Jack Williams passed away on November 13th, 2015, at the age of 72.

Jack obtained his PhD from the University of Oxford Computing Laboratory in 1968 and spent two years as a Lecturer in Mathematics at the University of Western Australia in Perth. He was appointed Lecturer in Numerical Analysis at the University of Manchester in 1971.

He was a member of the Numerical Analysis Group (along with Christopher Baker, Ian Gladwell, Len Freeman, George Hall, Will McLewin, and Joan Walsh) that, together with numerical analysis colleagues at UMIST, took the subject forward at Manchester from the 1970s onwards.

Jack’s main research area was approximation theory, focusing particularly on Chebyshev approximation of real and complex functions. He also worked on stiff ordinary differential equations (ODEs). His early work on Chebyshev approximation in the complex plane by polynomials and rationals was particularly influential and is among his most-cited. Example contributions are

J. Williams (1972). Numerical Chebyshev approximation by interpolating rationals. Math. Comp., 26(117), 199–206.

S. Ellacott and J. Williams (1976). Rational Chebyshev approximation in the complex plane. SIAM J. Numer. Anal., 13(3), 310–323.

His later work on discrete Chebyshev approximation was of particular interest to me as it involved linear systems with Chebyshev-Vandermonde coefficient matrices, which I, and a number of other people, worked on a few years later:

M. Almacany, C. B. Dunham and J. Williams (1984). Discrete Chebyshev approximation by interpolating rationals. IMA J. Numer. Anal. 4, 467–477.

On the differential equations side, Jack wrote the opening chapter “Introduction to discrete variable methods” of the proceedings of a summer school organized jointly by the University of Liverpool and the University of Manchester in 1975 and published in G. Hall and J. M. Watt, eds, *Modern Numerical Methods for Ordinary Differential Equations*, Oxford University Press, 1976. This book’s timely account of the state of the art, covering stiff and nonstiff problems, boundary value problems, delay-differential equations, and integral equations, was very influential, as indicted by its 549 citations on Google Scholar. Jack contributed articles on ODEs and PDEs to three later Liverpool–Manchester volumes (1979, 1981, 1986).

Jack’s interests in approximation theory and differential equations were combined in his later work on parameter estimation in ODEs, where a theory of Chebyshev approximation applied to solutions of parameter-dependent ODEs was established, as exemplified by

J. Williams and Z. Kalogiratou (1993). Least squares and Chebyshev fitting for parameter estimation in ODEs. Adv. Comp. Math., 1(3), 357–366.

More details on Jack’s publications can be found at his MathSciNet author profile (subscription required). Some of his later unpublished technical reports from the 1990s can be accessed at from the list of Numerical Analysis Reports of the Manchester Centre for Computational Mathematics.

Jack spent a sabbatical year in the Department of Computer Science at the University of Toronto, 1976–1977, at the invitation of Professor Tom Hull. Over a number of years several visits between Manchester and Toronto were made in both directions by numerical analysts in the two departments.

It’s a fact of academic life that seminars can be boring and even impenetrable. Jack could always be relied on to ask insightful questions, whatever the topic, thereby improving the experience of everyone in the room.

Jack was an excellent lecturer, who taught at all levels from first year undergraduate through to Masters courses. He was confident, polished, and entertaining, and always took care to emphasize practicalities along with the theory. He had the charisma—and the loud voice!—to keep the attention of any audience, no matter how large it might be.

He studied Spanish at the Instituto Cervantes in Manchester, gaining an A-level in 1989 and a Diploma Basico de Espanol Como Lengua Extranjera from the Spanish Ministerio de Educación y Ciencia in 1992. He subsequently set up a four-year degree in Mathematics with Spanish, linking Manchester with Universidad Complutense de Madrid.

Jack was promoted to Senior Lecturer in 1996 and took early retirement in 2000. He continued teaching in the department right up until the end of the 2014/2015 academic year.

I benefited greatly from Jack’s advice and support both as a postgraduate student and when I began as a lecturer. My office was next to his, and from time to time I would hear strains of classical guitar, which he studied seriously and sometimes practiced during the day. For many years I shared pots of tea with him in the Senior Common Room at the refectory, where a group of mathematics colleagues met for lunchtime discussions.

Jack was gregarious, ever cheerful, and a good friend to many of his colleagues. He will be sadly missed.

I attended Jack’s MSc course on approximation theory in VUM in 1980. His lectures were clear and inspiring. I will miss his charisma and wonderful sense of humour.

Jack taught me when I was an undergraduate, and he was a consummate lecturer. He was then a key presence when I went on to study for an MSc and a PhD. I always found him to be a positive and encouraging influence around the maths department. Reading Nick’s blog entry reminded me how Jack had that knack of asking penetrating and illuminating questions to seminar speakers. Thinking back to those years, three or four specific memories came to me (possibly blurred through time).

a) In a 3rd year undergrad numerical analysis class, in a section on the Shooting Method he told us that we would only be looking at bisection; he wasn’t being paid enough to teach us how to differentiate an ODE with respect to its initial condition.

b) Jack read a draft of my MSc thesis, and gave me advice along the lines of “this has got some decent content, why not hold some of it back for your PhD,” and I was never sure if he was being serious.

c) Jack always claimed that Cleve Moler (of MATLAB fame) owed him a supercomputer. Apparently Cleve gave a talk at Manchester where he put up a visualization of a complex function and offered the supercomputer to anybody in the audience who could correctly identify it. Jack had studied the gamma function in his PhD and immediately, and correctly, named it.

d) The ODE conference mentioned in that photo at the end of Nick’s blog took place in the days when papers were submitted in hardcopy form. Throughout the week of the conference, Jack was regularly mistaken for the conference organiser and handed brown envelopes containing maths articles. At the conference dinner, after a few drinks, he stood up and gave a hilarious 10 minute riff on the theme of “I am not Jeff Cash.”

Although I cannot claim to have known Jack well, I did have contact with him over many years and often used to see him on my visits to Manchester. He was always welcoming and friendly, and I was impressed with his commitment to his lectures, even well after his retirement. On one of Jack Dongarra’s summer stays in Manchester we went with our wives, one Saturday, to Tatton Park. I was surprised to see Jack Williams in the restaurant studying some notes. It turned out that he was teaching Françoise Tisseur’s numerical linear algebra course that semester and was studying her course notes! I shall miss him.

As mentioned by Sven Hammarling, Jack agreed to teach in 2010 the Matrix Analysis course that I had written and taught for the previous three years. He was relieved to find out that my problems “did not need solutions to the solutions”, whereas he used to joke that the opposite was true for

an optimization course that he had inherited from Nick Higham.

I shared many discussions with Jack over lunches during the 17 years I have been in Manchester. They were always entertaining and also enriching. Jack loved languages and we often discussed analogies and differences between English, French and Spanish. I will miss you Jack and will never forget your laugh.

It was a pleasure to work with Jack on the Service Teaching over the last few years. He taught to many schools, most recently to EEE and to Foundation Year. His lectures were well-received and well-rated by the students.

We’d talk about the teaching and we’d talk about other things. He always had something interesting to say.

When he was in, in the summer, it would appear in retrospect that he was far more ill than he was letting on. He explained that he was unable to teach in the autumn due to receiving some treatment but it was his intention to be back in the spring. Sadly, it was not to be.

Jack meant a lot to me. In 1977 I was an undergraduate at Harvard writing a thesis on Chebyshev approximation. I found Jack’s papers and wrote him an air mail letter, and a few weeks later, there in my mailbox was a wonderfully encouraging air mail response. This was my first ever communication with an outside academic, and it was thoroughly encouraging — it felt so good to be talking about mathematics (indeed about some very particular numbers involving exp(z) and

the unit disk) across the Atlantic.

Then I moved to England and began to love the Manchester area and see Jack a little in context. To a raw American, he had been just an Englishman, like Churchill or Paul McCartney. What fun to get to know him as a northerner! Churchill dropped from the equation but I began to feel I almost knew one of the Beatles personally. What a smile and a spirit! Jack just always made you feel good.

I met Jack four years ago when he called by our office talking to us in Spanish because all the people who shared that office were spanish speakers, he loved speaking in Spanish. Then, I had the opportunity to be twicely his teaching assistant in Numerical Analysis course. I can say that most or all of his students understood him very well and his notes were excellent. As a person I will always remember him because he gave some important support words when I needed and did some proof reading of some sections of my PhD thesis as he very kindly offered it very recently, and pecular laugh. Nos vemos pronto camarada!

How lucky was I to be one of Jack’s Manchester colleagues back in the mid 70s? For an anglophile post-doc, Jack was the best. Whether you were talking about the centrality of matrix computations or recapping the latest episode of The Archers, Jack would listen, smile, and then figure out some way to make you laugh at yourself. He was the perfect mentor to have at the front end of an academic career. Jack could be serious and funny at the same time—an absolute gift to us all.

I was doing my PhD in Toronto when Jack was on sabbatical there and I always remember Jack cycling into the department regardless of the weather, including snow storms. I really appreciated his sense of humour both then and when I did my post-doc in Manchester in 81.

Sorry to read this sad news. I read with interest Jack’s work on ODEs, and always found him interesting and helpful when I met him.

I met Jack several times in Oberwolfach, but also in Britain and possibly at other places, too.

Since we had mutual interests in approximation theory, meeting him was always a pleasure.

It is sad to hear that he passed away so early.

I am sad to hear that Jack is gone. I knew him fairly well in the early 80s after spending a year at Manchester. As has been said, it was a lot of fun to spend time with him. Also, in those early years, during coffee and tea breaks at Manchester, I recall plenty of light-hearted talk of gloom and doom. (Those were times of frequent redundancies.)

I am very sad to hear of Jack’s death. We shared many common interests,

and met many times at conferences etc. He was always good company,

and the NA community is the poorer for his loss.

Alistair Watson.

I am sad to hear about passing of Jack Williams .

Jack was my supervisor for my M.SC( 1981) and Ph. D ( 1984) theses .

He was always cheerful, had sense of humor, very encouraging, supportive, and some times tough .

The Math department occupied then the Math Tower. I remember when I was not getting any numerical results for my research (of course computers were not as advanced as now these days ) , frustrated and ready to give up , he always used to tell me , not to worry ,”this is how research works( one day you get some results and 10 days you don, just be positive”

He also was very interested in learning about different cultures, since he had many international graduate students. He asked about my Chaldean / Iraqi culture, we had many discussions about Iraq, the three languages I speak.

Chaldean (version of Aramaic language, Arabic and English . I had also the pleasure of meeting his family .

God Bless his soul

A colleague of Jack’s, who retired some time before Jack, contacted me recently to recount a story from around 20 years ago when the Department of Mathematics was having its teaching assessed. One of the assessors told this colleague that the lecture that he attended by Jack was the best lecture he had ever attended – that is ever, not just during the visit!