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Lawrence Berkeley National Laboratory (retired)

University of California, Davis, Computer Science

and other mathematical constants

We recently performed some very large mathematical calculations, uncovering digits of various mathematical constants that until quite recently were widely considered to be forever inaccessible to humans. Our computations stem from the “BBP” formula for Pi, which was discovered in 1997 using a computer program implementing the “PSLQ” integer relation algorithm. This formula has the remarkable property that it permits one to directly calculate binary or base-16 digits of Pi, beginning at an arbitrary position, without needing to calculate any of the preceding digits. Since 1997, numerous other BBP-type formulas have been discovered for various mathematical constants. In our Conant Prize article, we described the computation of base-64 (binary) digits of Pi^2, base-729 (ternary) digits of Pi^2, and base-4096 (binary) digits of Catalan’s constant, in each case beginning at the ten trillionth place. The computation of base-16 digits of Pi beginning at the 500 trillionth place has previously been described by other researchers. We also discussed intriguing connections between these BBP formulas and the age-old unsolved research question of whether and why constants such as Pi have “random” digits.

David H. Bailey received his PhD in mathematics from Stanford University in 1976 and in his subsequent career worked at the NASA Ames Research Center and then at the Lawrence Berkeley National Laboratory. He recently retired from the Berkeley Lab but continues as a research associate with the University of California Davis, Department of Computer Science. His published work includes over two hundred papers in experimental mathematics, computational number theory, parallel computing, high-precision computing, fast Fourier transforms, and mathematical finance. • Among his honors, he has received the Chauvenet and Merten M. Hasse Prizes from the Mathematical Association of America, the Sidney Fernbach Award from the IEEE Computer Society, and the Gordon Bell Prize from the Association of Computing Machinery.

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