- Richard Brent (scientist)
**Richard Peirce Brent**is anAustralia nmathematician andcomputer scientist , born in 1946. As of October 2005 he is an ARC Federation Fellow at theAustralian National University . His research interests includenumber theory (in particularfactorization ),random number generators,computer architecture , and analysis ofalgorithms .In 1973, he published a

root-finding algorithm (an algorithm for solving equations numerically) which is now known asBrent's method . [*Brent (1973). "Algorithms for Minimization without Derivatives." Prentice-Hall, Englewood Cliffs, NJ.*]In 1975 he and

Eugene Salamin independently discovered theBrent-Salamin algorithm , used in high-precision calculation of $pi$. At the same time, he showed that all theelementary 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 thearithmetic-geometric mean ofCarl 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 theRiemann Hypothesis .In 1980 he and Nobel laureate

Edwin McMillan found a new algorithm for high-precision computation of theEuler-Mascheroni constant $gamma$ usingBessel 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 10^{15000}).In 1980 he and John Pollard factored the eighth

Fermat number using a variant of thePollard rho algorithm. He later factored the tenth and eleventh Fermat numbers using Lenstra'selliptic 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*] ::$x^\{6972593\}\; +\; x^\{3037958\}\; +\; 1.$The degree 6972593 is the exponent of aMersenne prime .He is descended from

Hannah Ayscough , mother ofIsaac 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 theAssociation for Computing Machinery , theIEEE and theAustralian Academy of Science .**References****External links*** [

*http://wwwmaths.anu.edu.au/~brent/ Richard Brent's home page*]

*Wikimedia Foundation.
2010.*

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