Letter from the Editor: Jonathan M. Borwein (1951-2016)

[This is by Scott Chapman, Editor of the American Mathematical Monthly. It is scheduled to appear in the November 2016 issue of the Monthly.]

August 2, 2016 was a difficult day for us at the Monthly, as we learned of the untimely death of Monthly Associate Editor Jonathan Borwein. Many of you knew Jon as an internationally acclaimed mathematician. One of the world’s leading scholars in Experimental Mathematics, his long publication list spanned the breadth of pure and applied mathematics. Cited over 22,000 times (according to Google Scholar), Jon was perhaps the world’s leading authority on the study of pi. He co-edited the highly cited Pi: A Source Book [3] which was followed up earlier this year with a companion volume Pi: The Next Generation [2]. In 1993 when the writers of the TV cartoon The Simpsons wanted the 40,000th digit of pi to use in one of their episodes, Jon [ed: actually it is DHB] was happy to supply it to them (by the way, it is 1) [23].

Jon’s imprint on mathematics will not solely be his often ground breaking publications nor his impressive research output. Jon was one of those rare scholars with the ability to not only produce mathematics at an extremely high level, but also to communicate it to widely diverse groups. In 1993, his co-authored Monthly paper “Ramanujan, Modular Equations, and Approximations to Pi, or, How to Compute One Billion Digits of Pi,” [6] was awared the Chauvenet Prize, the MAA’s highest award for a noteworthy expository or survey paper. In recent years, he wrote widely to general audiences about mathematics for The Huffington Post. His annual Pi Day talks at his home institution of The University of Newcastle in Australia, have become the stuff of legend (one of these talks can be found at [1]).

My purpose here is not to survey Jon’s research career — there will be better and more thorough reviews of this at a later date. I wish today to honor his important and extensive contributions to the pages of the Monthly. I do not think that a list has been compiled of authors who most frequently published in the Monthly, but if it had, then Jon’s 22 papers have to be near the top of the list (his papers are listed in the references by order of appearance [4]–[25]). You will note that his Monthly papers deal with a wide variety of topics, from his favorite subjects (like pi and experimental mathematics), to core subjects in mathematics (series, integration, and the zeta function). Even this list may not do his contributions to the Monthly justice; space does not allow us to review his slew of both submitted and solved problems in our Problem Section.

One of my first acts as Editor of the Monthly, was to appoint Jon to our Editorial Board. I will never forget his first review of a paper for me — it consisted of 4 words: “This paper is ghastly.” I think this line says a lot about Jon. While I have probably never known anyone that loved mathematics as much as he did, he also had a keen eye for good mathematics. I think that some of the best papers that were published during my term were handled by Jon.

In June I spent a week with Jon when he was at Western Ontario University as a Visiting Distinguished Scholar. During that week, we began work on a project to expand [25] into a Carus Monograph. I hope someday to be able to finish this project, but the end result will never be what it would have been with Jon’s further input. It is hard for the Monthly to say goodbye to Jonathan Borwein. He was a great Associate Editor, a great contributor to our pages, and one of the best friends the Monthly ever had. The legacy he has left us in the pages of the Monthly will benefit the students and admirers of mathematics for many years to come.

1. J. M. Borwein, “The Life of Pi: History and Computation, a Talk for Pi Day,” https://www.carma.newcastle.edu.au/jon/piday.pdf.
2. D. H. Bailey and J. M. Borwein, Pi: The Next Generation, Springer Verlag, 2016.
3. J. L. Berggren, J. M. Borwein, and P. Borwein, Pi: A Source Book. Springer Science & Business Media,
4. D. Borwein and J. M. Borwein, “A Note on Alternating Series in Several Dimensions,” Amer. Math. Monthly 93 (1986) 531–539.
5. J. M. Borwein, P. B. Borwein, “The Way of All Means,” Amer. Math. Monthly 94 (1987) 519–522.
6. J. M. Borwein, P. B. Borwein, D. H. Bailey, “Ramanujan, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi,” Amer. Math. Monthly 96 (1989) 201–219.
7. J. M. Borwein, P. B. Borwein, and K. Dilcher, “Pi, Euler Numbers, and Asymptotic Expansions,” Amer. Math. Monthly 96 (1989) 681–687.
8. J. M. Borwein and G. de Barra, “Nested Radicals,” American Mathematical Monthly 98 (1991) 735–739.
9. J. M. Borwein, P. B. Borwein, “Strange Series and High Precision Fraud,” Amer. Math. Monthly 99 (1992) 622–640.
10. D. Borwein, J. M. Borwein, P. B. Borwein, R. Girgensohn, “Giuga’s Conjecture on Primality,” Amer. Math. Monthly 103 (1996) 40–50.
11. J. M. Borwein and X. Wang, “The Converse of the Mean Value Theorem May Fail Generically,” Amer. Math. Monthly 105 (1998) 847–848.
12. J. M. Borwein, R. M. Corless, “Emerging Tools for Experimental Mathematics,” Amer. Math. Monthly 106 (1999) 889–909.
13. D. Borwein, J. M. Borwein, P. Marecha, “Surprise Maximization,” Amer. Math. Monthly 107 (2000) 517–527.
14. J. M. Borwein, K. S. Choi, and W. Pigulla, “Continued Fractions of Tails of Hypergeometric Series,” Amer. Math. Monthly 112 (2005), 493–501.
15. D. H. Bailey, J. M. Borwein, V.l Kapoor, E. W. Weisstein, “Ten Problems in Experimental Mathematics,” Amer. Math. Monthly 13 (2006), 481–509.
16. J. M. Borwein, “A Class of Dirichlet Series Integrals,” Amer. Math. Monthly 114 (2007) 70–76.
17. J. M. Borwein, “Hilbert’s Inequality and Witten’s Zeta-Function,” Amer. Math. Monthly 115 (2008) 125–137.
18. R. Baillie, D. Borwein, and J. M. Borwein, “Surprising Sinc Sums and Integrals,” Amer. Math. Monthly 115 (2008) 888–901.
19. J. M. Borwein, N. J. Calkin, D. Manna, “Euler-Boole Summation Revisited,” Amer. Math. Monthly 116 (2009) 387–412.
20. D. Borwein, J. M. Borwein, I. E. Leonard, “Lp Norms and the Sinc Function,” Amer. Math. Monthly 117 (2010) 528–539.
21. D. Borwein, J. M. Borwein, A. Straub, “A Sinc that Sank,” Amer. Math. Monthly 119 (2012) 535–549.
22. D. H. Bailey, J. M. Borwein, “Ancient Indian Square Roots: An Exercise in Forensic Paleo-Mathematics,” Amer. Math. Monthly 119 (2012) 646–657.
23. D. H. Bailey and J. M. Borwein, “Pi Day is upon us again and we still do not know if Pi is normal,” Amer. Math. Monthly 121 (2014) 191–206.
24. D. Borwein, J. M. Borwein, B. Sims, “On the Solution of Linear Mean Recurrences”, Amer. Math. Monthly 121 (2014) 486–498.
25. J. M. Borwein and S. T. Chapman, “I Prefer Pi: A Brief History and Anthology of Articles in the American Mathematical Monthly,” Amer. Math. Monthly 122 (2015) 195–216.

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