2026 Steve Smale: Mathematics Researcher – H-Index, Publications & Awards

Discipline name	D-Index	World Ranking	Current World Ranking	National Ranking	Current National Ranking	Publications	Citations
Mathematics	79	157	128	7	7	189	46694

Steve Smale publication distribution in Mathematics in 2026

The chart shows the distribution of publications by all Research.com ranked scientists in the field of Mathematics in 2026. The highlighted bar marks where Steve Smale sits on this spectrum.

42 publications 537+

This scientist: 189 publications — 57th percentile

57% of scientists in this discipline score the same or lower.

The last bar groups every scientist with 537 publications or more.

Steve Smale D-index placement in Mathematics in 2026

The chart shows the D-index (discipline H-index) distribution of Mathematics scientists ranked by Research.com in 2026. The highlighted bar marks where Steve Smale sits on this spectrum.

30 D-Index 86+

This scientist: 79 D-Index — 96th percentile

96% of scientists in this discipline score the same or lower.

The last bar groups every scientist with 86 D-Index or more.

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

6022
Citations
Differentiable dynamical systems

Steve Smale

4985
Citations
Differential Equations, Dynamical Systems, and Linear Algebra

Morris W. Hirsch;Stephen Smale

4091
Citations
On the mathematical foundations of learning

Felipe Cucker;Steve Smale;Steve Smale

2389
Citations
Emergent Behavior in Flocks

F. Cucker;S. Smale

2097
Citations
Complexity and Real Computation

Lenore Blum;Felipe Cucker;Michael Shub;Steve Smale

2032
Citations
Mathematical problems for the next century

Steve Smale

1709
Citations
On a theory of computation and complexity over the real numbers: $NP$- completeness, recursive functions and universal machines

Lenore Blum;Mike Shub;Steve Smale

1405
Citations
On the mathematics of emergence

Felipe Cucker;Steve Smale

764
Citations
An Infinite Dimensional Version of Sard's Theorem

S. Smale

753
Citations
Learning Theory Estimates via Integral Operators and Their Approximations

Steve Smale;Ding-Xuan Zhou

689
Citations
The Mathematics of Learning: Dealing With Data

T. Poggio;S. Smale

651
Citations
Topology and mechanics. I

S. Smale

649
Citations
Generalized Poincare's Conjecture in Dimensions Greater Than Four

Stephen Smale

632
Citations
On the Structure of Manifolds

S. Smale

619
Citations
On Gradient Dynamical Systems

Stephen Smale

614
Citations
Diffeomorphisms with Many Periodic Points

Unknown

595
Citations
Newton’s Method Estimates from Data at One Point

Steve Smale

546
Citations
A convergent process of price adjustment and global newton methods

Steve Smale

509
Citations
DIFFEOMORPHISMS OF THE 2-SPHERE

Unknown

442
Citations
Topology and Mechanics. II. The Planar n-Body Problem.

S. Smale

416
Citations
The fundamental theorem of algebra and complexity theory

Steve Smale

412
Citations

Frequent Co-Authors

Felipe Cucker City University of Hong Kong

Michael Shub City College of New York

Robert L. Devaney Boston University

Ding-Xuan Zhou University of Sydney

Tomaso Poggio MIT

Lorenzo Rosasco MIT

Morris W. Hirsch University of California, Berkeley

Hau-San Wong City University of Hong Kong

Pierre Baldi University of California, Irvine

Sijia Liu Michigan State University

External Links

Wikipedia of Steve Smale Google Scholar page

If you think any of the details on this page are incorrect, let us know.

Related Online Degrees & Career Pathways

For students interested in expanding their expertise beyond Mathematics, exploring related online degrees can open diverse career pathways. Business and finance sectors are popular choices, with flexible options such as the easiest MBA program to get into offering a manageable entry point for working professionals and recent graduates alike.

Those looking for convenience and quality may consider the easy online MBA options, which combine affordable tuition with accessible formats, helping learners balance education with other commitments.

For individuals aiming at leadership positions in academia or industry, pursuing advanced credentials like online DBA programs can provide a strong foundation in strategic management and research methodologies.

Additionally, finance professionals can upgrade their qualifications through masters in finance online programs, which highlight quantitative skills and financial theory essential for careers in investment, banking, or financial analysis.

These diverse online degree pathways complement a Mathematics background, offering practical skills and enhancing career versatility in an evolving job market.