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Mathematics
China
2026

D-Index & Metrics

Mathematics

D-Index
79
Citations
46694
World Ranking
157
National Ranking
7

Research.com Recognitions

  • 2026 - Research.com Mathematics in China Leader Award
  • 2025 - Research.com Mathematics in China Leader Award
  • 2023 - Research.com Mathematics in China Leader Award
  • 2006 - Wolf Prize in Mathematics for his groundbreaking contributions that have played a fundamental role in shaping differential topology, dynamical systems, mathematical economics, and other subjects in mathematics.
  • 1996 - US President's National Medal of Science "For his pioneering contributions to mathematics in the fields of differential topology and dynamical systems, and for applications to physics, biology, economics, and the theory of computation.", Awarded by President Clinton in a White House ceremony on July 26, 1996. Note: Dr. Smale is also Professor, City University of Hong Kong.
  • 1989 - John von Neumann Lecturer
  • 1970 - Fellow of the American Association for the Advancement of Science (AAAS)
  • 1970 - Member of the National Academy of Sciences
  • 1968 - Fellow of the American Academy of Arts and Sciences
  • 1966 - Fields Medal of International Mathematical Union (IMU) Worked in differential topology where he proved the generalized Poincaré conjecture in dimension n≥5: Every closed, n-dimensional manifold homotopy-equivalent to the n-dimensional sphere is homeomorphic to it. Introduced the method of handle-bodies to solve this and related problems.
  • 1960 - Fellow of Alfred P. Sloan Foundation

Overview

Steve Smale is affiliated with the City University of Hong Kong in China. The academic's research spans multiple areas of mathematics and interdisciplinary applications, with a particular focus on differential topology and dynamical systems.

Throughout their career, the researcher has been recognized with several notable awards. These include the Wolf Prize in Mathematics in 2006, awarded for contributions to differential topology, dynamical systems, mathematical economics, and related subjects.

In 1996, Steve Smale received the US President's National Medal of Science. The citation highlights pioneering contributions to mathematics in differential topology and dynamical systems, along with applications to physics, biology, economics, and the theory of computation. This award was presented at a White House ceremony by President Clinton on July 26, 1996.

Additional distinctions include the John von Neumann Lectureship awarded in 1989, and election as a Member of the National Academy of Sciences in 1970. The researcher is also a Fellow of the American Association for the Advancement of Science (AAAS) from 1970, a Fellow of the American Academy of Arts and Sciences since 1968, and was recognized as a Fellow of the Alfred P. Sloan Foundation in 1960.

One of the most prominent accolades in their career is the Fields Medal from the International Mathematical Union (IMU), received in 1966. The award citation notes work in differential topology, including the proof of the generalized Poincaré conjecture for dimensions n≥5, demonstrating that every closed, n-dimensional manifold homotopy-equivalent to the n-dimensional sphere is homeomorphic to it. This research introduced the method of handle-bodies to resolve this and related problems.

Best Publications

  • Differential Equations, Dynamical Systems, and an Introduction to Chaos

    Morris W. Hirsch;Stephen Smale;Robert L. Devaney

  • Differentiable dynamical systems

    Steve Smale

  • Differential Equations, Dynamical Systems, and Linear Algebra

    Morris W. Hirsch;Stephen Smale

  • On the mathematical foundations of learning

    Felipe Cucker;Steve Smale;Steve Smale

  • Emergent Behavior in Flocks

    F. Cucker;S. Smale

  • Complexity and Real Computation

    Lenore Blum;Felipe Cucker;Michael Shub;Steve Smale

  • Mathematical problems for the next century

    Steve Smale

  • On a theory of computation and complexity over the real numbers: $NP$- completeness, recursive functions and universal machines

    Lenore Blum;Mike Shub;Steve Smale

  • On the mathematics of emergence

    Felipe Cucker;Steve Smale

  • An Infinite Dimensional Version of Sard's Theorem

    S. Smale

  • Learning Theory Estimates via Integral Operators and Their Approximations

    Steve Smale;Ding-Xuan Zhou

  • The Mathematics of Learning: Dealing With Data

    T. Poggio;S. Smale

  • Topology and mechanics. I

    S. Smale

  • Generalized Poincare's Conjecture in Dimensions Greater Than Four

    Stephen Smale

  • On the Structure of Manifolds

    S. Smale

  • On Gradient Dynamical Systems

    Stephen Smale

  • Diffeomorphisms with Many Periodic Points

    Unknown

  • Newton’s Method Estimates from Data at One Point

    Steve Smale

  • A convergent process of price adjustment and global newton methods

    Steve Smale

  • DIFFEOMORPHISMS OF THE 2-SPHERE

    Unknown

  • Topology and Mechanics. II. The Planar n-Body Problem.

    S. Smale

  • The fundamental theorem of algebra and complexity theory

    Steve Smale

Frequent Co-Authors

Felipe Cucker
Felipe Cucker City University of Hong Kong
Michael Shub
Michael Shub City College of New York
Robert L. Devaney
Robert L. Devaney Boston University
Ding-Xuan Zhou
Ding-Xuan Zhou University of Sydney
Morris W. Hirsch
Morris W. Hirsch University of California, Berkeley
Hau-San Wong
Hau-San Wong City University of Hong Kong
Pierre Baldi
Pierre Baldi University of California, Irvine
Sijia Liu
Sijia Liu Michigan State University

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