Special issue of American Mathematical Monthly devoted to Jon Borwein

Jonathan Borwein

The American Mathematical Monthly, the world’s largest-circulation mathematical journal, has published a special issue devoted to the career of Jonathan Borwein.

Here are some of the articles of the issue:

  1. Introduction to the Special Issue, by David H. Bailey and Scott Chapman. This gives a brief overview of Borwein’s career and the contents of the special issue. This article is freely available HERE.
  2. Jonathan Borwein: Renaissance Mathematician, by David H. Bailey. This gives an overview of Borwein’s research, emphasizing how that Borwein, in sharp contrast to the prevailing trend to specialization in modern academic research, published significant work in numerous different fields, including optimization, functional analysis, computer science, visualization, mathematics education and, of course, experimental / computational mathematics, for which he can deservedly be called a pioneer. The article is available at the Monthly (T&F) website: HERE (subscription required).
  3. Apéry Limits: Experiments and Proofs, by Marc Chamberland and Armin Straub. This describes recent work in evaluating infinite series, in the spirit of Apery’s series for zeta(3) (and his proof, using this series, that zeta(3) is irrational). The authors’ methods employ an experimental approach that demonstrates key techniques. The article is available HERE (subscription required).
  4. Analytic Continuations of Character and Alternating Tornheim Zeta Functions, by Karl Dilcher. This explores infinite series sums in three complex variables, known as Tornheim or Mordell-Tornheim-Witten sums, which can be evaluated in terms of generalized Bernoulli numbers. The article is available HERE (subscription required).
  5. The False Strategy Theorem: A Financial Application of Experimental Mathematics, by Marcos López de Prado and David H. Bailey. This articles notes that Jonathan Borwein has published articles in financial mathematics, emphasizing that much of what is published in the academic finance field fails to account for difficulties such as “backtest overfitting” — using a computer, in the development of a model, fund or strategy, to search over a broad range of parameters, but failing to recognize that such searches almost certainly render results that are statistically overfit and thus useless in real-world usage. The article is available HERE (subscription required).
  6. On Experimental Mathematics and Mathematics Education, by Veselin Jungića and Andrijana Burazin. This article mentions some of the numerous connections between experimental mathematics and mathematics education, and ways in which both disciplines can enrich each other. The article is available HERE (subscription required).

The issue includes several other articles relating to experimental mathematics, mathematics education and related topics.

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