# Tributes to Jonathan Borwein

We give below a number of short extracts from various tributes paid to Jonathan Borwein following his death in 2016.

**1.**

**Author:**Adrian Lewis, co-author with Jon Borwein of

*Convex Analysis and Nonlinear Optimization*(2000).

**Source:**Jon Borwein: a personal reflection,

*SIAM Activity Group on Optimization Views and News*

**24**(1) (2016), 8-10.

Jon's mathematical breadth and energy make a fascinating but bewildering picture, extending far beyond traditional optimisation, and challenging to sketch. He delighted in collaboration, and many of us knew first-hand his research style: whirling, exuberant, defamiliarising, endlessly curious, elegant, scholarly, generous, and honest. He made time for everyone, no matter their rank or eccentricity.

...

Life at the Borweins' home was an inspiring and exhausting blur. A typical evening involved prodigious and virtuoso culinary feats from Judi, feisty debates from Rachel and Naomi, and multiple simultaneous media playing at full volume. At a minimum, these included political news (Jon was intensely active, politically, serving for a while as treasurer of the Nova Scotia New Democratic Party), major league baseball (another domain of erudition), and music. All gradually dissolved into large glasses of Scotch (Jon's Scotchness, like Healey Willan's, was mostly "by absorption"), and then a call to arms from Jon to prove some reluctant theorem. The exuberant and dizzying environment mirrored Jon's mathematics, a style so appealing it quickly sealed my own career choice as a mathematician.

**2.**

**Authors:**Tim R Marchant, President of the Australian Mathematical Society, and George A Willis, editor of the Journal of the Australian Mathematical Society.

**Source:**Editorial. Professor Jonathan M Borwein,

*J. Aust. Math. Soc.*

**101**(2016), 289.

Jon's characteristic energy and quickness of mind immediately impressed all who met him, while his humour, generosity and optimism soon became apparent on further acquaintance. He brought all these characteristics plus his vast expertise and network of contacts to the role of co-editor of the

*Journal of the Australian Mathematical Society*as well as to the many other service roles in the Australian mathematical community that he took on after moving to this country in 2008.

**3.**

**Author:**Scott T Chapman, editor of the

*American Mathematical Monthly*.

**Source:**A letter from the editor: Jonathan M Borwein (1951-2016),

*Amer. Math. Monthly*

**123**(9) (2016), 847-848.

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 π. ...

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," was awarded the Chauvenet Prize, the Mathematical Association of America'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 ...

I wish today to honour 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. You will note that his Monthly papers deal with a wide variety of topics, from his favourite subjects (like 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.

**4.**

**Author:**Richard P Brent, an Australian mathematician and computer scientist.

**Source:**Jonathan Michael Borwein 1951-2016: Life and Legacy,

*Papers with Code*(13 July 2021).

Jon had a passion for sharing his joy of mathematics with students and a more general audience. Some of his research topics were particularly well-suited for communication to high school and undergraduate students. For example, we have already mentioned his interest in experimental mathematics and π. Jon was a keen blogger, starting this activity in 2009 when he and David Bailey founded the "Math Drudge" (now "Math Scholar") blog, which now has over 200 articles on a wide range of topics, covering many facets of modern mathematics, computing, and science. ...

Jon regarded visualisation as a powerful tool for both experimental mathematicians and mathematical communicators. He was fond of the maxims "it is often easier to see something than to explain it in words" and "a picture is worth a thousand words." Examples may be found in his paper 'Walking on real numbers',

*The Mathematical Intelligencer*

**35**(2013), 42-60, which contains striking images of walks in the plane associated with various mathematical constants such as

*π*,

*e*, and Champernowne's number$C_{4}$.

**5.**

**Source:**Distinguished Service Award - Jonathan M Borwein,

*Australian Mathematical Sciences Institute*(2017).

Jonathan Borwein led the Australian Mathematical Sciences Institute's Scientific Advisory Committee with distinction from 2010 until his untimely death in 2016. He also served on the Australian Mathematical Sciences Institute's Research and Higher Education Committee and as a key observer on the Board. He was a tireless ambassador for the Institute. ...

Jon Borwein was a mathematician of astonishing range and versatility and a leader in every way. A highly respected advocate for the Australian mathematical sciences, his past roles included President of the Canadian Mathematical Society and Editor in Chief of the Journal of the Australian Mathematical Society. He was an International Scientific Indexing highly cited scientist and his work in mathematics and computing, including optimisation, computational number theory and classical functional analysis continues to be of great impact.

...

Jon's deep international leadership experience, coupled with his great generosity of spirit, was of extraordinary value to the mathematical sciences in Australia and to the Australian Mathematical Sciences Institute in particular.

...

During his leadership of the Scientific Advisory Committee he encouraged wider access, especially by younger research leaders, to the Australian Mathematical Sciences Institute's workshop program and oversaw the successful program collaboration with the Australian Mathematical Society. His energetic and always thoughtful engagement with the Board, the Australian Mathematical Sciences Institute Members and the committees was outstanding.

Jon was an intense driver of collaboration and was himself an inveterate speaker and collaborator, always encouraging his hosts to make use of the Australian Mathematical Sciences Institute's support. He had a natural affinity with the Australian Mathematical Sciences Institute's collaborative model and his strategic view of the world made his contribution singular and his loss acute.

**6.**

**Authors:**David H Bailey (co-author with Jon Borwein), Judith Borwein (Jon Borwein's wife), Naomi Simone Borwein (Jon Borwein's daughter) and Richard P Brent (an Australian mathematician and computer scientist).

**Source:**Jonathan Borwein: Mathematician Extraordinaire, in

*D H Bailey, N S Borwein, R P Brent, R S Burachik, J-A H Osborn, B Sims and Q J Zhu (eds.), From Analysis to Visualisation*(Springer, 2017), 1-10.

One bane of modern academic research in general, and of the field of mathematics in particular, is that most researchers today focus on a single specialised niche, seldom attempting to branch out into other specialties and disciplines or to forge potentially fruitful collaborations with researchers in other fields. In contrast, Borwein not only learned about numerous different specialities, but in fact did significant research in a wide range of fields, including experimental mathematics, optimisation, convex analysis, applied mathematics, computer science, scientific visualisation, biomedical imaging and mathematical finance.

...

Jonathan Borwein's prodigious output in optimisation and experimental mathematics is certainly his singular contribution to modern mathematics. But beyond his technical accomplishments, he was a master of mathematical communication (his lectures were always paragons of well-organised and visually appealing mathematics and graphics), mathematical education (part of his interest in π was to bring the joy of mathematical discovery to students), and in promoting science, mathematics and computing to the general public. To this end, he wrote and lectured tirelessly. By one reckoning he presented an average of one lecture per week for decades, and wrote hundreds of articles targeted to the general public. His death is a loss to all those who treasure modern mathematics, science and clear thinking.

**7.**

**Author:**David H Bailey, co-author with Jon Borwein.

**Source:**Jonathan Borwein: renaissance mathematician,

*Amer. Math. Monthly*

**128**(9) (2021), 773-779.

Even if one focuses only on his published books and refereed articles, there are over 500 items. One paper on optimisation theory has been cited over 1300 times.

In examining Borwein's writings, what is most striking is their breadth. In an era when many in the academic mathematical community focus ever more tightly on a single specialty, Borwein did notable research in a wide range of fields, ranging from experimental mathematics (in which he can rightly be regarded as a pioneer and leading exponent) and optimisation to biomedical imaging, mathematical finance, and computer science. Yet Borwein was equally at home writing for the general public. He published numerous articles in venues such as the Conversation, the Huffington Post and various blogs that were very much targeted to a wide range of readers. In short, Borwein can certainly be credited as both a master mathematician and a master communicator - truly a Renaissance mathematician.

...

Not long before Jon passed, the present author recalls being engaged in a particularly intense collaboration with Jon, marked by frequent Skype video calls, countless exchanged emails and numerous computer runs. He thought he had Prof Borwein's full attention during this time, but, as he subsequently discovered, Borwein simultaneously was advancing at least three completely different lines of research with other colleagues, and this was in addition to teaching classes, managing students, handling significant editorial responsibilities and writing articles for the public.

**8.**

**Author:**Francisco Aragón, Jon Borwein's postdoctoral student and collaborator.

**Source:**Adiós a Jonathan Borwein, el Doctor π,

*El País*(7 September 2016).

Jon directed 13 doctoral theses and was in charge of 42 postdoctoral students (I'm proudly one of them). Jon was a great mentor. Perhaps his best quality as tutor was his ability to discover and develop the potential of each of his students, while doing his best to promote the professional success of them all. Someone told me once at a conference, right after an interesting presentation of one of his students, that there was something special in all his disciples. Unquestionably, Jon left his mark. It was impossible to work alongside without learning, as his vast knowledge would inexorably force you to expand yours. He was an excellent communicator who always made an effort to make everyone learn something in each of his captivating presentations. Even during his more technical talks, he included anecdotes, quotes and cartoons on his slides, managing to catch the attention of anyone in the room. His great talk about π was without any doubts my favourite.

I had the chance to work with Jon, his brother Peter and David Bailey in one of the subjects that interested him the most: the number

*π*. After a month of calculations that occupied 20 cores in a cluster of computers in CARMA, we managed to draw a walk based on the first one hundred billion digits of Pi in base 4. Our goal was to experimentally check if the digits of

*π*behave randomly. We got a beautiful image with a resolution of 108 gigapixels (which would be equivalent to paste more than ten thousand photos taken with a normal camera, of ten megapixels each). I must admit that I am delighted that, among all the images created in his experimental work in mathematics, he chose this one as a background image for his webpage.

...

Besides being an enthusiastic and tireless researcher, he was a jovial person who seemed to only perceive the positive aspects of each person. Perhaps that is why his sudden absence has saddened us more to all who were lucky to know him. Personally, I feel that it has been created a void in the world that cannot be filled with all the digits of

*π*. We miss you, Jon.

**9.**

**Author:**Michel Théra, a co-author of Jon Borwein.

**Source:**Jonathan M Borwein (1951-2016) homo sapiens, homo ludens,

*Matapli*(111) (2016), 43-47.

He was a scientific consultant to Apple Computers. A good portion of his ideas came from his ability to quickly draw subtle images on his computer and to develop dependable ideas of his own. He liked to cite David Berlinski's review of T W Korner's book

*The Pleasures of Counting*: "In its time, the computer has changed the very nature of the mathematical experience, suggesting for the first time that mathematics, like physics, could become an empirical discipline, an area where one could discover things because one sees them." He thus devoted a large portion of his mathematical life in the hope of refuting Picasso, who had said "Computers are useless, only capable of rendering answers."

I will conclude by mentioning what Jon said in his address given on the occasion of his Doctorat Honoris Causa at the University of Limoges:

- Mathematics is a human endeavour. It takes part in and adapts itself to culture (it is not a question of abstract reality, immutable, eternal, unearthly constructs as conceived of by Frege).

- Mathematical knowledge is not infallible. In concert with empirical science, mathematics can move forward while errors are made, then corrected, and then perhaps corrected again. (This flawed nature of the subject is brilliantly described in Proofs and Refutations by Lakatos.)

- There exist several conceptions of proof and of mathematical rigor, as a function of time, place and other considerations. The use of computers to construct proofs constitutes a non-traditional version of rigour.

- Empirical evidence, numerical techniques, and probabilistic evidence, help all of us to decide what ought to be believed as true in mathematics. Aristotelean logic isn't always the best means to come to a decision.

His intelligence and quickness of mind, his knowledge, his ideas, his willingness to make himself available, and his sense of humour are going to be missed among those who knew and respected Jon. I of course include myself in this group, and his leaving us took away from me the possibility to honour him once more in person. I will always be personally grateful for what he taught me and for his friendship. His acknowledgement of me last June, on the occasion of my 70th birthday celebrated in Alicante, will remain forever in my memory.

**10.**

**Author:**Michael Rose, a postgraduate student of Jon Borwein.

**Source:**A mathematical family man,

*Jonathan Borwein Memorial Website*(30 October 2016).

Jon went well above and beyond for us students in many ways. First and foremost, though he was always extremely busy he took the time to really know his students, the better to help them potential. He had a knack for zeroing right in on our strengths and especially our weaknesses. In my case, it was Jon's idea to check out a science communication pathway after my PhD - and when did he first have that insight? Well, literally days after that first meeting he'd invited me in to one of talks to a local primary school, and that was quickly followed by him nudging me into various outreach events, school visits, radio talks, you name it. Not only was Jon a passionate mathematician, but he was also a passionate advocate of mathematics and he shared the joy of maths as far and wide as he could, from primary students to fellow professors, always with a wonderful sense of humour. He was ever and always an outstanding role model.

But after all that, the thing that left the biggest impression on me, was Jon's warm-hearted willingness to play a supporting role even beyond mathematical concerns. When I was struggling with some personal crises, Jon always had a sympathetic ear and some fantastic advice to give. Jon's door was always open when he was in Newcastle, his inbox was always open when he was away, and let alone his office, but Jon and Judy's house was open to me. I fondly remember attending numerous conferences on Jon's invitation, some overseas, where Jon introduced to many outstanding mathematicians, drinking coffee and dining with Jon and Judy, sightseeing after conferences, you name it.

Jon was very much a mathematical family man, pouring much care and attention into the relationships between himself and his students, and his students with each other. With the utmost sincerity and conviction I can say to you that truly, we who were fortunate enough to study with Jon could not possibly have had a greater supervisor in any sense I know. Not only was he a great mentor, but a great friend who will be dearly missed and fondly remembered.

**11.**

**Author:**Michel Théra, a co-author of Jon Borwein.

**Source:**Introduction for the Paris Jon Borwein Memorial Conference,

*Jonathan Borwein Memorial Website*(13 February 2017).

Any of you knew Jon as an internationally acclaimed mathematician. He was one of the world's leading scholars in Experimental Mathematics, in Optimisation Theory, in Applied Nonlinear Functional Analysis, in algorithmic number theory. His long publication list spanned the breadth of pure and applied mathematics. He has been cited over 22,000 times (according to Google Scholar). As Shakespeare suggests, brevity is indeed the soul of wit. Also, a conclusion I would like to add two thoughts about Jon:

The first one has been sent to me by Scott Lindstrom, who was the last student to start a PhD with Jon:

When Jon became excited about something I did or discovered, I felt big. I felt big because Jon was big, but I also felt big because Jon - in his uniquely uninhibited fashion - gave me permission to feel that way. I am grateful that Jon gave to me - and to so many others - the chance to feel big.

The second one is personal:

Jon, you have inspired me over the years since 1978 when I first met you in Montreal.

Dear Jon, I am the one, and many of us also in our community, of those fortunate people who had the opportunity to meet you, to work with you and to appreciate you.

Today, we all miss you very, very much. Thank you!

**12.**

**From:**University of Newcastle, Australia.

**Source:**Report on the Jon Borwein remembrance day meeting in Paris,

*Jonathan Borwein Memorial Website*(15 February 2017).

From all of us in Newcastle who, while a hemisphere away, are united with you in paying tribute to our friend and colleague Jonathan M Borwein. Jon first visited Australia, and the University of Newcastle in particular, in the mid 80's; the first of numerous short and mid term visits. So he was no stranger to us when in January 2008 he, together with his wonderful wife Judi, two of his three daughters; Naomi and Tova, and grandson Jacob, moved to Newcastle to become Laureate Professor of Mathematics. Jon's impact on mathematics at Newcastle and more generally Australia was both immediate and profound. Within months he had established the Priority Research Centre for Computer Assisted Research Mathematics and its Application (CARMA) and actively engaged with the Australian mathematical community assuming various roles in the Australian Mathematical Society, Australian Mathematical Sciences Institute and soon as an elected member of the Australian Academy of Sciences. Jon was a unique and amazing colleague. His personality and love of scholarship were infectious, and equalled only by his enjoyment of good company and a good debate. His sense of fairness and the easy generosity with which he shared his great knowledge, insightfulness and creativity made Jon an outstanding mentor and the best and most natural of collaborators. And, for many of us a close and much valued friend. We thank you all for the honour you bestowing on Jon today. It is a day of profound sadness, but also a celebration of the great privilege of having known and in so many cases worked with him. Jon has left us with an indelible legacy, but also a great void. We miss him more and more with every passing day.

**13.**

**Author:**Sarah Borwein, Jon Borwein's sister.

**Source:**My brother Jon,

*Jonathan Borwein Memorial Website*(27 August 2016).

Jon was not only a decade older than me. He was also very precocious, so by the time I was 5 he was already in university and not living at home. By the time I was 7 he had met Judi and I had acquired a sister. I was not allowed to visit Jon and Judi after they moved in together because they were 'living in sin'. But Judi won me over by sewing me clothes! Clothes my mother wouldn't buy me. Like a red wet look outfit that was the height of fashion in the late 1960s and that I got to wear with white GoGo boots. After that Jon was not just Jon to me, he was Jon and Judi. And so it has been for many decades. Judi, I know how deeply this loss impacts on you and I want you to know how much we all love and support you.

Later, when his first child Rachel was born, Jon and Judi invited me to Halifax to "help look after her" in the new-born period. I'm sure I wasn't that much help. Jon was utterly delighted to be a father and completely enchanted with his child. He would hold her to his chest and pretend that he was breastfeeding her coca cola. I was still a little girl myself, and I was also enchanted with that little girl - my first niece of the six wonderful nieces I now have - and she became a sister too. Years later, when my own first child was born - prematurely and scarily in Paris –Jon and Judi and Rachel were there with me. They helped me more than they can know through a terrifying time. And later still, when that first child of mine grew up healthy and strong and decided to join the family business as a mathematician, Jon gave him a summer internship in Australia. There was always a kind of cosmic karma that bound us, and it was woven together by Jon's incredible energy, his generosity of spirit and his remarkable ability to make connections.

...

Jon was not always an easy person. Genius often isn't. His energy filled every room and his brilliance could be blinding, and intimidating. But he was inspiring, he was magnanimous, he was tender-hearted. He was a mensch. He lived more in 65 years than most people do in 100. And he has left a tremendous legacy. As Irving Berlin said, the song is ended, but the melody lingers on.

**14.**

**Author:**Peter Borwein, brother of Jon Borwein.

**Source:**My brother Jon,

*Jonathan Borwein Memorial Website*(27 August 2016).

We co-authored over 25 papers and books, and he solo wrote over 200. He had a remarkable clock speed, a term he liked to use for how fast people worked. He could accomplish in a day or two what took other people weeks, which is one of the reasons he was so prolific. We worked together for over 35 years; we were in the same department for about 20, one of the periods at Dalhousie and one at Simon Fraser. I owe much of my career to him, because people thought they were getting him when they hired me.

I would like to comment on how we worked together, which was intensive. And I also want to comment on the fact that many people thought we ought to compete, that there ought to be sibling rivalry. In fact there really was no rivalry. He was a very generous co-author. Not always an easy co-author (he could be very demanding), but he was always generous with ideas, and with acknowledgment, and with giving credit, not just to me, but to his graduate students, and colleagues - who he could drive very hard, but if they could keep up with him the pay-off was rewarding.

He was obviously very smart. But what doesn't show necessarily is that he had a phenomenal memory. When he worked on a problem intensely he would store the facts and not have to look them up. I think he inherited this from my mother. I certainly don't share this ability. He had a remarkable memory for books, authors – details like that.