Jonathan M. Borwein
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View article: Do Financial Gurus Produce Reliable Forecasts?
Do Financial Gurus Produce Reliable Forecasts? Open
Many investors rely on market experts and forecasters when making investment decisions, such as when to buy or sell securities. Ranking and grading market forecasters provide investors with metrics on which they may choose forecasters with…
View article: Ergodic behaviour of a Douglas-Rachford operator away from the origin
Ergodic behaviour of a Douglas-Rachford operator away from the origin Open
It is shown that away from the origin, the Douglas-Rachford operator with respect to a sphere and a convex set in a Hilbert space can be approximated by a another operator which satisfies a weak ergodic theorem. Similar results for other p…
View article: Computation and Experimental Evaluation of Mordell–Tornheim–Witten Sum Derivatives
Computation and Experimental Evaluation of Mordell–Tornheim–Witten Sum Derivatives Open
In the previous work, the present authors and others have studied Mordell–Tornheim–Witten sums and their connections with multiple-zeta values. In this note, we describe the numerical computation of derivatives at zero of a specialization …
View article: Gamma and Factorial in the Monthly
Gamma and Factorial in the Monthly Open
The Monthly has published roughly fifty papers on the $Γ$ function or Stirling's formula. We survey those papers (discussing only our favourites in any detail) and place them in the context of the larger mathematical literature on $Γ$.
View article: A Computational Mathematics View of Space, Time and Complexity
A Computational Mathematics View of Space, Time and Complexity Open
Modern computational mathematics requires a philosophical perspective largely at odds with that of traditional mathematics, since current computational mathematics (as distinct from computer science) is by its very nature is discrete, not …
View article: The probability of backtest overfitting
The probability of backtest overfitting Open
Many investment firms and portfolio managers rely on backtests (ie, simulations of performance based on historical market data) to select investment strategies and allocate capital. Standard statistical techniques designed to prevent regre…
View article: Reproducibility in Computational Science: A Case Study: Randomness of the Digits of Pi
Reproducibility in Computational Science: A Case Study: Randomness of the Digits of Pi Open
Mathematical research is undergoing a transformation from a mostly theoretical enterprise to one that involves a significant amount of experimentation. Indeed, computational and experimental mathematics is now a full-fledged discipline wit…
View article: Computer Discovery and Analysis of Large Poisson Polynomials
Computer Discovery and Analysis of Large Poisson Polynomials Open
In two earlier studies of lattice sums arising from the Poisson equation of mathematical physics, it was established that the lattice sum 1/π · ∑m, n oddcos (mπx)cos (nπy)/(m2 + n2) = log A, where A is an algebraic number, and explicit min…
View article: Facilitating Reproducibility in Scientific Computing: Principles and Practice
Facilitating Reproducibility in Scientific Computing: Principles and Practice Open
The foundation of scientific research is theory and experiment, carefully documented in open publications, in part so that other researchers can reproduce and validate the claimed findings. Unfortunately, the field of scientific and mathem…
View article: Generalized Continued Logarithms and Related Continued Fractions
Generalized Continued Logarithms and Related Continued Fractions Open
We study continued logarithms as introduced by Bill Gosper and studied by J. Borwein et. al.. After providing an overview of the type I and type II generalizations of binary continued logarithms introduced by Borwein et. al., we focus on a…
View article: A Short Walk can be Beautiful
A Short Walk can be Beautiful Open
The story I tell is of research undertaken, with students and colleagues, in the last six or so years on short random walks. As the research progressed, my criteria for `beauty' changed. Things seemingly remarkable became `simple' and othe…
View article: Walking on real numbers (2013)
Walking on real numbers (2013) Open
Paper 21: Francisco J. Aragon Artacho, David H. Bailey, Jonathan M. Borwein and Peter B. Borwein, "Walking on real numbers," Mathematical Intelligencer, vol. 35 (2013), p. 42–60. With permission of Springer. Synopsis: As mentioned earlier,…
View article: The computation of previously inaccessible digits of π2 and Catalan’s constant (2013)
The computation of previously inaccessible digits of π2 and Catalan’s constant (2013) Open
Paper 20: David H. Bailey, Jonathan M. Borwein, Andrew Mattingly and Glenn Wightwick, "The computation of previously inaccessible digits of π 2 and Catalan's constant," Notices of the American Mathematical Society, vol. 60 (2013), p. 844–8…
View article: Pi day is upon us again and we still do not know if pi is normal (2014)
Pi day is upon us again and we still do not know if pi is normal (2014) Open
Paper 23: David H. Bailey and Jonathan Borwein, "Pi day is upon us again and we still do not know if pi is normal," American Mathematical Monthly, vol. 121 (2014), p. 191–206. Copyright 2014 Mathematical Association of America. All Rights …
View article: Ramanujan, modular equations, and approximations to pi or how to compute one billion digits of pi (1989)
Ramanujan, modular equations, and approximations to pi or how to compute one billion digits of pi (1989) Open
Paper 11: Jonathan M. Borwein, Peter B. Borwein, and David H. Bailey, "Ramanujan, modular equations, and approximations to pi, or how to compute one billion digits of pi," American Mathematical Monthly, vol. 96 (1989), p. 201–219. Copyrigh…