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Michael Ira Shub (born August 17, 1943) is an American
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...
who has done research into dynamical systems and the complexity of
real number In mathematics, a real number is a number that can be used to measure a ''continuous'' one-dimensional quantity such as a distance, duration or temperature. Here, ''continuous'' means that values can have arbitrarily small variations. Every ...
algorithms.


Biography

Shub obtained his
Ph.D. A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is ...
degree at the
University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...
with a thesis entitled '' Endomorphisms of
Compact Compact as used in politics may refer broadly to a pact or treaty; in more specific cases it may refer to: * Interstate compact * Blood compact, an ancient ritual of the Philippines * Compact government, a type of colonial rule utilized in British ...
Differentiable Manifolds'' on 1967. His advisor was Stephen Smale. From 1967 to 1985 he worked at
Brandeis University , mottoeng = "Truth even unto its innermost parts" , established = , type = Private research university , accreditation = NECHE , president = Ronald D. Liebowitz , ...
, the
University of California, Santa Cruz The University of California, Santa Cruz (UC Santa Cruz or UCSC) is a public land-grant research university in Santa Cruz, California. It is one of the ten campuses in the University of California system. Located on Monterey Bay, on the edge of ...
and the Queens College at the City University of New York. From 1985 to 2004 he joined IBM's
Thomas J. Watson Research Center The Thomas J. Watson Research Center is the headquarters for IBM Research. The center comprises three sites, with its main laboratory in Yorktown Heights, New York, U.S., 38 miles (61 km) north of New York City, Albany, New York and wit ...
. From 2004 to 2010 he worked at the
University of Toronto The University of Toronto (UToronto or U of T) is a public university, public research university in Toronto, Ontario, Canada, located on the grounds that surround Queen's Park (Toronto), Queen's Park. It was founded by royal charter in 1827 ...
. After 2010 he is a researcher at the
University of Buenos Aires The University of Buenos Aires ( es, Universidad de Buenos Aires, UBA) is a public research university in Buenos Aires, Argentina. Established in 1821, it is the premier institution of higher learning in the country and one of the most prestigi ...
and at the City University of New York. Shub was the Chair of the Society for the Foundations of Computational Mathematics from 1995 to 1997. In 2012, a conference, ''From Dynamics to Complexity'', was organised at the Fields Institute in
Toronto Toronto ( ; or ) is the capital city of the Canadian province of Ontario. With a recorded population of 2,794,356 in 2021, it is the most populous city in Canada and the fourth most populous city in North America. The city is the anch ...
celebrating his work. In 2015 he was elected as a
fellow A fellow is a concept whose exact meaning depends on context. In learned or professional societies, it refers to a privileged member who is specially elected in recognition of their work and achievements. Within the context of higher education ...
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, ...
"for contributions to smooth dynamics and to complexity theory." Since August 2016, he has been Martin and Michele Cohen Professor and Chair of the Mathematics Department at City College of New York.


Work

Shub has produced publications in dynamical systems and in the complexity of real number algorithms. In his Ph.D. thesis in 1967, he introduced the notion of expanding maps, which gave the first examples of structurally stable strange attractors. In 1974 he proposed the Entropy Conjecture, an open problem in dynamical systems, which was proved by Yosef Yomdin for C^\infty mappings in 1987. This same year, Shub published his book ''Global Stability of Dynamical Systems'', which is often used as a reference in introductory and advanced books on the subject of dynamical systems. Shub, along with coauthors Lenore and Manuel Blum, described a simple, unpredictable, secure
random number generator Random number generation is a process by which, often by means of a random number generator (RNG), a sequence of numbers or symbols that cannot be reasonably predicted better than by random chance is generated. This means that the particular outc ...
(see
Blum Blum Shub Blum Blum Shub (B.B.S.) is a pseudorandom number generator proposed in 1986 by Lenore Blum, Manuel Blum and Michael Shub that is derived from Michael O. Rabin's one-way function. __TOC__ Blum Blum Shub takes the form :x_ = x_n^2 \bmod M, where ...
). This random generator is useful from theoretical and practical perspectives. In 1989 he proposed with
Lenore Blum Lenore Carol Blum (née Epstein, born December 18, 1942) is an American computer scientist and mathematician who has made pioneering contributions to the theories of real number computation, cryptography, and pseudorandom number generation. She ...
and Stephen Smale the notion of
Blum–Shub–Smale machine In computation theory, the Blum–Shub–Smale machine, or BSS machine, is a model of computation introduced by Lenore Blum, Michael Shub and Stephen Smale, intended to describe computations over the real numbers. Essentially, a BSS machine is ...
, an alternative to the classical Turing model of computation. Their model is used to analyse the computability of functions. In 1993, Shub and Smale initiated a rigorous analysis of
homotopy In topology, a branch of mathematics, two continuous functions from one topological space to another are called homotopic (from grc, ὁμός "same, similar" and "place") if one can be "continuously deformed" into the other, such a defor ...
-based algorithms for solving systems of nonlinear algebraic equations, which has inspired much of the work in that area during the last two decades. Shub was one of the founders of the nonprofit association
Foundations of Computational Mathematics Foundations of Computational Mathematics (FoCM) is an international nonprofit organization that supports and promotes research at the interface of mathematics and computation. It fosters interaction among mathematics, computer science, and other ...
, and editor of their journal ''
Foundations of Computational Mathematics Foundations of Computational Mathematics (FoCM) is an international nonprofit organization that supports and promotes research at the interface of mathematics and computation. It fosters interaction among mathematics, computer science, and other ...
'' with the same name until 2009.


Selected publications

* * * * * * *


References


External links


Personal website
at the City College of New York. {{DEFAULTSORT:Shub, Michael Ira 1943 births Living people 20th-century American mathematicians 21st-century American mathematicians University of California, Berkeley alumni Fellows of the American Mathematical Society Brandeis University faculty City University of New York faculty Graduate Center, CUNY faculty City College of New York faculty University of California, Santa Cruz faculty University of Toronto faculty University of Buenos Aires faculty IBM Research computer scientists