#1,111

Most Influential Person

American mathematician

According to Wikipedia, Stephen Smale is an American mathematician, known for his research in topology, dynamical systems and mathematical economics. He was awarded the Fields Medal in 1966 and spent more than three decades on the mathematics faculty of the University of California, Berkeley . Currently, he is Professor Emeritus at the University of California, Berkeley with research interests in algorithms, numerical analysis and global analysis.

- Differential Equations, Dynamical Systems, and Linear Algebra (1974) (2846)
- Differentiable dynamical systems (1967) (1741)
- On the mathematical foundations of learning (2001) (1428)
- Emergent Behavior in Flocks (2007) (1280)
- On a theory of computation and complexity over the real numbers: $NP$- completeness, recursive functions and universal machines (1989) (1108)
- Mathematical problems for the next century (1998) (1090)
- Differential Equations, Dynamical Systems, and an Introduction to Chaos (2003) (1065)
- An Infinite Dimensional Version of Sard's Theorem (1965) (600)
- Finding the Homology of Submanifolds with High Confidence from Random Samples (2008) (568)
- The Mathematics of Learning: Dealing with Data (2005) (539)
- Diffeomorphisms with Many Periodic Points (1965) (529)
- Learning Theory Estimates via Integral Operators and Their Approximations (2007) (494)
- Generalized Poincare's Conjecture in Dimensions Greater Than Four (1961) (475)
- Convergent process of price adjust-ment and global newton methods (1976) (415)
- On the Structure of Manifolds (1962) (407)
- Topology and mechanics. I (1970) (404)
- On the mathematics of emergence (2007) (399)
- Newton’s Method Estimates from Data at One Point (1986) (385)
- On Gradient Dynamical Systems (1961) (360)
- DIFFEOMORPHISMS OF THE 2-SPHERE (1959) (356)
- The fundamental theorem of algebra and complexity theory (1981) (344)
- On the differential equations of species in competition (1976) (295)
- On the efficiency of algorithms of analysis (1985) (281)
- Complexity of Bézout’s theorem. I. Geometric aspects (1993) (271)
- The Classification of Immersions of Spheres in Euclidean Spaces (1959) (266)
- A generalized Morse theory (1964) (265)
- Best Choices for Regularization Parameters in Learning Theory: On the Bias—Variance Problem (2002) (253)
- Complexity of Bezout's Theorem: III. Condition Number and Packing (1993) (246)
- On the average number of steps of the simplex method of linear programming (1983) (246)
- ESTIMATING THE APPROXIMATION ERROR IN LEARNING THEORY (2003) (245)
- Topology and mechanics. II (1970) (240)
- Morse inequalities for a dynamical system (1960) (240)
- Complexity of Bezout’s Theorem II Volumes and Probabilities (1993) (229)
- Shannon sampling and function reconstruction from point values (2004) (229)
- On the Structure of 5-Manifolds (1962) (200)
- Shannon sampling II: Connections to learning theory (2005) (195)
- On a theory of computation and complexity over the real numbers; np-completeness (1989) (190)
- The mathematics of time (1980) (169)
- Complexity of Bezout's theorem IV: probability of success; extensions (1996) (168)
- Structurally Stable Systems are not Dense (1966) (168)
- Complexity of Bezout's Theorem V: Polynomial Time (1994) (155)
- On the topology of algorithms, I (1987) (152)
- Complexity theory and numerical analysis (1997) (150)
- The Prisoner's Dilemma and Dynamical Systems Associated to Non-Cooperative Games (1980) (146)
- A Topological View of Unsupervised Learning from Noisy Data (2011) (141)
- On the mathematical foundations of electrical circuit theory (1972) (131)
- A classification of immersions of the two-sphere (1959) (130)
- Online Learning Algorithms (2006) (129)
- On Algorithms for Solving f(x)=0 (1979) (127)
- ONLINE LEARNING WITH MARKOV SAMPLING (2009) (123)
- A Vietoris mapping theorem for homotopy (1957) (122)
- Global analysis and economics III: Pareto Optima and price equilibria (1974) (120)
- Dynamics in General Equilibrium Theory (1976) (115)
- Global Analysis and Economics I: Pareto Optimum and a Generalization of Morse Theory† (1975) (110)
- Global analysis and economics IIA: Extension of a theorem of Debreu (1974) (104)
- Exchange processes with price adjustment (1976) (104)
- Functional organization of the human 4D Nucleome (2015) (102)
- Morse theory and a non-linear generalization of the Dirichlet problem (1964) (101)
- Regular curves on Riemannian manifolds (1958) (101)
- A Mathematical Model of Two Cells Via Turing’s Equation (1976) (100)
- The Mathematics of Time: Essays on Dynamical Systems, Economic Processes, and Related Topics (1980) (99)
- Global analysis and economics VI: Geometric analysis of Pareto Optima and price equilibria under classical hypotheses (1976) (95)
- Finding a horseshoe on the beaches of Rio (1998) (83)
- Computational Complexity: On the Geometry of Polynomials and a Theory of Cost: II (1986) (82)
- Algorithms for Solving Equations (2010) (80)
- Modeling Language Evolution (2004) (78)
- Global analysis and economics V: Pareto theory with constraints (1974) (77)
- Stable Manifolds for Differential Equations and Diffeomorphisms (2011) (77)
- The Problem of the Average Speed of the Simplex Method (1982) (76)
- Lectures of Smale on differential topology (1963) (75)
- Computational complexity: on the geometry of polynomials and a theory of cost. I (1985) (74)
- Dynamics retrospective: great problems, attempts that failed (1991) (72)
- Complexity estimates depending on condition and round-off error (1999) (70)
- Some Remarks on the Foundations of Numerical Analysis (1990) (69)
- Geometry on Probability Spaces (2009) (69)
- On a theory of computation over the real numbers; NP completeness, recursive functions and universal machines (1988) (68)
- Global analysis and economics (2004) (64)
- Mathematics of the Neural Response (2010) (63)
- The qualitative analysis of a difference equation of population growth (1976) (61)
- The generalized Poincaré conjecture in higher dimensions (1960) (60)
- Global analysis and economics IV: Finiteness and stability of equilibria with general consumption sets and production (1974) (59)
- COMPLEXITY AND REAL COMPUTATION: A MANIFESTO (1996) (55)
- A Polynomial Time Algorithm for Diophantine Equations in One Variable (1999) (49)
- On the Immersion of Manifolds in Euclidean Space (1958) (46)
- THE DYNAMICAL SYSTEMS APPROACH TO DIFFERENTIAL EQUATIONS (2007) (41)
- Separation of Complexity Classes in Koiran's Weak Model (1994) (38)
- Algebraic Settings for the Problem “P ≠ NP?” (1998) (36)
- Problems on the nature of relative equilibria in celestial mechanics (1971) (35)
- Discrete Dynamical Systems (2013) (34)
- The mathematics of numerical analysis (1996) (32)
- Dynamical systems and the topological conjugacy problem for diffeomorphisms (1963) (29)
- On the existence of generally convergent algorithms (1986) (29)
- A survey of some recent developments in differential topology (1963) (28)
- Stability and Isotopy in Discrete Dynamical Systems (1973) (28)
- Differentiable and Combinatorial Structures on Manifolds (1961) (26)
- Self-Intersections of Immersed Manifolds (1959) (25)
- The Gödel Incompleteness Theorem and Decidability over a Ring (1993) (25)
- Smooth solutions of the heat and wave equations (1980) (24)
- The mathematics of numerical analysis : 1995 AMS-SIAM Summer Seminar in Applied Mathematics, July 17-August 11, 1995, Park City, Utah (1996) (23)
- A Structurally Stable Differentiable Homeomorphism with an Infinite Number of Periodic Points (2007) (23)
- Review: E. C. Zeeman, Catastrophe theory: Selected papers, 1972–1977 (1978) (22)
- Hodge Theory on Metric Spaces (2012) (20)
- Reproducing kernel hilbert spaces in learning theory (2006) (19)
- Sufficient conditions for an optimum (1975) (19)
- Emergence of function from coordinated cells in a tissue (2017) (18)
- Genome Architecture Mediates Transcriptional Control of Human Myogenic Reprogramming (2018) (17)
- ON INVOLUTIONS OF THE 3-SPHERE.* (1959) (16)
- On the complexity of path-following newton algorithms for solving systems of polynomial equations with integer coefficients (1993) (16)
- On the Morse index theorem (1967) (16)
- A NOTE ON OPEN MAPS (1957) (15)
- The story of the higher dimensional poincaré conjecture (what actually happened on the beaches of rio) (1989) (14)
- NP and mathematics – a computational complexity perspective (2006) (14)
- Mathematics of the Genome (2017) (14)
- ON THE PROBLEM OF REVIVING THE ERGODIC HYPOTHESIS OF BLOTZMANN AND BIRKHOFF (1980) (14)
- The Collected Papers of Stephen Smale (2000) (13)
- Derived Distance : towards a mathematical theory of visual cortex (2007) (12)
- Generalization and Properties of the Neural Response (2010) (12)
- Lecture III Dynamical systems and turbulence (1977) (11)
- The Lorenz System (2013) (11)
- First-Order Equations (2013) (11)
- Genome Architecture Leads a Bifurcation in Cell Identity (2017) (11)
- Dynamics of the Genome (2015) (11)
- From Topology to Computation: Proceedings of the Smalefest (2011) (10)
- Chapter 8 Global analysis and economics (1981) (10)
- On How I Got Started in Dynamical Systems (1980) (9)
- Stability and genericity in dynamical systems (1971) (9)
- On the steps of Moscow University (1984) (8)
- The Pitchfork Bifurcation (2017) (8)
- A Dynamic Theory of Learning (2008) (8)
- Theory of computation (1992) (7)
- What is Global Analysis (1969) (7)
- Continuation methods. (1979) (7)
- Some Dynamical Questions in Mathematical Economics (1980) (6)
- ABSTRACT AND CLASSICAL HODGE–DE RHAM THEORY (2012) (6)
- Algebraic Settings for the Problem P 6 = Np?" 1. Statement of Main Theorems (1996) (6)
- Complexity Estimates Depending on Condition and Round-Off Error (1998) (6)
- An Approach to the Analysis of Dynamic Processes in Economic Systems (1977) (6)
- CBCL Paper April 4 , 2008 On a model of visual cortex : learning invariance and selectivity from image sequences (2008) (6)
- Risk Bounds for Random Regression Graphs (2007) (5)
- ON COMPARATIVE STATICS AND BIFURCATION IN ECONOMIC EQUILIBRIUM THEORY (1979) (5)
- The Mathematics of Learning: Dealing With Data (2005) (5)
- Some Lower Bounds for the Complexity of Continuation Methods (1998) (5)
- Global Analysis in Economic Theory (1989) (5)
- Global stability questions in dynamical systems (1969) (5)
- On a model of visual cortex: learning invariance and selectivity (2008) (5)
- On How I Got Started In Dynamical Systems, 1959–1962 (1993) (5)
- Modelling Language Evolution ∗† (2003) (4)
- Gerard Debreu wins the Nobel Prize (1984) (3)
- RKHS Representation of Measures Applied to Homogeneity, Independence, and Fourier Optics (2008) (3)
- On the average cost of solving polynomial equations (1983) (3)
- Review: Marston Morse, Global variational analysis: Weierstrass integrals on a Riemannian manifold (1977) (3)
- The Condition Number in ℙ(H(d)) (1998) (2)
- Personal Perspectives on Mathematics and Mechanics (1980) (2)
- Modelling Language Evolution ⁄y (2003) (2)
- Neurons That Confuse Mirror-Symmetric Object Views (2010) (2)
- On the Problem of Reviving the Ergodic Hypothesis of Boltzmann and Birkhoff: Dedicated to the memory of Rufus Bowen (1980) (2)
- Notes on the Shannon Entropy of the Neural Response (2009) (1)
- Newton’s Method (1998) (1)
- Phase Portraits for Planar Systems (2013) (1)
- Definitions and First Properties of Computation (1998) (1)
- Beyond Hyperbolicity (2017) (1)
- Learning Theory: An Approximation Theory Viewpoint: Foreword (2007) (1)
- Vladimir I. Arnold (2014) (1)
- Surveys in Modern Mathematics: On problems of computational complexity (2005) (1)
- Data and learning (2006) (1)
- Smale horseshoe (2007) (1)
- Closed Orbits and Limit Sets (2013) (1)
- The Condition Number for Nonlinear Problems (1998) (1)
- AFRL-OSR-VA-TR-2013-0116 Hierarchical Kernel Machines : The Mathematics of Learning Inspired by Visual CortexTitle , i . e , Synthetic Aperture Ladar for Tactical Imaging (2013) (0)
- Condition Numbers and the Loss of Precision of Linear Equations (1998) (0)
- Classification of Planar Systems (2013) (0)
- Professional Biography, Bibliography, and Graduate Students (1993) (0)
- Complexity and the Condition Number (1998) (0)
- The impact of Thom's cobordism theory (2004) (0)
- Continuation Methods (1979) (0)
- Basic elements of the qualitative theory of ordinary differential equations (2019) (0)
- DIFFERENTIABLE AND COMBINATORIAL STRUCTURES (2016) (0)
- Continuous Direct Adaptive Control with Saturation Input Constraint (1994) (0)
- Otopy classes of equivariant maps (2010) (0)
- On the Evolution of Language (2002) (0)
- Letter to the Editor: A planetary classification scheme (2006) (0)
- Fundamental Theorem of Algebra: Complexity Aspects (1998) (0)
- Mathematical and Computational Foundations of Learning Theory (Dagstuhl Seminar 11291) (2011) (0)
- Continuation Methods (1979) (0)
- Real‐Valued Computation and Complexity (2006) (0)
- Comparative Statics and Algorithms for Finding Economic Equilibria (1995) (0)
- Finding a I lorseshoe on the Beaches of Rio What is Chaos ? (2009) (0)
- Equilibria in Nonlinear Systems (2013) (0)
- On Involutions of the 3-Sphere Author ( s ) : (2017) (0)
- Applications in Circuit Theory (2013) (0)
- 1 Differential equations and solutions 2 . 1 . 1 Existence and uniqueness of solutions (2019) (0)
- Some Separations of Complexity Classes (1998) (0)
- Remembering Raoul Bott (1923–2005) (2013) (0)
- 2006 Fields Medals Awarded, Volume 53, Number 9 (2006) (0)
- Some Autobiographical Notes (1993) (0)
- Catastrophe theory : Selected papers , 1972-1977 (2007) (0)
- Is the Mandelbrot Set Decidable (1995) (0)
- Nonuniform Complexity Classes (1998) (0)
- Emergence of Function (2016) (0)
- THE STRUCTURE OF COMPLETE MANIFOLDS OF NONNEGATIVE CURVATURE BY JEFF CHEEGER AND DETLEF GROMOLL (2007) (0)
- REGULAR CURVES ON RIEMANNIAN MANIFOLDS ( J ) (2010) (0)
- Decision Problems and Complexity over a Ring (1998) (0)
- On a Theory of Cost for Equation Solving (1983) (0)
- The Smale Collection: Beauty in Natural Crystals (2006) (0)
- [After 100 years of stagnation, some progress]. (1983) (0)
- Essays in mathematics and its applications : in honor of Stephen Smale's 80th birthday (2012) (0)
- Remembering Raoul Bott (2013) (0)
- Finding a Horseshoe on the Beaches of Rio (2000) (0)
- Foundations of computational mathematics : proceedings of the Smalefest 2000, Hon Kong, 13-17 2000 (2002) (0)
- Complexity and RealComputation : A Manifesto Lenore (1995) (0)
- Higher-Dimensional Linear Algebra (2013) (0)
- Applications in Mechanics (2013) (0)
- Computation over a Ring (1998) (0)
- Planar Linear Systems (2013) (0)
- Robert Edward Bowen (1980) (0)
- Data-Guided Controllability : Learning from the Human Genome (2015) (0)
- Existence and Uniqueness Revisited (2013) (0)
- THE CLASSIFICATION OF IMMERSIONS OF SPHERES (2016) (0)
- Higher-Dimensional Linear Systems (2013) (0)
- ALGEBRAIC TOPOLOGY AT THE STEKLOV MATHEMATICAL INSTITUTE OF THE ACADEMY OF SCIENCES OF THE USSR (2008) (0)
- Complexity aspects of numerical analysis (1986) (0)
- Deterministic Lower Bounds (1998) (0)
- The mathematics of time : essays on dynamical systems, economics processes, and related topics / Steve Smale (1980) (0)
- S . S MALE Stable manifolds for differential equations and diffeomorphisms (2018) (0)
- Applications in Biology (2013) (0)
- Global Nonlinear Techniques (2013) (0)
- Hierarchical Kernel Machines: The Mathematics of Learning Inspired by Visual Cortex (2013) (0)
- The Class NP and NP-Complete Problems (1998) (0)
- The mathematics of theories of learning and intellegence (2000) (0)
- COMMENTARY ON “DIFFERENTIABLE DYNAMICAL SYSTEMS” BY STEPHEN SMALE (2018) (0)
- A Dynamic Formulation of Ring Oscillator as Solitary-Wave Propagator (1998) (0)
- PSEUDO-DIVISION MACHINE (I): A MODEL OF SYMBOLIC COMPUTATION (2007) (0)

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