Michael Shub
Michael Ira Shub | |
|---|---|
| Born | August 17, 1943 |
| Alma mater | University of California, Berkeley |
| Occupation | Mathematician |
| Years active | 1967–present |
| Known for | Contributions to dynamical systems and computational complexity; co-developer of the Blum Blum Shub random number generator; co-creator of the Blum–Shub–Smale machine |
Michael Ira Shub (born August 17, 1943) is a prominent American mathematician recognized for his contributions to dynamical systems and the computational complexity of algorithms over real numbers.
1967: Doctorate and initial academic roles
Shub completed his Ph.D. at the University of California, Berkeley in 1967, presenting a dissertation titled Endomorphisms of Compact Differentiable Manifolds, where he introduced expanding maps that served as early examples of structurally stable strange attractors. His doctoral advisor was Stephen Smale.
From 1967 until 1985, he held academic appointments at Brandeis University, the University of California, Santa Cruz, and Queens College (CUNY). In 1974, he formulated the Entropy Conjecture within dynamical systems theory, which was subsequently proven by Yosef Yomdin for smooth functions.
1985–2004: Tenure at IBM Research
Shub was employed at IBM's Thomas J. Watson Research Center from 1985 through 2004. His influential book Global Stability of Dynamical Systems, published in 1987, remains a foundational text in the discipline. In 1993, together with Stephen Smale, he initiated rigorous investigations into homotopy methods for solving nonlinear algebraic equations, shaping future studies in this area.
He served as the inaugural chair of the Society for the Foundations of Computational Mathematics from 1995 to 1997 and played a key role as a founding editor for its journal, Foundations of Computational Mathematics, launched in 2001.
1986: Development of Blum Blum Shub
Alongside Lenore and Manuel Blum, Shub co-developed the Blum Blum Shub random number generator in 1986. This generator is valued for its simplicity and cryptographic security properties, with extensive theoretical and applied significance.
1989: Introduction of the Blum–Shub–Smale machine
In 1989, Shub collaborated with Lenore Blum and Stephen Smale to propose the Blum–Shub–Smale machine—a computational framework distinct from the classical Turing model—providing a novel approach to studying function computability.
2004–2010: Academic positions after IBM
Following his IBM tenure, Shub was affiliated with the University of Toronto until 2010. Subsequently, he joined both the University of Buenos Aires and the Graduate Center of the City University of New York. Since 2016, he has held the position of Martin and Michele Cohen Professor and Chair of Mathematics at City College of New York.
Honors and distinctions
- 1972: Awarded fellowship by the Alfred P. Sloan Foundation
- 2000: Named Fellow of the American Association for the Advancement of Science
- 2012: Celebrated through a conference titled From Dynamics to Complexity at the Fields Institute in Toronto
- 2015: Elected Fellow of the American Mathematical Society for his work in smooth dynamics and complexity theory
- 2016: Recipient of a Fulbright Specialist grant
Notable publications
- Lenore Blum, Manuel Blum, Michael Shub, A Simple Unpredictable Pseudo-Random Number Generator, SIAM Journal on Computing, 1986
- Michael Shub, Dynamical systems, filtrations and entropy, Bulletin of the American Mathematical Society, 1974
- Michael Shub, Global Stability of Dynamical Systems, Springer-Verlag, 1987
- Lenore Blum, Michael Shub, Stephen Smale, On a theory of computation and complexity over the real numbers, Bulletin of the American Mathematical Society, 1989
- Michael Shub, Stephen Smale, Complexity of Bézout's Theorem I: Geometric Aspects, Journal of the American Mathematical Society, 1993
- Lenore Blum, Felipe Cucker, Michael Shub, Stephen Smale, Complexity and Real Computation, Springer-Verlag, 1997
External links
- Official webpage hosted by the City College of New York.
- Pages with script errors
- Articles with short description
- Articles with hCards
- No local image but image on Wikidata
- 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
- CUNY Graduate Center faculty
- City College of New York faculty
- University of California, Santa Cruz faculty
- Academic staff of the University of Toronto
- Academic staff of the University of Buenos Aires
- IBM Research computer scientists
- Queens College, City University of New York faculty