Philip J. Aston · Anthony J. Mulholland Katherine M.M. Tant Editors UK Success Stories in Industrial Mathematics UK Success Stories in Industrial Mathematics Philip J. Aston • Anthony J. Mulholland Katherine M.M. Tant Editors UK Success Stories in Industrial Mathematics 123 Editors Philip J. Aston Katherine M.M. Tant Department of Mathematics Department of Mathematics and Statistics University of Surrey University of Strathclyde Guildford Glasgow UK UK Anthony J. Mulholland Department of Mathematics and Statistics University of Strathclyde Glasgow UK ISBN 978-3-319-25452-4 ISBN 978-3-319-25454-8 (eBook) DOI 10.1007/978-3-319-25454-8 Library of Congress Control Number: 2015954600 Springer Cham Heidelberg New York Dordrecht London © Springer International Publishing Switzerland 2016 This work is subject to copyright. 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Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer International Publishing AG Switzerland is part of Springer Science+Business Media (www.springer.com) Foreword An Apology for a Mathematician Let’s face it, a Foreword is included in a book mostly for decorative purposes! It offers pleasant statements about the authors and the book’s contents in the safe knowledge that only the authors themselves, and occasionally perhaps the authors’ relatives, will read it. After all, why read the Foreword when you want to get on with the real thing? I hope that my title will tempt the odd reader or two to dally a while before turning the page on their i-readers. My aim is to make a couple of, I believe, important points that can be extrapolated from the contents herein, and from recent activity within the UK Mathematical Sciences community more broadly. In a nutshell, I believe that we have entered a golden age for mathematics1 and mathematicians to engage with, and have impact on, industry, commerce, business, government, policy makers, other sciences and the broader reaches of academe, the general public and school students. What name we give to this activity is prob- lematic: ‘knowledge transfer’ or ‘exchange’, ‘industrial’ or ‘applicable’ or ‘applied mathematics’, ‘interdisciplinary research’, ‘mathematics communication’, …,so please don’t criticise any shorthand terminology that I resort to below. The contents of this book show far more effectively than I can, the power and utility of math- ematical research within the UK, the diversity both in the ‘flavours’ of mathematics employed and the areas or sectors of application, and the impact that this work is having. It is a unique snapshot of the collective efforts of the mathematical sciences community in engaging with communities outside academe, made possible by the 1I use mathematics henceforth to refer to the whole subject including pure and applied mathe- matics, mathematical physics, probability and statistics, operational research and the more math- ematical parts of computer science. v vi Foreword Impact Case Studies submitted to the 2014 Research Excellence Framework2 (REF). This book contains a sample cross-section of 38 articles derived from approximately 250 such studies submitted to the Mathematical Sciences Unit of Assessment and so, whilst these are exemplary, they cannot convey the wide breadth of impact across the full range of application areas. I was fortunate to have served on the panel that reviewed these case studies and, although I have spent a large part of my recent career interacting with industry, I was genuinely surprised at the diversity of the impacts we examined and their ‘reach and significance’. Now, everyone knows that mathematics is important: school students, members of the general public, the Engineering and Physical Sciences Research Council (EPSRC) and other funders, even politicians (who often preface it with “of course I was no good at maths in school, but ….”); however, they may not easily be able to say why it is important. From the outside maths is seen as deep, maths is seen as hard, maths is seen as elegant, and some may actually suggest that maths is useful without knowing why. That was acceptable in the past but times have changed. Government, through its research councils and other bodies (Innovate UK, Knowledge Transfer Network etc.) requires us to justify our existence and prove our worth, so we now need to find ways to measure the value and utility of our discipline. The quest for quantifying the intrinsic quality of mathematics, and the value of its researches outwith the subject, is perhaps more advanced here in the UK than in any other country in the world; the stakes are also much higher. At the same time it does seem that the community is genuinely embracing the need for connecting our mathematical researches with other academics and with the users of mathematics; I expand on this below. The results have been tremendously positive: in REF over 80 % of Impact was recognised as ‘internationally excellent’ or ‘world leading’; and EPSRC commissioned Deloitte3 to undertake a study to assess the economic benefits of mathematical science research in the UK. This refers to the “high-end mathematics research, as carried out by academic institutions, research centres, businesses, individuals and Government, that adds to the store of accumulated mathematical knowledge”. Deloitte’s results were that the quantified contribution of mathematical science research to the UK economy in 2010 was estimated to be approximately 2.8 million in employment terms (around 10 % of all jobs in the UK) and £208 billion in terms of gross value added (GVA) contribution (around 16 % of total UK GVA). But is this enough? Several years ago the European Science Foundation (ESF) initiated a Forward Look4 on Mathematics and Industry that was coordinated by the Applied Mathematics Committee of the European Mathematical Society 2Details and results of the UK’s REF2014 are available at http://www.ref.ac.uk/. 3Deloitte Report is available at http://www.ima.org.uk/viewItem.cfm-cit_id=384406.html. 4ESF Forward Look Report is available at http://www.esf.org/index.php?id=6264. Foreword vii (EMS). This Forward Look aimed to compare the state of the art at the mathe- matics–industry interface and the needs for the future development of science and technology in Europe. One of the key factors in this respect was recognition that mathematics is a driving factor for innovation, but they found the landscape rather ‘patchy’. Only via mathematics, they argued, can the complex processes and products in current key technologies and short innovation cycles be managed in an efficient, robust and sustainable way. Further, in 2013 David Willetts, the then Minister for Universities and Science, gave a speech introducing the Eight Great Technologies. In it he asked for a refocusing of the science effort away from primarily blue skies research to a more balanced economy in which a greater percentage of scientific research is aimed at tackling topics such as big data, synthetic biology and advanced materials. EPSRC has adopted this principle and now expects that all subjects within its remit embrace the “Challenge Themes”. Fields such as engineering find it far easier than mathe- matics to engage in an interdisciplinary fashion on topics such as “Manufacturing the Future” or “Healthcare Technologies”, but the situation is changing and more and more mathematicians are learning to work in a multidisciplinary environment and to speak several scientific languages. But this presents a problem, which we in the international mathematics com- munity have wrestled with for a long time. In its crudest form, the question is: should mathematicians be concerned with abstraction or application? G.H. Hardy certainly had an opinion on this matter; in his oft-cited essay, ‘A Mathematician’s Apology’ (1940), he states “It is not possible to justify the life of any genuine professional mathematician on the ground of the ‘utility’ of his work.” He goes further: “No one foresaw the applications of matrices and groups and other purely mathematical theories to modern physics, and it may be that some of the ‘highbrow’ applied mathematics will become ‘useful’ in as unexpected a way; but the evidence so far points to the conclusion that, in one subject as in the other, it is what is commonplace and dull that counts for practical life.” So, his conclusion, which is the one that prevailed over most of the twentieth century, seems to be that areas of mathematics that have the most value are exactly those that are not pursued for their utility. By this metric, I can perhaps be considered as an apology for a mathe- matician! There will, no doubt, be individuals in the community who still hold this opinion, but it appears that their numbers now are dwindling. Instead I am confident that there is a healthier consensus, that abstraction and application can and should coexist, and in fact are just ‘two sides of the same coin’.