cambridge, England. Founded in 1209, the University of Cambridge is the List of oldest universities in continuous operation, wo ...
on the connection between this work and little known work of Turing. Her recent work with Manuel Blum, inspired by Turing’s simple but powerful model of computation and
Bernard Baars Bernard J. Baars (born 1946 in Amsterdam, the Netherlands) is a former Senior Fellow in Theoretical Neurobiology at the Neurosciences Institute in San Diego, US. He is currently an Affiliated Fellow there. He is best known as the originator of ...
’ theater model of consciousness, develops a simple formal machine model for consciousness from a
theoretical computer science Theoretical computer science is a subfield of computer science and mathematics that focuses on the Abstraction, abstract and mathematical foundations of computation. It is difficult to circumscribe the theoretical areas precisely. The Associati ...
(TCS) perspective. Currently she is president of the Association for Mathematical Consciousness Science (AMCS).


Recognition

In 2002, Blum was selected to be an Association for Women in Mathematics Noether Lecturer. In 2005, Blum was a recipient of the Presidential Award for Excellence in Science, Mathematics, and Engineering Mentoring, given by president
George W. Bush George Walker Bush (born July 6, 1946) is an American politician and businessman who was the 43rd president of the United States from 2001 to 2009. A member of the Bush family and the Republican Party (United States), Republican Party, he i ...
"for her efforts to mentor girls and women in technology fields where traditionally they are underrepresented". She was given the Simmons University 2018 Distinguished Alumnae Lifetime Achievement Award in 2018. Blum was elected as a Fellow of the
American Association for the Advancement of Science The American Association for the Advancement of Science (AAAS) is a United States–based international nonprofit with the stated mission of promoting cooperation among scientists, defending scientific freedom, encouraging scientific responsib ...
in 1979. In 2012, Blum became an inaugural fellow of the
American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...
. In 2017 she was selected as an fellow of the Association for Women in Mathematics in the inaugural class. In 2024, she was elected to the
American Academy of Arts and Sciences The American Academy of Arts and Sciences (The Academy) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and other ...
. Blum is included in a deck of playing cards featuring notable women mathematicians published by the Association of Women in Mathematics.


Personal life

Lenore Blum is married to
Manuel Blum Manuel Blum (born 26 April 1938) is a Venezuelan-born American computer scientist who received the Turing Award in 1995 "In recognition of his contributions to the foundations of computational complexity theory and its application to cryptography ...
and is the mother of
Avrim Blum Avrim Louis Blum (born 27 May 1966) is a computer scientist. In 2007, he was made a Fellow of the Association for Computing Machinery "for contributions to learning theory and algorithms." Blum attended MIT, where he received his Ph.D. in 1991 ...
. All three are
MIT alumni This list of Massachusetts Institute of Technology alumni includes students who studied as undergraduates or graduate students at MIT's MIT School of Engineering, School of Engineering; MIT School of Science, School of Science; MIT Sloan ...
and have been professors of Computer Science at
Carnegie Mellon Carnegie may refer to: People *Carnegie (surname), including a list of people with the name **Andrew Carnegie, Scottish-American industrialist and philanthropist * Clan Carnegie, a lowland Scottish clan Institutions Named for Andrew Carnegie * ...
.


Selected publications


References


External links


Lenore Blum's Home Page
{{DEFAULTSORT:Blum, Lenore Living people 1942 births 20th-century American mathematicians 21st-century American mathematicians American computer scientists American women computer scientists Jewish American scientists Theoretical computer scientists Simmons University alumni Massachusetts Institute of Technology School of Science alumni Mills College faculty University of California, Berkeley College of Letters and Science faculty Carnegie Mellon University faculty Fellows of the American Association for the Advancement of Science Fellows of the American Mathematical Society Fellows of the Association for Women in Mathematics 20th-century American women mathematicians 21st-century American women mathematicians