# Richard Brent (scientist)

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Richard Brent (scientist)

Richard Peirce Brent is an Australian mathematician and computer scientist, born in 1946. As of October 2005 he is an ARC Federation Fellow at the Australian National University. His research interests include number theory (in particular factorization), 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. [Brent (1973). "Algorithms for Minimization without Derivatives." Prentice-Hall, Englewood Cliffs, NJ.]

In 1975 he and Eugene Salamin independently discovered the Brent-Salamin algorithm, used in high-precision calculation of $pi$. 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 $pi$ (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 $gamma$ using Bessel functions, and showed that $gamma$ 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 factorization algorithm.

In 2002 he (with Samuli Larvala and Paul Zimmermann) discovered a very large primitive trinomial [http://web.comlab.ox.ac.uk/oucl/work/richard.brent/trinom.html] ::$x^\left\{6972593\right\} + x^\left\{3037958\right\} + 1.$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 [http://www.complex.org.au 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.

References

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