I have fond memories of growing up with Jon, as young boys in St Andrews, Scotland. An early memory ... is of us fishing off the pier in St Andrews with our dad David. We would catch rock cod, and make my mother Bessie clean them and make fish cakes. Jon and I also spent much of our childhood with our guinea pigs, Gilbert and Gulliver. My dad built a cage for them with no bottom, so that the guinea pigs would move around the lawn, acting as lawnmowers. As young boys we also shared a bedroom in St Andrews. I used to keep Jon awake at night, by reminding him that the universe was infinite. This bothered him to no end. It's no surprise that he ended up as a mathematician.

As kids a big treat was to be allowed to camp and freeze in the garden - in a one-man tent that had been to the top of K2 in the early 1950s.

Peter lived with a future CBC Morningside producer, an ex porn publisher, and a large python.

This paper will exhibit positive, non-decreasing, infinitely differentiable functions f with the property that the best rational approximations of degree n in the supremum norm to 1/f on [0, ∞) tend to zero arbitrarily slowly. Furthermore, such f can be chosen to have very general growth characteristics at infinity. In particular, this demonstrates that two conjectures of Erdős and Reddy are false.

The author wishes to thank Dr D W Boyd for many useful discussions.

Some of the results of this paper occur in the author's Ph.D. dissertation at the University of British Columbia under the supervision of Dr D Boyd, to whom the author wishes to express his gratitude.

There has recently been considerable interest in an essentially quadratic method for computing π. The algorithm, first suggested by Salamin, is based upon an identity known to Gauss. This iteration has been used by two Japanese researchers, Y Tamura and Y Kanada, to compute $2^{23}$ decimal digits of π in under 7 hours. They have now successfully computed $2^{24}$ digits (more than 16.7 million places). This is reported in the January 1983 'Scientific American' and the February 1983 'Discover Magazine'. In the process of surveying this and related fast methods of computing elementary functions, the authors discovered a new quadratically convergent product expansion for π. Our algorithm, like Salamin's, is intimately related to the Gaussian arithmetic-geometric mean iteration. However, it requires considerably less elliptic function theory to establish.

This exciting and well-written book is the product of the sound scholarship and enormous enthusiasm of its authors. The subtitle, 'A study in analytic number theory and computational complexity', captures its central theme very well.

The authors are cultured mathematicians. They have selected what has amused and intrigued them in the hope that it will do the same for us. Frankly, I cannot think of a more provocative and generous recipe for writing a book. Intellectually, what can we really offer one another more genuine than our own excitement? - for, as much as some pretend otherwise, there is no trustworthy yardstick for the value of a piece of mathematics. The book is cleanly, even beautifully, written ...

Peter Borwein's published research spanned classical analysis, computational number theory, Diophantine number theory, symbolic computing, experimental mathematics and applied mathematics. This research includes several rather important results. As one example, Peter Borwein, together with Tamás Erdélyi, Ronald Ferguson, and Richard Lockhart, settled Littlewood's Problem 22. ... In another notable example, Peter, in collaboration with Edward Dobrowolski and Michael J Mossinghoff, solved a problem of Lehmer on polynomials with odd coefficients.

... arose when Peter posed the question to some students and postdocs of whether there was any economical way to calculate digits in some base of a mathematical constant such as π, beginning at a given digit position, without needing to calculate the preceding digits. Peter himself subsequently found [a] surprisingly simple scheme for binary digits of log 2 ...

Peter Borwein gave a lovely talk interspersed with cartoons. My favourite was the research institute with two signs: "Unanswered questions" and "Unquestioned answers." He asked, "If Erdős had got the job at the IAS in Princeton, would he have touched our lives in the way he did?"

Move over creators of Max Head-room, Matrix and Metropolis. What researchers can accomplish at Simon Fraser University's IRMACS centre rivals the high tech feats of the most memorable futuristic films.

The $14 million centre's acronym stands for Interdisciplinary Research in the Mathematical and Computational Sciences. The centre's expansive view of the Lower Mainland from atop Burnaby Mountain echoes its limitless potential as a facility dedicated to fostering interdisciplinary research among scientists whose primary laboratory tool is the computer.

A newly constructed 2,500 square metre space atop the applied sciences building, the centre has eight labs, five meeting rooms and a presentation theatre, seating up to 100 people. They are equipped with easily upgradable computational, multimedia, internet and remote conferencing (including satellite) technology. High performance distributed computing and clustering technology, designed at SFU, and access to WestGrid, an ultra high-speed, interprovincial network, with shared computing and multimedia resources, make IRMACS unique in Western Canada.

... left him confined to a wheelchair, increasingly unable to pursue his research, and increasingly dependent on family and caregivers. I recall visiting Peter in January 2019 at his home in Burnaby, British Columbia. In spite of his paralysis and infirmity, I was astonished at his pleasant demeanour and ever-present humour. Would that we could all bear our misfortunes with as much strength and courage!

I guess some of the things that come to mind are how my first paper with Peter came about. We were at the International Symposium on Symbolic and Algebraic Computation conference in Vancouver. Peter came up to me over lunch and said something to the effect of "This afternoon looks really boring, did you want to go hiking instead?" Next thing I knew, he had organised a few people to go up the grouse grind. On the way up he decided to start asking me math questions. (And I guess more importantly, I was able to ask him math questions without him getting distracted by phone calls.)

I found his approach to supervising was basically, toss lots of questions at me and hope that one of them sticks. If anybody has ever sat beside him during a conference talk, they know exactly what I mean by that. Or, I guess anybody that has been sitting with him in a pub/coffee shop while conference talks are going on also knows what I am talk about.

The only other thing I can think of really is his addiction to coffee. I remember going to a conference in Portland while he was driving us all in a mini-van. I suspect during what should have been a 6 hour drive, we stopped for coffee about 8 times. It was during this drive that he decided on the naming conventions for all of the Mitacs machines, (all after some type of coffee). Since then, he got his espresso machine in his office, and he is probably even more addicted.

Peter was my "official" Post Doctoral Fellow supervisor, and I believe I was his first Post Doctoral Fellow. Without his support and encouragement I would probably not be where I am now. What I admired (and still admire) most about Peter is the fact that he always has a problem, or problems, on his mind; he will ask you, prod you, share insights with you and be very persistent. When he has found a truly exciting and worthwhile problem, he will not let go until it is solved. He will hack away at it from all directions, will try to get others interested and involved (and often succeed in this), and more often than not he will eventually make substantial progress, either alone, or in collaboration with others.

An example for this is the spectacular Bailey-Borwein-Plouffe formula. Already during his time at Dalhousie he often said that he wanted to find the 10 billionth (I believe) digit of pi without having to know all the previous digits. I had no doubt that he would eventually succeed, and I consider Bailey-Borwein-Plouffe as a result of this (though hexadecimal instead of decimal).

Peter likes funny anecdotes, often related to mathematics or mathematicians. [One] I remember: A visit with daughter Alex as a toddler to Point Pleasant Park, when Alex pointed to the Sailors Memorial and said, 'look, Daddy, a big plus!' Peter was and is an excellent writer and expositor. But there wasn't a name, usually foreign, that he wouldn't find a way to misspell. One time in the mid-90s I got a (positive) referee report in which every name was incorrect; I KNEW that Peter had to be the referee. When I gave him an off-print later on, I remarked that I thought he might already be familiar with the paper. Peter, very surprised, "How do you know I refereed it?" I had to tell him the truth.

It's always a pleasure to visit Peter and his family and friends in "Mahler measure heaven", as Jeff Vaaler has called Vancouver. But one of my most memorable meetings with Peter was in Nashville, at an approximation theory meeting in the late 90's. I was just passing through, driving from North Carolina to Texas, but my wife and I briefly crashed the conference to join Peter for lunch at a local Indian buffet. I'd visited Simon Fraser University the prior summer, and we'd had some correspondence on some problems. But it was at lunch in Nashville that we hammered out plans for our first joint paper.

Working with Peter has always been just as comfortable. Since that lunch meeting, I have visited Peter some six or seven times at Simon Fraser and the Centre for Experimental and Constructive Mathematics and IRMACS, and we now have some nine papers together.

Coming to Simon Fraser University was always an exciting time. Peter seems to have an incredible knack for suggesting just the right sort of problem to his collaborators - problems that are not only irresistible, but very well-suited to the listener's interests. He's a lot like Erdős in this respect. Each time I arrived in Vancouver, Peter always had a fascinating new project that was just irresistible to join.

... bore with remarkable grace and courage. He was until the end smart, funny, mischievous, kind, interesting and interested.