2026 Stephen G. Simpson: Mathematics Researcher – H-Index, Publications & Awards

Discipline name	D-Index	World Ranking	Current World Ranking	National Ranking	Current National Ranking	Publications	Citations
Mathematics	33	3003	2682	1213	1016	118	6681

Discipline name

D-Index

World Ranking

Current World Ranking

National Ranking

Current National Ranking

Publications

Citations

Mathematics

3003

2682

1213

1016

118

6681

Research.com Recognitions

1980 - Fellow of Alfred P. Sloan Foundation

Overview

Stephen G. Simpson is affiliated with Pennsylvania State University in the United States. Their research spans the fields of Computer Science and Mathematics, with a focus on Computational Theory and Mathematics.

Their scholarly work includes contributions to subfields such as Geometry and Topology, Statistics and Probability, Mathematical Physics, and Discrete Mathematics and Combinatorics. The main topics addressed by their research are:

Computability, Logic, AI Algorithms
Semigroups and Automata Theory
Advanced Topology and Set Theory
Benford's Law and Fraud Detection
Mathematical and Theoretical Analysis
Limits and Structures in Graph Theory
Geometric and Algebraic Topology

Stephen G. Simpson has published in the following venues:

arXiv (Cornell University)
University of Thessaly Institutional Repository (University of Thessaly)

Selected recent papers include:

Reverse mathematics, young diagrams, and the ascending chain condition, 2023, University of Thessaly Institutional Repository (University of Thessaly)
Very weak fragments of weak Kőnig's lemma, 2021, arXiv (Cornell University)
Pseudojump inversion in special r. b. Π⁰₁ classes, 2021, arXiv (Cornell University)
Turing Degrees of Hyperjumps, 2021, arXiv (Cornell University)

Frequent co-authors collaborating with Stephen G. Simpson include:

Hayden Jananthan
Kostas Hatzikiriakou
Keita Yokoyama

In 1980, Stephen G. Simpson was recognized as a Fellow of the Alfred P. Sloan Foundation.

Best Publications

Subsystems of Second Order Arithmetic

Stephen G. Simpson

1883
Citations
Partial Realizations of Hilbert's Program

Stephen G. Simpson

225
Citations
Countable algebra and set existence axioms

Harvey M. Friedman;Stephen G. Simpson;Rick L. Smith

185
Citations
A Dual Form of Ramsey's Theorem

Timothy J Carlson;Stephen G Simpson

165
Citations
Nonprovability of Certain Combinatorial Properties of Finite Trees

Stephen G. Simpson

148
Citations
Which Set Existence Axioms are Needed to Prove the Cauchy/Peano Theorem for Ordinary Differential Equations?

Stephen G. Simpson

129
Citations
A Finite Combinatorial Principle Which is Equivalent to the 1-Consistency of Predicative Analysis

Harvey M. Friedman;Harvey M. Friedman;Harvey M. Friedman;Kenneth McAloon;Kenneth McAloon;Kenneth McAloon;Stephen G. Simpson;Stephen G. Simpson;Stephen G. Simpson

116
Citations
Ordinal numbers and the Hilbert basis theorem

Stephen G. Simpson

103
Citations
The α-finite injury method

G.E. Sacks;S.G. Simpson

96
Citations
Measure theory and weak König's lemma

Xiaokang Yu;Stephen G. Simpson

93
Citations
Mass Problems and Randomness

Stephen G. Simpson

93
Citations
Factorization of polynomials and Σ10 induction

Stephen G. Simpson;Rick L. Smith

87
Citations
Degrees of Unsolvability: A Survey of Results

Stephen G. Simpson

82
Citations
Located sets and reverse mathematics

Mariagnese Giusto;Stephen G. Simpson

74
Citations
An extension of the recursively enumerable Turing degrees

Stephen G. Simpson

74
Citations
First-order theory of the degrees of recursive unsolvabilityl

Unknown

72
Citations
Which set existence axioms are needed to prove the separable Hahn-Banach theorem?

Douglas K. Brown;Stephen G. Simpson

71
Citations
Ein in der reinen Zahlentheorie unbeweisbarer Satz über endliche Folgen von natürlichen Zahlen

Kurt Schütte;Stephen G. Simpson

69
Citations
Schnorr randomness and the Lebesgue differentiation theorem

Noopur Pathak;Cristóbal Rojas;Stephen G. Simpson

67
Citations
Almost everywhere domination and superhighness

Stephen G. Simpson

66
Citations
Logic and Combinatorics

Stephen G. Simpson

65
Citations

Frequent Co-Authors

Solomon Feferman Stanford University

Rodney G. Downey Victoria University of Wellington

Carl G. Jockusch University of Illinois at Urbana-Champaign

External Links

Wikipedia of Stephen G. Simpson Personal website of Stephen G. Simpson 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 pursuing Mathematics in the USA, exploring related online degrees can open diverse career opportunities. Many professionals complement their math background with business-oriented programs. For example, the quickest online MBA offers a fast-track route into management roles, blending quantitative skills with leadership training.

Cost is a significant consideration when choosing further education. Programs like the MS in digital marketing degree cost USA attract math graduates who want to pivot toward data-driven marketing roles without prohibitive tuition fees.

If time is a constraint, some professionals prefer year long MBA programs, which help students quickly gain business expertise and return to the workforce. Additionally, flexibility is enhanced by MBA programs that accept transfer credits, allowing learners to reduce overall study time by leveraging prior coursework.

These pathways illustrate how mathematical skills can seamlessly integrate with business and marketing acumen, expanding career prospects in analytics, finance, management, and beyond.