# Alexander Duncan Davidson Craik

### Quick Info

Brechin, Angus, Scotland

St Andrews, Fife, Scotland

**Alexander D D Craik**was an expert on fluid mechanics writing many significant papers on the topic, but he was also interested in the history of mathematics, particularly Scottish mathematics, and wrote over 30 historical works.

### Biography

**Alex Craik**was the son of Alexander Craik (1896-1997), who ran a small draper's shop in Brechin, and Mary Ford Wyllie Thomson (1902-1994). Alexander and Mary Craik were married on 10 May 1933 in the Cooperative Rooms, High Street, Brechin. On their Marriage Certificate, Alexander gives his address as 107 River Street, Brechin and his occupation as Trader (Master) while Mary gives her address as 13 City Road, Brechin and her occupation as Photographer's Assistant. Alex's name Davidson comes from his paternal grandfather Davidson Craik while the name Duncan comes from his maternal grandfather Duncan Thomson. Let me [EFR] add as this point that I knew Alex for nearly 60 years and it is difficult for me to refer to him in any way other than "Alex" but, to be consistent with our other biographies, I shall try to refer to him as "Craik" for at least most of this biography.

Craik attended primary school in Brechin, continuing to study at Brechin High School from 1950 to 1956. His academic record was outstanding and, while at the high school, he gained a high reputation as a cricketer. Don Shaw kindly sent us the following information:-

At Brechin High School in 1955 the Mathematics class for Highers contained six pupils, four of whom went on to take Sixth Year Mathematics (at that time comprising Geometry, Elementary Analysis and Dynamics): Alex Craik, Ian Currie, Marion Greig and Don Shaw. The mathematics teacher was David McGregor, and in the sixth year the headmaster, Sam Anderson, taught Geometry and Elementary Analysis, while Arthur Paterson, the science teacher, taught Dynamics.In 1956 he sat the University of St Andrews Bursary Competition and was awarded a Harkness Bursary of £100 per annum, the highest award made to the very top male students. Later in the same year he entered the University of St Andrews where he missed out the first year mathematics class, going straight into Special Mathematics, the second year course. He performed exceptionally well in this class as he did in all his classes. At this time Edward Copson was the Regius Professor of Mathematics and, among those who taught Craik, were Daniel Rutherford, David Borwein and Jim Tatchell. Craik wrote in May 2019 following Tatchell's death:-

I was a student in perhaps Jim Tatchell's first lecture course in St Andrews. As always, his lectures were remarkably clear and precise. He was an analyst of distinction.In May-June 1960 Craik sat the honours examinations in Applied Mathematics. At this time honours students sat seven papers on the work of the two honours years at a single diet of examinations at the end of the second of their honours years. He sat the papers General Analysis, Geometry and Algebra (a special paper for Applied Mathematics), Statics, Dynamics, Fluid Dynamics, Quantum Mechanics and Relativity. He was awarded First Class Honours in Applied Mathematics.

After graduating from St Andrews, Craik went to Churchill College, Cambridge, to undertake research for his doctorate. He was supervised by Brooke Benjamin who, at that time, was working partly in the Engineering Department and partly in the Applied Mathematics and Theoretical Physics Department. In 1963 Craik was appointed as a lecturer in the Department of Applied Mathematics, St Salvator's College, University of St Andrews. I [EFR] took one of the first courses that he taught in session 1963-64, namely 'Incompressible Fluids'. I kept the lecture notes I took throughout my career but, sadly, I binned them when I retired from teaching. He also gave a course on 'Compressible Fluids' but since I was doing a joint degree in Pure and Applied Mathematics, I only took the 'Incompressible Fluids' course. Craik was an excellent lecturer, delivering well-prepared and well thought out material.

On 15 July 1964, Craik married Elizabeth Mary Farmer, the daughter of John Farmer and Annie Watson. Elizabeth had studied at Bell Baxter High School, Cupar, Fife, before entering the University of St Andrews to study Classics. She had then studied at Cambridge, after which she held a research post at Birmingham University before returning to St Andrews where she was appointed to the Department of Humanity (Latin). Alex and Elizabeth Craik had two children: Peter Alexander Craik (born 1970) and Katharine Anne Craik (born 1972).

At the time of his appointment to St Andrews, Craik was still working on his Ph.D. dissertation

*Wind-generated waves in thin liquid films*which he submitted to the University of Cambridge and was awarded a Ph.D. in 1965. He published material from his thesis in a paper with the same title in 1966. Craik gives the following acknowledgement in that paper:-

I should like to thank Dr T Brooke Benjamin for his guidance and helpful criticism throughout the course of this work.The paper has the following Abstract:-

In the presence of an air stream, a uniform liquid film on a horizontal flat plate may be unstable to small disturbances, and waves may arise. In this paper the hydrodynamic stability of thin liquid films is examined both experimentally and theoretically. The experiments concern water films thinner than those which have been examined in the past. It is found that, when the film thickness is sufficiently 'small', a previously unknown type of instability occurs. The theoretical analysis explains this surprising phenomenon. Due to interaction of the mean airflow and small disturbances of the liquid-air interface, normal and tangential stress perturbations are produced at the liquid surface. It is shown that small wave-like disturbances become unstable when the joint influence of the component of normal stress in phase with the wave elevation and the component of tangential stress in phase with the wave slope is sufficient to overcome the 'stiffness' of the liquid surface due to gravity and surface tension. It is found that the destabilising role of the tangential stress component is dominant for very thin films, and that instability may occur whatever the velocity of the air stream, provided the film is made sufficiently thin.Craik made a visit to the University of California's Cecil H and Ida M Green Institute of Geophysics and Planetary Physics at La Jolla, California. He worked with several people at the Institute, in particular with John Miles, the Professor of Applied Mechanics and Geophysics. Three of the four papers Craik published in 1968 related to his research to La Jolla. The fourth paper is a joint paper with Frank Smith, Craik's first Ph.D. student. We list these four papers and give Craik's Acknowledgements in each in each of them.

1.

*A note on the static stability of an elastico-viscous fluid*(1968). Acknowledgements:-

I am grateful to Dr T Brooke Benjamin for some helpful comments. This work was done during a visit to the University of California, Institute of Geophysics and Planetary Physics, La Jolla. This visit was supported by the National Science Foundation, by the Office of Naval Research and by a travel grant from the Sir James Caird Trust.2.

*Resonant gravity-wave interactions in a shear flow*(1968). Acknowledgements:-

I am grateful to Dr R E Kelly, Dr R E Davis, Professor J W Miles and Dr H Huppert, with whom I had numerous helpful discussions. This work was performed during a visit to the University of California, Institute of Geophysics and Planetary Physics, La Jolla, California. The visit was supported by the National Science Foundation, by the Office of Naval Research, and by a travel grant from the Sir James Caird Trust.3.

*Wind-generated waves in contaminated liquid films*(1968). Acknowledgements:-

I am grateful to Dr T Brooke Benjamin for helpful discussions throughout the course of this work, and to Prof J W Miles and Mr F I P Smith for comments on an earlier draft of this paper. The manuscript was completed during a visit to the University of California, Institute of Geophysics and Planetary Physics, La Jolla, California. This visit was supported by the National Science Foundation, by the Office of Naval Research, and by a travel grant from the Sir James Caird Trust.4. (with Frank I P Smith)

*The stability of free-surface flows with viscosity stratification*(1968). Acknowledgements:-

Part of this work was performed while one of us (Frank Smith) was the recipient of an S.R.C. research studentship. The computations were carried out on the IBM 1620 computer of the University of St Andrews.It is worth quoting the comments Craik made about the start of his career when he retired in September 2003 [9]:-

I intended staying [in St Andrews] for only a few years; but have remained for forty! ... There was no electronic computer of any kind in St Andrews; nor were there any Xerox copiers. Almost all letters, teaching material and research papers were written by hand and typed by a departmental secretary. Though the computer has revolutionised how mathematics is done, there have been many other advances too.Craik continued to publish high quality papers on wave motion and hydrodynamic stability. In 1985 he published the book

*Wave Interactions and Fluid Flows*which incorporated much of his earlier research. For further information about this book including extracts from reviews, see THIS LINK.

Beginning in the 1980s Alex Craik, George Phillips and myself [EFR] began teaching an undergraduate module on the History of Mathematics. The first time we gave the 24-lecture course, we gave 8 lectures each and, in addition to giving our own lectures, we attended each other's lectures. Perhaps the 'MacTutor History of Mathematics Archive' would never have existed if Alex Craik had not been so helpful and encouraging to me at this time. He began publishing papers on the history of mathematics in the 1990s beginning with

*John West in Scotland and Jamaica*(1998),

*Calculus and analysis in early 19th century Britain: the work of William Wallace*(1999) and

*Geometry versus analysis in early 19th century Scotland: William Wallace, John Leslie and Thomas Carlyle*(2000). His publication list contains over 30 high quality papers on the history of mathematics particularly studying Scottish mathematicians of the eighteenth and nineteenth centuries. Of course being an expert on fluid mechanics, it was natural that he would also publish on the history of this area with papers such as:

*G G Stokes and his precursors on water wave theory*(2003),

*The origins of water wave theory*(2004),

*Thomas Young on fluid mechanics*(2010) and

*Lord Kelvin on fluid mechanics*(2012).

In [3] Peter Cameron writes about Craik's:-

... paper in the 'American Mathematical Monthly' ... entitled "Prehistory of Faà di Bruno's formula". This formula gives the $n$th derivative of a composite function $f(g(x))$, in an analogous way to Leibniz's formula for the $n$th derivative of a product. It is particularly relevant to discrete mathematics, for two reasons: first, it applies to general formal power series over commutative rings with identity, no issues of convergence need to be considered; and second, the coefficients that arise are slightly disguised Stirling numbers (much as Leibniz's formula involves binomial coefficients). Francesco Faà di Bruno (1825-1888) is perhaps the only mathematician to be also a Roman Catholic saint. He was a student of Cauchy and friend of Hermite. He returned to Turin and devoted himself to work among the poor, for which he was canonised in 1988. In his paper, Alex Craik describes several authors who had anticipated the formula to varying extents, and awards the palm of discovery to Arbogast in 1800. I recommend the paper to you.Craik's book on the history of mathematics is not specifically on either of the two areas we have just mentioned. It is

*Mr Hopkins' Men: Cambridge Reform and British Mathematics in the Nineteenth Century*(2008). For more information about this book including extracts from the preface and from reviews, see THIS LINK.

In 1997 Elizabeth Craik was appointed as Professor of Classics at Kyoto University, Japan. She was the first woman, indeed, the first westerner, to be appointed a full professor in the Faculty of Letters at Kyoto. Alex Craik spent periods in Japan where he made many friends among the mathematicians, particularly the fluid dynamicist Hisashi Okamoto, and became interested in the history of Japanese mathematics. He wrote several papers with Hisashi Okamoto including

*A three-dimensional autonomous system with unbounded 'bending' solutions*(2002) and

*A four-leaf chaotic attractor of a three-dimensional dynamical*system (2015).

He reviewed the book

*Sacred Mathematics: Japanese Temple Geometry*by Fukagawa Hidetoshi and Tony Rothman for the London Mathematical Society. At the end of his very positive review, Craik make the following comment, clearly based on his experience in Japan:-

In his Foreword, Freeman Dyson comments on the scant recognition given in Japan to Fukagawa, and the lack of interest among Japanese academics, that first drove him to publish his work in English with help from Dan Pedoe. But, in more recent years, there has been a resurgence of interest in traditional Japanese mathematics. Many Japanese mathematicians are now knowledgeable about, and proud of, their distinctive heritage. ... Is it not now the British, rather than the Japanese, who neglect their cultural heritage?May I [EFR] add the personal comment that after one of his trips to Japan, Alex told me how he loved watching sumo wrestling when he was in Japan.

Craik died at his home in St Andrews after a short illness, leukamia having been diagnosed in July 2019. Sally Mapstone, Principal of the University of St Andrews, wrote in [8]:-

Alex was respected by staff and students as a fine lecturer and a thoughtful, supportive and very modest colleague. In 1983 he was elected Fellow of the Royal Society of Edinburgh, in 1987 he was awarded a Personal Chair at St Andrews and from 1993 to 1995 he was President of the Edinburgh Mathematical Society.Craik's interests outside his mathematics and his family (including his four grandchildren Gregor, Stuart, Heather and Jamie) were music (and he played classical guitar to a high standard), travelling (especially in Greece) and enjoyment of his large house and garden.

May I [EFR] add a final comment saying how much I appreciated having Alex as a teacher, and as a colleague and friend for over 50 years. After we both retired Alex would come to the Mathematical Institute, take the opportunity to talk to me about his latest research, often giving me a copy of one of his newly published papers, and would ask with interest about my latest MacTutor project. He was a great support and a very dear friend whom I miss greatly.

I [JOC] taught with Alex and shared some courses with him. Although he was an applied mathematician and I was pure, his approach to the areas we lectured on (complex analysis and differential equations) agreed very much with mine. I was able to write software to help him display the three dimensional solutions of differential equations and we cooperated on several topics in the history of mathematics. I valued him greatly as a colleague and will miss him very much.

### References (show)

- T R Akylas, Review: Wave Interactions and Fluid Flows, by Alex D D Craik,
*Science, New Series***235**(4795) (1987), 1522-1523. - D J Benney, Review: Wave Interactions and Fluid Flows, by Alex D D Craik,
*SIAM Review***29**(4) (1987), 648. - P Cameron, Alex Craik,
*Peter Cameron's Blog*(3 December 2019).

https://cameroncounts.wordpress.com/2019/12/03/alex-craik/ - G T Csanady, Review: Wave Interactions and Fluid Flows, by Alex D D Craik,
*Limnology and Oceanography***32**(5) (1987), 1177. - I Falconer, Professor Alexander (Alex) D. D. Craik: 1938-2019,
*British Journal for the History of Mathematics***35**(2) (2020), 178-179. - I Grattan-Guinness, Review: Mr Hopkins' Men: Cambridge Reform and British Mathematics in the Nineteenth Century, by Alex D D Craik,
*The Mathematical Gazette***94**(530) (2010), 358-359. - V Krishan, Review: Wave Interactions and Fluid Flows, by Alex D D Craik,
*Bulletin of the Astronomical Society of India***15**(2) (1987), 166-167. - S Mapstone, Professor Emeritus Alexander Craik, Email to University Staff (27 November 2019).
- Maths Professor bids farewell after 40 years, University of St Andrews (30 September 2003).

https://news.st-andrews.ac.uk/archive/maths-professor-bids-farewell-after-40-years/ - K H Parshall, Review: Mr Hopkins' Men: Cambridge Reform and British Mathematics in the Nineteenth Century, by Alex D D Craik,
*Isis***100**(3) (2009), 669-670. - St Andrews University professor of mathematics Alexander Craik,
*The Courier & Advertiser*(29 November 2019). - P D Straffin, Review: Mr Hopkins' Men: Cambridge Reform and British Mathematics in the Nineteenth Century, by Alex D D Craik,
*The American Mathematical Monthly***116**(3) (2009), 284-288.

### Additional Resources (show)

Other pages about Alex Craik:

Other websites about Alex Craik:

### Honours (show)

Honours awarded to Alex Craik

### Cross-references (show)

Last Update November 2020