David H. Bailey (mathematician)

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David H. Bailey
David Harold Bailey.jpg
Bailey in 2010
Born
David Harold Bailey

1948 (age 75–76)
Alma mater Brigham Young University
Stanford University
Known for Bailey–Borwein–Plouffe formula
Awards Sidney Fernbach Award (1993)
Chauvenet Prize (1993)
Gordon Bell Prize (2008)
Levi L. Conant Prize (2017)
Scientific career
Fields Computer science
Experimental mathematics
Institutions Lawrence Berkeley National Laboratory (Retired)
Doctoral advisor Donald Samuel Ornstein

David Harold Bailey (born 14 August 1948) is a mathematician and computer scientist. He received his B.S. in mathematics from Brigham Young University in 1972 and his Ph.D. in mathematics from Stanford University in 1976. [1] He worked for 14 years as a computer scientist at NASA Ames Research Center, and then from 1998 to 2013 as a Senior Scientist at the Lawrence Berkeley National Laboratory. He is now retired from the Berkeley Lab.

Contents

Bailey is perhaps best known as a co-author (with Peter Borwein and Simon Plouffe) of a 1997 paper that presented a new formula for π (pi), which had been discovered by Plouffe in 1995. This Bailey–Borwein–Plouffe formula permits one to calculate binary or hexadecimal digits of pi beginning at an arbitrary position, by means of a simple algorithm. Subsequently, Bailey and Richard Crandall showed that the existence of this and similar formulas has implications for the long-standing question of "normality" [2] —whether and why the digits of certain mathematical constants (including pi) appear "random" in a particular sense.

Bailey was a long-time collaborator with Jonathan Borwein (Peter's brother). They co-authored five books and over 80 technical papers on experimental mathematics.

Bailey also does research in numerical analysis and parallel computing. He has published studies on the fast Fourier transform (FFT), high-precision arithmetic, and the PSLQ algorithm (used for integer relation detection). He is a co-author of the NAS Benchmarks, which are used to assess and analyze the performance of parallel scientific computers. A "4-step" method of calculating the FFT is widely known as Bailey's FFT algorithm (Bailey himself credits it to W. M. Gentleman and G. Sande [3] [4] ).

He has also published articles in the area of mathematical finance, including a 2014 paper "Pseudo-mathematics and financial charlatanism," which emphasizes the dangers of statistical overfitting and other abuses of mathematics in the financial field.

In 1993, Bailey received the Sidney Fernbach award from the IEEE Computer Society, as well as the Chauvenet Prize [5] and the Hasse Prize from the Mathematical Association of America. In 2008 he was a co-recipient of the Gordon Bell Prize from the Association for Computing Machinery. In 2017 he was a co-recipient of the Levi L. Conant Prize from the American Mathematical Society.

Bailey is a member of the Church of Jesus Christ of Latter-day Saints. He has positioned himself as an advocate of the teaching of science and that accepting the conclusions of modern science is not incompatible with a religious view. [6]

Selected works

Related Research Articles

The number π is a mathematical constant that is the ratio of a circle's circumference to its diameter, approximately equal to 3.14159. The number π appears in many formulae across mathematics and physics. It is an irrational number, meaning that it cannot be expressed exactly as a ratio of two integers, although fractions such as are commonly used to approximate it. Consequently, its decimal representation never ends, nor enters a permanently repeating pattern. It is a transcendental number, meaning that it cannot be a solution of an equation involving only finite sums, products, powers, and integers. The transcendence of π implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straightedge. The decimal digits of π appear to be randomly distributed, but no proof of this conjecture has been found.

Borwein's algorithm was devised by Jonathan and Peter Borwein to calculate the value of . This and other algorithms can be found in the book Pi and the AGM – A Study in Analytic Number Theory and Computational Complexity.

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The Cooley–Tukey algorithm, named after J. W. Cooley and John Tukey, is the most common fast Fourier transform (FFT) algorithm. It re-expresses the discrete Fourier transform (DFT) of an arbitrary composite size in terms of N1 smaller DFTs of sizes N2, recursively, to reduce the computation time to O(N log N) for highly composite N (smooth numbers). Because of the algorithm's importance, specific variants and implementation styles have become known by their own names, as described below.

<span class="mw-page-title-main">Simon Plouffe</span> Canadian mathematician

Simon Plouffe is a French Canadian mathematician who discovered the Bailey–Borwein–Plouffe formula which permits the computation of the nth binary digit of π, in 1995. His other 2022 formula allows extracting the nth digit of π in decimal. He was born in Saint-Jovite, Quebec.

<span class="mw-page-title-main">Pseudomathematics</span> Work of mathematical cranks

Pseudomathematics, or mathematical crankery, is a mathematics-like activity that does not adhere to the framework of rigor of formal mathematical practice. Common areas of pseudomathematics are solutions of problems proved to be unsolvable or recognized as extremely hard by experts, as well as attempts to apply mathematics to non-quantifiable areas. A person engaging in pseudomathematics is called a pseudomathematician or a pseudomath. Pseudomathematics has equivalents in other scientific fields, and may overlap with other topics characterized as pseudoscience.

Jonathan Michael Borwein was a Scottish mathematician who held an appointment as Laureate Professor of mathematics at the University of Newcastle, Australia. He was a close associate of David H. Bailey, and they have been prominent public advocates of experimental mathematics.

A spigot algorithm is an algorithm for computing the value of a transcendental number that generates the digits of the number sequentially from left to right providing increasing precision as the algorithm proceeds. Spigot algorithms also aim to minimize the amount of intermediate storage required. The name comes from the sense of the word "spigot" for a tap or valve controlling the flow of a liquid. Spigot algorithms can be contrasted with algorithms that store and process complete numbers to produce successively more accurate approximations to the desired transcendental.

Peter Benjamin Borwein was a Canadian mathematician and a professor at Simon Fraser University. He is known as a co-author of the paper which presented the Bailey–Borwein–Plouffe algorithm for computing π.

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Chronology of computation of <span class="texhtml mvar" style="font-style:italic;">π</span>

The table below is a brief chronology of computed numerical values of, or bounds on, the mathematical constant pi. For more detailed explanations for some of these calculations, see Approximations of π.

Approximations of <span class="texhtml mvar" style="font-style:italic;">π</span> Varying methods used to calculate pi

Approximations for the mathematical constant pi in the history of mathematics reached an accuracy within 0.04% of the true value before the beginning of the Common Era. In Chinese mathematics, this was improved to approximations correct to what corresponds to about seven decimal digits by the 5th century.

Bellard's formula is used to calculate the nth digit of π in base 16.

<span class="mw-page-title-main">Computational complexity of mathematical operations</span> Algorithmic runtime requirements for common math procedures

The following tables list the computational complexity of various algorithms for common mathematical operations.

Tanh-sinh quadrature is a method for numerical integration introduced by Hidetoshi Takahashi and Masatake Mori in 1974. It is especially applied where singularities or infinite derivatives exist at one or both endpoints.

A K Peters, Ltd. was a publisher of scientific and technical books, specializing in mathematics and in computer graphics, robotics, and other fields of computer science. They published the journals Experimental Mathematics and the Journal of Graphics Tools, as well as mathematics books geared to children.

An integer relation between a set of real numbers x1, x2, ..., xn and a set of integers a1, a2, ..., an, not all 0, such that

The Bailey–Borwein–Plouffe formula is a formula for π. It was discovered in 1995 by Simon Plouffe and is named after the authors of the article in which it was published, David H. Bailey, Peter Borwein, and Plouffe. Before that, it had been published by Plouffe on his own site. The formula is:

Borwein is a surname. Notable people with the surname include:

References

  1. ↑ David H. Bailey at the Mathematics Genealogy Project
  2. ↑ Bailey, David H.; Crandall, Richard E. (2002). "Random Generators and Normal Numbers". Experimental Mathematics. 11 (4). Taylor & Francis: 527–546. doi:10.1080/10586458.2002.10504704. ISSN   1058-6458. S2CID   8944421.
  3. ↑ Bailey 1989.
  4. ↑ Gentleman, W.M.; Sande, G. (1966). "Fast Fourier Transforms—For Fun and Profit". AFIPS Conference Proceedings Volume 29. Fall Joint Computer Conference, November 7-10, 1966. San Francisco, California. pp. 563–578.
  5. ↑ Bailey, David H.; Borwein, Jonathan M.; Borwein, Peter B. (1989). "Ramanujan, Modular Equations, and Approximations to Pi, or, How to Compute One Billion Digits of Pi". Amer. Math. Monthly. 96 (3): 201–219. doi:10.2307/2325206. JSTOR   2325206.
  6. ↑ "David H. Bailey". FAIR. Retrieved 2024-09-30.

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