Richard Brent (scientist)
Encyclopedia
Richard Peirce Brent is an Australia
n mathematician
and computer scientist
, born in 1946. He holds the position of Distinguished Professor of Mathematics and Computer Science with a joint appointment in the Mathematical Sciences Institute and the College of Engineering and Computer Science at the Australian National University
. From March 2005 to March 2010 he was a Federation Fellow
at the Australian National University
. His research interests include number theory
(in particular factorisation), random number generators, computer architecture
, and analysis of algorithms
.
In 1973, he published a root-finding algorithm
(an algorithm for solving equations numerically) which is now known as Brent's method
.
In 1975 he and Eugene Salamin independently discovered the Salamin–Brent algorithm, used in high-precision calculation of
. At the same time, he showed that all the elementary functions (such as log(x), sin(x) etc.) can be evaluated to high precision in the same time as 
(apart from a small constant factor) using the arithmetic-geometric mean of Carl Friedrich Gauss
.
In 1979 he showed that the first 75 million complex zeros of the Riemann zeta function lie on the critical line, providing some experimental evidence for the Riemann Hypothesis
.
In 1980 he and Nobel laureate Edwin McMillan
found a new algorithm for high-precision computation of the Euler-Mascheroni constant
using Bessel functions, and showed that 
can not have a simple rational form p/q (where p and q are integers) unless q is extremely large (greater than 1015000).
In 1980 he and John Pollard
factored the eighth Fermat number using a variant of the Pollard rho algorithm. He later factored the tenth and eleventh Fermat numbers using Lenstra's elliptic curve factorisation algorithm.
In 2002, Brent, Samuli Larvala and Paul Zimmermann discovered a very large primitive trinomial
:
The degree 6972593 is the exponent of a Mersenne prime
.
He is descended from Hannah Ayscough
, mother of Isaac Newton
.
He is currently a Chief Investigator of the ARC Centre of Excellence for Mathematics and Statistics of Complex Systems.
He is a Fellow of the Association for Computing Machinery
, the IEEE and the Australian Academy of Science
. In 2005, he was awarded the Hannan Medal
by the Australian Academy of Science
.
Australia
Australia , officially the Commonwealth of Australia, is a country in the Southern Hemisphere comprising the mainland of the Australian continent, the island of Tasmania, and numerous smaller islands in the Indian and Pacific Oceans. It is the world's sixth-largest country by total area...
n mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
and computer scientist
Computer scientist
A computer scientist is a scientist who has acquired knowledge of computer science, the study of the theoretical foundations of information and computation and their application in computer systems....
, born in 1946. He holds the position of Distinguished Professor of Mathematics and Computer Science with a joint appointment in the Mathematical Sciences Institute and the College of Engineering and Computer Science at the Australian National University
Australian National University
The Australian National University is a teaching and research university located in the Australian capital, Canberra.As of 2009, the ANU employs 3,945 administrative staff who teach approximately 10,000 undergraduates, and 7,500 postgraduate students...
. From March 2005 to March 2010 he was a Federation Fellow
Federation Fellowship
Federation Fellowships are Australian professorial research fellowships that were instigated by the Australian Government as part of their Backing Australia's Ability initiative. They were initially designed to compete with prestigious overseas grants in an attempt to lure back high profile...
at the Australian National University
Australian National University
The Australian National University is a teaching and research university located in the Australian capital, Canberra.As of 2009, the ANU employs 3,945 administrative staff who teach approximately 10,000 undergraduates, and 7,500 postgraduate students...
. His research interests include number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
(in particular factorisation), random number generators, computer architecture
Computer architecture
In computer science and engineering, computer architecture is the practical art of selecting and interconnecting hardware components to create computers that meet functional, performance and cost goals and the formal modelling of those systems....
, and analysis of algorithms
Analysis of algorithms
To analyze an algorithm is to determine the amount of resources necessary to execute it. Most algorithms are designed to work with inputs of arbitrary length...
.
In 1973, he published a root-finding algorithm
Root-finding algorithm
A root-finding algorithm is a numerical method, or algorithm, for finding a value x such that f = 0, for a given function f. Such an x is called a root of the function f....
(an algorithm for solving equations numerically) which is now known as Brent's method
Brent's method
In numerical analysis, Brent's method is a complicated but popular root-finding algorithm combining the bisection method, the secant method and inverse quadratic interpolation. It has the reliability of bisection but it can be as quick as some of the less reliable methods...
.
In 1975 he and Eugene Salamin independently discovered the Salamin–Brent algorithm, used in high-precision calculation of
. At the same time, he showed that all the elementary functions (such as log(x), sin(x) etc.) can be evaluated to high precision in the same time as (apart from a small constant factor) using the arithmetic-geometric mean of Carl Friedrich GaussCarl Friedrich Gauss
Johann Carl Friedrich Gauss was a German mathematician and scientist who contributed significantly to many fields, including number theory, statistics, analysis, differential geometry, geodesy, geophysics, electrostatics, astronomy and optics.Sometimes referred to as the Princeps mathematicorum...
.
In 1979 he showed that the first 75 million complex zeros of the Riemann zeta function lie on the critical line, providing some experimental evidence for the Riemann Hypothesis
Riemann hypothesis
In mathematics, the Riemann hypothesis, proposed by , is a conjecture about the location of the zeros of the Riemann zeta function which states that all non-trivial zeros have real part 1/2...
.
In 1980 he and Nobel laureate Edwin McMillan
Edwin McMillan
Edwin Mattison McMillan was an American physicist and Nobel laureate credited with being the first ever to produce a transuranium element. He shared the Nobel Prize in Chemistry with Glenn Seaborg in 1951....
found a new algorithm for high-precision computation of the Euler-Mascheroni constant
Euler-Mascheroni constant
The Euler–Mascheroni constant is a mathematical constant recurring in analysis and number theory, usually denoted by the lowercase Greek letter ....
using Bessel functions, and showed that can not have a simple rational form p/q (where p and q are integers) unless q is extremely large (greater than 1015000).In 1980 he and John Pollard
John Pollard (mathematician)
John M. Pollard is a British mathematician who has invented algorithms for the factorization of large numbers and for the calculation of discrete logarithms....
factored the eighth Fermat number using a variant of the Pollard rho algorithm. He later factored the tenth and eleventh Fermat numbers using Lenstra's elliptic curve factorisation algorithm.
In 2002, Brent, Samuli Larvala and Paul Zimmermann discovered a very large primitive trinomial
Primitive polynomial
In field theory, a branch of mathematics, a primitive polynomial is the minimal polynomial of a primitive element of the finite extension field GF...
:
The degree 6972593 is the exponent of a Mersenne prime
Mersenne prime
In mathematics, a Mersenne number, named after Marin Mersenne , is a positive integer that is one less than a power of two: M_p=2^p-1.\,...
.
He is descended from Hannah Ayscough
Hannah Ayscough
Hannah Ayscough was the mother of Sir Isaac Newton.-Early life:Hannah was born in Market Overton in Rutland in 1623. Her parents were James Ayscough and his wife Margery Blythe.-Motherhood:...
, mother of Isaac Newton
Isaac Newton
Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...
.
He is currently a Chief Investigator of the ARC Centre of Excellence for Mathematics and Statistics of Complex Systems.
He is a Fellow of the Association for Computing Machinery
Association for Computing Machinery
The Association for Computing Machinery is a learned society for computing. It was founded in 1947 as the world's first scientific and educational computing society. Its membership is more than 92,000 as of 2009...
, the IEEE and the Australian Academy of Science
Australian Academy of Science
The Australian Academy of Science was founded in 1954 by a group of distinguished Australians, including Australian Fellows of the Royal Society of London. The first president was Sir Mark Oliphant. The Academy is modelled after the Royal Society and operates under a Royal Charter; as such it is...
. In 2005, he was awarded the Hannan Medal
Hannan Medal
The Hannan Medal in the Mathematical Sciences is awarded every two years by the Australian Academy of Science to recognize achievements by Australians in the fields of pure mathematics, applied and computational mathematics, and statistical science....
by the Australian Academy of Science
Australian Academy of Science
The Australian Academy of Science was founded in 1954 by a group of distinguished Australians, including Australian Fellows of the Royal Society of London. The first president was Sir Mark Oliphant. The Academy is modelled after the Royal Society and operates under a Royal Charter; as such it is...
.