S. Smale

2.4k total citations
18 papers, 1.1k citations indexed

About

S. Smale is a scholar working on Computational Theory and Mathematics, Mathematical Physics and Artificial Intelligence. According to data from OpenAlex, S. Smale has authored 18 papers receiving a total of 1.1k indexed citations (citations by other indexed papers that have themselves been cited), including 7 papers in Computational Theory and Mathematics, 5 papers in Mathematical Physics and 4 papers in Artificial Intelligence. Recurrent topics in S. Smale's work include Mathematical Dynamics and Fractals (4 papers), Polynomial and algebraic computation (2 papers) and Neural Networks and Applications (2 papers). S. Smale is often cited by papers focused on Mathematical Dynamics and Fractals (4 papers), Polynomial and algebraic computation (2 papers) and Neural Networks and Applications (2 papers). S. Smale collaborates with scholars based in United States, Hong Kong and France. S. Smale's co-authors include M. Shub, R. F. Williams, James Renegar, Felipe Cucker, Andrea Caponnetto, Pascal Koiran, Lorenzo Rosasco and Tomaso Poggio and has published in prestigious journals such as Annals of the New York Academy of Sciences, Inventiones mathematicae and SIAM Journal on Computing.

In The Last Decade

S. Smale

18 papers receiving 978 citations

Peers — A (Enhanced Table)

Peers by citation overlap · career bar shows stage (early→late) cites · hero ref

Name	h						Papers	Cites
S. Smale United States	15	292	222	192	145	125	18	1.1k
G.-C Rota United States	17	427 1.5×	265 1.2×	346 1.8×	61 0.4×	225 1.8×	56	1.9k
Harold R. Parks United States	12	294 1.0×	149 0.7×	260 1.4×	45 0.3×	135 1.1×	37	1.3k
C. E. Langenhop United States	10	295 1.0×	216 1.0×	156 0.8×	45 0.3×	254 2.0×	27	1.3k
Solomon Lefschetz United States	12	199 0.7×	469 2.1×	341 1.8×	56 0.4×	252 2.0×	39	1.8k
Aleksandr I︠A︡kovlevich Khinchin United Kingdom	6	303 1.0×	540 2.4×	221 1.2×	173 1.2×	80 0.6×	13	1.8k
Mark A. Pinsky United States	24	285 1.0×	251 1.1×	126 0.7×	43 0.3×	101 0.8×	126	1.6k
J. L. Brenner United States	19	607 2.1×	312 1.4×	406 2.1×	39 0.3×	223 1.8×	86	2.3k
F. S. Van Vleck United States	15	500 1.7×	219 1.0×	343 1.8×	93 0.6×	454 3.6×	33	1.9k
David A. Singer United States	16	192 0.7×	309 1.4×	394 2.1×	43 0.3×	33 0.3×	49	1.7k
Hiroshi Kunita Japan	22	364 1.2×	210 0.9×	80 0.4×	157 1.1×	68 0.5×	49	2.2k

Countries citing papers authored by S. Smale

Since Specialization

Citations

This map shows the geographic impact of S. Smale's research. It shows the number of citations coming from papers published by authors working in each country. You can also color the map by specialization and compare the number of citations received by S. Smale with the expected number of citations based on a country's size and research output (numbers larger than one mean the country cites S. Smale more than expected).

Fields of papers citing papers by S. Smale

Since Specialization

Physical SciencesHealth SciencesLife SciencesSocial Sciences

This network shows the impact of papers produced by S. Smale. Nodes represent research fields, and links connect fields that are likely to share authors. Colored nodes show fields that tend to cite the papers produced by S. Smale. The network helps show where S. Smale may publish in the future.

Co-authorship network of co-authors of S. Smale

This figure shows the co-authorship network connecting the top 25 collaborators of S. Smale. A scholar is included among the top collaborators of S. Smale based on the total number of citations received by their joint publications. Widths of edges represent the number of papers authors have co-authored together. Node borders signify the number of papers an author published with S. Smale. S. Smale is excluded from the visualization to improve readability, since they are connected to all nodes in the network.

All Works

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18 of 18 papers shown

Smale, S., et al.. (2009). Mathematics of the Neural Response. Foundations of Computational Mathematics. 10(1). 67–91. 34 indexed citations

Caponnetto, Andrea & S. Smale. (2007). Risk Bounds for Random Regression Graphs. Foundations of Computational Mathematics. 7(4). 495–528. 3 indexed citations

Smale, S.. (2005). The Mathematics of Learning: Dealing With Data. x–x. 33 indexed citations

Cucker, Felipe, Pascal Koiran, & S. Smale. (1999). A Polynomial Time Algorithm for Diophantine Equations in One Variable. Journal of Symbolic Computation. 27(1). 21–29. 24 indexed citations

Renegar, James, M. Shub, & S. Smale. (1996). The mathematics of numerical analysis. OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information). 60 indexed citations

Cucker, Felipe, M. Shub, & S. Smale. (1994). Separation of complexity classes in Koiran's weak model. Theoretical Computer Science. 133(1). 3–14. 23 indexed citations

Shub, M. & S. Smale. (1994). Complexity of Bezout's theorem V: polynomial time. Theoretical Computer Science. 133(1). 141–164. 80 indexed citations

Shub, M. & S. Smale. (1986). Computational Complexity: On the Geometry of Polynomials and a Theory of Cost: II. SIAM Journal on Computing. 15(1). 145–161. 62 indexed citations

Smale, S.. (1980). ON THE PROBLEM OF REVIVING THE ERGODIC HYPOTHESIS OF BLOTZMANN AND BIRKHOFF. Annals of the New York Academy of Sciences. 357(1). 260–266. 12 indexed citations

10.

Smale, S. & R. F. Williams. (1976). The qualitative analysis of a difference equation of population growth. Journal of Mathematical Biology. 3(1). 1–4. 43 indexed citations

11.

Smale, S.. (1976). On the differential equations of species in competition. Journal of Mathematical Biology. 3(1). 5–7. 219 indexed citations

12.

Smale, S.. (1976). Global analysis and economics VI. Journal of Mathematical Economics. 3(1). 1–14. 59 indexed citations

13.

Smale, S.. (1974). Global analysis and economics IIA. Journal of Mathematical Economics. 1(1). 1–14. 54 indexed citations

14.

Smale, S.. (1974). Global analysis and economics V. Journal of Mathematical Economics. 1(3). 213–221. 47 indexed citations

15.

Smale, S.. (1974). Global analysis and economics IV. Journal of Mathematical Economics. 1(2). 119–127. 30 indexed citations

16.

Smale, S.. (1972). On the mathematical foundations of electrical circuit theory. Journal of Differential Geometry. 7(1-2). 80 indexed citations

17.

Smale, S.. (1970). Topology and mechanics. II. Inventiones mathematicae. 11(1). 45–64. 213 indexed citations

18.

Smale, S.. (1969). What is Global Analysis?. American Mathematical Monthly. 76(1). 4–9. 3 indexed citations

Rankless uses publication and citation data sourced from OpenAlex, an open and comprehensive bibliographic database. While OpenAlex provides broad and valuable coverage of the global research landscape, it—like all bibliographic datasets—has inherent limitations. These include incomplete records, variations in author disambiguation, differences in journal indexing, and delays in data updates. As a result, some metrics and network relationships displayed in Rankless may not fully capture the entirety of a scholar's output or impact.

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