2026 Richard P. Brent: Mathematics Researcher – H-Index, Publications & Awards

Discipline name	D-Index	World Ranking	Current World Ranking	National Ranking	Current National Ranking	Publications	Citations
Computer Science	56	3961	3849	112	111	285	20313
Mathematics	53	879	750	21	19	276	18849

Research.com Recognitions

2025 - Research.com Computer Science in Australia Leader Award
2022 - Research.com Computer Science in Australia Leader Award
2009 - SIAM Fellow For contributions to algorithms, numerical analysis, and computational number theory.
1995 - ACM Fellow For research in the areas of parallel algorithms, computational number theory, multiple-precision arithmetic, computational complexity and numerical analysis, and leadership in Australian Computer Science.
1991 - IEEE Fellow For contributions to the development and analysis of parallel algorithms.

Overview

Richard P. Brent is affiliated with the Australian National University in Australia. Their research spans key areas in mathematics and computer science, with a focus on algebra, number theory, and computational theory.

Their recent publications include:

Accurate estimation of sums over zeros of the Riemann zeta-function, 2021, Mathematics of Computation
The mean square of the error term in the prime number theorem, 2021, Journal of Number Theory
Asymptotic approximation of central binomial coefficients with rigorous error bounds, 2021, Open Journal of Mathematical Sciences
On two theorems of Vassilev-Missana, 2021, Notes on Number Theory and Discrete Mathematics
Algorithms for Finding Almost Irreducible and Almost Primitive Trinomials, 2021, ANU Open Research (Australian National University)

Frequent co-authors include:

David J. Platt
Timothy S. Trudgian
Paul Zimmermann
David H. Bailey
Naomi Simone Borwein

The main venues where their work has appeared include:

Maple Transactions
Mathematics of Computation
Journal of Number Theory
Notes on Number Theory and Discrete Mathematics
Open Journal of Mathematical Sciences

Richard P. Brent's research fields encompass:

Mathematics
Computer Science

Their subfields of study cover:

Algebra and Number Theory
Computational Theory and Mathematics
Artificial Intelligence
Applied Mathematics
Theoretical Computer Science

Research topics include:

Analytic Number Theory Research
Advanced Mathematical Identities
Mathematical functions and polynomials
Coding theory and cryptography
Polynomial and algebraic computation
History and Theory of Mathematics
Computability, Logic, AI Algorithms

Among book publications, the work includes a contribution to a volume published by Springer International Publishing titled From Analysis to Visualization (2020).

Richard P. Brent has been recognized by several professional organizations with fellowships:

SIAM Fellow (2009), cited for contributions to algorithms, numerical analysis, and computational number theory
ACM Fellow (1995), cited for research in parallel algorithms, computational number theory, multiple-precision arithmetic, computational complexity, numerical analysis, and leadership in Australian computer science
IEEE Fellow (1991), cited for contributions to the development and analysis of parallel algorithms

Best Publications

Algorithms for Minimization Without Derivatives

Richard P Brent

4212
Citations
The Parallel Evaluation of General Arithmetic Expressions

Richard P. Brent

1164
Citations
Table errata: Algorithms for minimization without derivatives (Prentice-Hall, Englewood Cliffs, N. J., 1973)

Richard P. Brent

950
Citations
An algorithm with guaranteed convergence for finding a zero of a function

Richard P. Brent

718
Citations
Fast solution of toeplitz systems of equations and computation of Padé approximants

Richard P Brent;Fred G Gustavson;David Y.Y Yun

564
Citations
Fast Multiple-Precision Evaluation of Elementary Functions

Richard P. Brent

536
Citations
The Solution of Singular-Value and Symmetric Eigenvalue Problems on Multiprocessor Arrays

Richard P. Brent;Franklin T. Luk

470
Citations
Modern Computer Arithmetic

Richard Brent;Paul Zimmermann

405
Citations
Fast Algorithms for Manipulating Formal Power Series

R. P. Brent;H. T. Kung

383
Citations
An improved Monte Carlo factorization algorithm

Richard P. Brent

367
Citations
A Fortran Multiple-Precision Arithmetic Package

Richard P. Brent

336
Citations
Some Efficient Algorithms for Solving Systems of Nonlinear Equations

Richard P. Brent

281
Citations
The Area-Time Complexity of Binary Multiplication

R. P. Brent;H. T. Kung

274
Citations
Computation of the Singular Value Decomposition Using Mesh-Connected Processors

Richard P. Brent;Franklin T. Luk;Charles Van Loan

259
Citations
Fast training algorithms for multilayer neural nets

R.P. Brent

258
Citations
On the zeros of the Riemann zeta function in the critical strip

Richard P. Brent

248
Citations
MULTIPLE-PRECISION ZERO-FINDING METHODS AND THE COMPLEXITY OF ELEMENTARY FUNCTION EVALUATION

Richard P. Brent

205
Citations
Factorization of the eighth Fermat number

Richard P. Brent;John M. Pollard

182
Citations
The chip complexity of binary arithmetic

R. P. Brent;H. T. Kung

180
Citations
Systolic VLSI Arrays for Polynomial GCD Computation

Richard P. Brent;H. T. Kung

180
Citations

Frequent Co-Authors

H. T. Kung Harvard University

Albert Y. Zomaya University of Sydney

Weifa Liang City University of Hong Kong

Brendan D. McKay Australian National University

Helmut Prodinger Stellenbosch University

Anthony J. Guttmann University of Melbourne

Joseph F. Traub Columbia University

Hong Shen Sun Yat-sen University

Jonathan M. Borwein University of Newcastle Australia

Howard C. Elman University of Maryland, College Park

External Links

Wikipedia of Richard P. Brent Personal website of Richard P. Brent

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