Mathematics Today
Mathematics Today is the membership publication of the Institute of Mathematics and its Applications.
Issued six times a year, this general interest mathematics publication provides articles, reports, reviews and news for mathematicians.
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Current features and articles
Editorial 
During the early years of the eighteenth century the accurate determination of longitude at sea was a very pressing concern, particularly acute for a maritime nation like Great Britain. A number of shipwrecks and the associated loss of life were directly attributable to mistakes in the computation of longitude and aside from highprofile major disasters the difficulties in navigation caused by the inability to accurately determine one’s position led to longer voyages which in turn led to greater risk of scurvy and other illnesses which afflicted the sailors of the age. The impact on trade was also significant and many fortunes were ruined for want of a solution to this basic problem of navigation. 
The IMA’s 50th Anniversary Celebration 
The IMA’s 50th Anniversary Celebration at the Royal Society on 14 May was a great success. The IMA President, Professor Dame Celia Hoyles DBE welcomed The Princess Royal and expressed warm thanks to her for agreeing to be our Patron in our anniversary year and for graciously agreeing to come to our event. 
50 Years of Mathematics in Industry 
How does maths affect the lives of ordinary people? How does it benefit us all, improving our quality of life? And how best can we bring mathematicians and business people together, so that maths can continue to contribute to our economy in the UK? 
Mathematics for the Billion 
My title pays homage to Lancelot Hogben’s Mathematics for the Million, a book that explained basic mathematics and practical uses in simple terms for a general audience. I think that today we have to be more ambitious. 
Two Trains and a Crazy Bird 
The examples of leastsquares applications given in Parts I and II have been used by the author when invited to give lectures about the importance of mathematics to nonspecialists, including teenagers still at school with different abilities and interests. The mathematics of the communications example is arguably too technical for such audiences, but the explanation of how we form different speech sounds and then model them for use in mobile telephones ensures that they at least appreciate the value of the mathematics. The underlying principles of the navigation examples are perhaps easier to understand, as is the idea of making a guess and then iterating to converge to a solution. 
Full contents page of the August 2014 printed issue to receive Mathematics Today subscribe or join the IMA! 

Content from the June 2014 issue 
Editorial 
At some point in my school education (in the late 1970s if my memory serves) I was introduced to logarithms as a means of facilitating calculations. I was taught how to use log tables to multiply, divide and take roots at a time when calculators were just becoming commonplace and I doubt many children younger than me were exposed to these techniques. What those who have grown up in the calculator age perhaps don’t realise is that logarithms were the principal means of calculating with decimals for over 300 years. Log tables and their associated techniques arrived from nowhere, were an instant sensation, dominated scientific calculation for centuries, and disappeared just as quickly as they had arisen. It seems appropriate to reflect on this in 2014 as the first set of such tables were published in 1614 in Napier’s Mirifici logarithmorum canonis descriptio (‘A Description of the Wonderful Principle of Logarithms’) which contained tables and a brief explanation of how they were to be used; the theory behind the construction of the tables appeared posthumously in 1619. 
Why Does Mathematics Matter in the Digital Arts? 
Celia Hoyles, Malcolm Sabin and Jon Macey presented Why Does Mathematics Matter? The Case of the Digital Arts at the British Congress of Mathematics Education in April 2014. 
The Festival of Mathematics and its Applications 
A major activity to celebrate the IMA’s 50th anniversary will be the Festival of Mathematics and its Applications, to be hosted in the Alan Turing Building, School of Mathematics at the University of Manchester. The event will bring together all elements of our broad community: academic mathematicians; mathematicians working in the corporate, industrial and business sectors; undergraduate and postgraduate students; teachers and lecturers; members of the general public with an interest in mathematics; school and college students and their families. 
How Microinsurance can Help to Reduce Poverty 
According to the World Bank around 2.2 billion people, or almost 31% of the global population, live on incomes less than $1.25 a day, with 3.6 billion living on less than $2 per day [1]. People living on such low incomes usually have no access to formal financial services. In particular, they often have little access to formal risk management solutions, including traditional insurance products. As a result, the world's poor are often the most exposed to the impact of many highrisk events that can cause financial difficulties in their lives. This article gives an introduction to one possible approach to mitigating the impact of highrisk events on lowincome groups: microinsurance. 
Fifty Visions of Mathematics Solution 
The IMA’s book Fifty Visions of Mathematics was launched at the 50th anniversary celebration at the Royal Society on 14 May. The book contains 50 Images – Visions – of Mathematics and 50 articles on many topics, including sport, sports gambling, CAT scans, viruses, space, biographies, to name a few. 
Full contents page of the June 2014 printed issue to receive Mathematics Today subscribe or join the IMA! 

Content from the April 2014 issue 
Editorial 
As many readers will know, EPSRC commissioned international reviews of UK mathematics research (IRMs) which were published in 2004 and 2010. The reports, available on the EPSRC website, make interesting reading. A considerable part of these two reports addresses the question of the strength or otherwise of the UK mathematics research community at the time of writing and how this compares with the best worldwide. Both the reports, and the review processes that led to them, were valuable but it is arguable that the 2010 report has had limited impact on the research landscape. In contrast, the 2004 report led, more or less directly, to a significant investment in a number of areas that had been highlighted by the review. Having said that, neither report is as bold in scope, as thought provoking, as challenging or as important as the recently published The Mathematical Sciences in 2025. 
The Festival of Mathematics and its Applications 
A major activity to celebrate the IMA’s 50th anniversary will be the Festival of Mathematics and its Applications, to be hosted in the Alan Turing Building, School of Mathematics at the University of Manchester. The event will bring together all elements of our broad community: academic mathematicians; mathematicians working in the corporate, industrial and business sectors; undergraduate and postgraduate students; teachers and lecturers; members of the general public with an interest in mathematics; school and college students and their families. 
Maths Joins the RollsRoyce Science Prize 
The RollsRoyce Science Prize was first implemented as an annual awards programme in 2004 as an incentive for teachers to enhance science teaching in their schools and colleges. There is a total of £120,000 to be won by schools each year. In 2014 RollsRoyce, in partnership with the IMA and the NCETM, has extended the Prize to include mathematics teaching in addition to science. The Prize recognises and rewards excellence in Science and Mathematics teaching for all children, from those with special education needs to high ability pupils, and covers Primary, Secondary and post16 age ranges. 
Beautiful Music 
Beautiful music is not easy to define. Some would claim that it is impossible to define because the terms `beautiful' and to some extent `music' are entirely subjective  the aural equivalent of `in the eye of the beholder' (presumably `in the ear of the listener', although the phrase doesn't have quite such a ring to it). Such people might contend that anyone who finds the sound of rushhour traffic more beautiful musically than, say, Mozart's Elvira Madigan Concerto is taking a perfectly reasonable position. 
Communication, Navigation and Mathematics: Part I 
This article is based on a public lecture given by the author at the University of Reading on 13 November 1997 to celebrate his appointment as a Visiting Industrial Professor. The material has remained in his files and unpublished until now. The primary aim of the lecture was to demonstrate that the basic mathematics which underpins one technology (e.g. digital speech communications) can often be applied to a quite different technology (e.g. navigation systems). This article follows the basic theme of the lecture, but includes more of the mathematics. This is the first part of the article, Speech Communications, the second part on Navigation will appear in the next issue of Mathematics Today. 
The Dome that Touches the Heavens 
This year is the 50th year of the IMA and my 50th year too. Birthdays are times for celebration and reflection – to identify what really inspires us. Appropriately then, very soon, on my birthday, I will give a talk to a group of architects in Paris about when architecture inspired new mathematics and vice versa. One example is the invention of the catenary curve, which is popularly attributed to Sir Christopher Wren (1632–1723) and his design of St Paul’s Cathedral (built 1675–1720). 
Full contents page of the April 2014 printed issue to receive Mathematics Today subscribe or join the IMA! 

Content from the February 2014 issue 
Editorial 
What the IMA is for can readily be seen from its website, where the first paragraph is the following: ‘The Institute of Mathematics and its Applications (IMA) is the UK’s learned and professional society for mathematics and its applications. The IMA exists to support the advancement of mathematical knowledge and its applications and to promote and enhance mathematical culture in the United Kingdom and elsewhere, for the public good.’ 
A Message from HRH The Princess Royal, the IMA Patron for 2014 
I am delighted to be the Patron of the Institute of Mathematics and its Applications (IMA) in its 50th Anniversary year. This is not the first occasion in which my family has been involved with the Institute: His Royal Highness The Duke of Edinburgh was President from 1976 to 1977, and the Institute was incorporated by Royal Charter in 1990. 
The Next 50 Years 
In trying to write a vision for where (applied) mathematics, (applied) mathematicians and the IMA will be in the next 50 years, I am ever mindful of John von Neumann’s attempt to do this for the subject of computing, in which he said that any statement about the future was bound to look pretty silly in just a few years time. Given the exponential rate at which mathematics and its applications are developing, and the incredible creativity of mathematicians in thinking up utterly new ideas, I think I will be lucky if I even get a few years grace. But having said this, here goes. 
Interview with Celia Hoyles, the New IMA President 
Professor Dame Celia Hoyles, CMath CMathTeach FIMA is a Professor of Mathematics Education at the London Knowledge Lab, Institute of Education, University of London. She took over as President of the IMA at the beginning of the year. Professor Hoyles interests include mathematics policy and research in students’ conceptions of proof, mathematical skills in modern workplaces, computational environments for learning and sharing mathematics and systemic change in teaching mathematics. She was awarded the International Commission of Mathematics Instruction (ICMI) Hans Freudenthal medal in 2004 and the Royal Society Kavli Education Medal 2011. I interviewed Celia Hoyles in May 2013. 
Sherlock Holmes and the ThreeBody Problem 
One of the joys of reading fiction is speculating on how the world created by the author can relate to the real world. No series has been more successful in this respect than Conan Doyle’s Sherlock Holmes stories, which have spawned a considerable literature of interpretation based on the pretence that Sherlock Holmes was a real person, perhaps for the following reasons: 
Full contents page of the February 2014 printed issue to receive Mathematics Today subscribe or join the IMA! 

Content from the December 2013 issue 
Editorial 
There can be few readers who have failed to notice that the issue of Big Data is a hot topic. Datasets are becoming so large that standard database software tools are entirely inadequate to capture, store, manage and analyse their content. Projects such as the Square Kilometre Array (which will be the world’s largest and most sensitive radio telescope) and the 100,000 genome project (part of the UK’s attempt to lead the world in unlocking the power of DNA data) are just two examples of the type of project that will ensure this becomes an evermore important issue. The government has identified eight technologies where it feels that with the right investment the UK can lead the world, and first in the list in David Willetts’ pamphlet published by Policy Exchange [1] is ‘The Big Data Revolution and EnergyEfficient Computing’. 
The Maths and Computing Magic Show 
The British Science Festival in Newcastle this year saw Matt Parker, with assistance from Peter McOwan, again perform their popular Maths and Computing Magic Show. The show has proved something of a hit with festival goers over the past few years combining a magic show, and a glimpse behind the curtain to see the maths and computing ideas that power the tricks. Card magic and conjuring tricks have proved popular and effective methods to open the door to maths. They have been used in engaging students with mathematical concepts for many years, and the current popularity of UK television shows focusing on street magic and high profile celebrity magicians such as David Blaine, Dynamo and Derren Brown has given this particular approach a new and enhanced awareness with the public. In this article we explore the history of mathematical magic, the fascinating stories of some of the main practitioners of the art and some useful tips for those who wish to try it for themselves. 
Mathematical Techniques behind the Gas Turbine Engine 
Air travel is now common and significant advances have been made in the way aircraft are designed and operated since their first introduction. They are now much quieter and more efficient than their earlier counterparts and perform this feat whilst carrying greater payloads. The use of modern materials and manufacturing techniques play a significant part in this achievement; as do the methods of design, test, validation and certification. In this article focus is given to the gas turbine engine, which provides the thrust for the aircraft, and a brief overview of some of the mathematical techniques that underpin the monitoring of the engine through its operational life. 
Presidential Address: Complex Systems in Science and Society 
I had the pleasure to give the IMA’s Presidential Address at the Royal Society and five IMA branches around the country in 2012–13. This is a written version. The core message is that mathematics has a vital role to play in understanding, predicting, controlling and designing the complex systems that are around us or of which we are part. I will give a mathematical formulation of the concept of ‘emergence’, which focuses on the key issue of statistical behaviour of complex systems. I will illustrate how ‘tipping points’ from one statistical regime to another can arise, how ‘nudges’ may push the system into a different regime or be used to prevent a system tipping, and comment on the role that observation may play in management of complex systems. 

Full contents page of the December 2013 printed issue to receive Mathematics Today subscribe or join the IMA! 

Content from the October 2013 issue
Editorial  
Can every even number greater than 2 be written as the sum of two primes? The affirmative answer to this question is known as Goldbach’s conjecture since it was suggested by the Prussian mathematician Christian Goldbach in correspondence with Euler in 1742. (Goldbach’s formulation of the conjecture was slightly different because he considered 1 to be a prime number, a convention that was common throughout the 18th and 19th centuries.) This is one of the most famous unsolved problems in mathematics, its acclaim being due in large part to two important characteristics – the problem is easy to state and understand, and it has remained unsolved for a very long time. Incidentally, it is also the subject of a 1992 novel, Uncle Petros and Goldbach’s Conjecture, by Apostolos Doxiadis, which first appeared in English in 2000 along with an offer from the publishers to award a prize of one million dollars to anyone who could prove the conjecture within two years. 

An Interview with Greg Ryder 

Greg Ryder AMIMA was one of two people at the University of Dundee to win this year’s IMA prize, because of his excellent grades in his honours degree in mathematics. He is now an Associate Member of the Institute. In July, Richard Crawford CMath MIMA caught up with Greg to ask him a few questions for Mathematics Today. What do you hope to do with your maths degree? In August, I’m away to start as a trainee chartered accountant. But I definitely haven’t ruled out the possibility of returning to university to study mathematics further. For example, doing a masters or even a PhD. Before starting university, I really wasn’t sure what I wanted to do to be honest, but I knew studying maths would give me a lot of options. 



Of Bombs and Boats and Mice and Men 

I will begin with a true story which has become semimythical. Shortly after World War Two, the US Atomic Energy Commission released a film of the 1945 Trinity atomic bomb test. The energy yield remained secret, having been estimated only with some difficulty. So the Americans were most surprised when the British fluid dynamicist Geoffrey Taylor published, in 1950, an accurate estimate merely by studying the AEC’s pictures [1,2]. Embellishments of the tale have the Americans wondering how on Earth he did it, with the CIA visiting his house in the middle of the night to search through his papers.


Full contents page of the October 2013 printed issue 


Content from the August 2013 issue
Editorial 
The problems that I tackled as a postgraduate student, and the techniques that I employed to solve them, were ones that made considerable use of special functions. I was thus exposed, at an early age, to one of the great mathematical works of the 20th century: Handbook of Mathematical Functions, edited by Milton Abramowitz and Irene A. Stegun, published by the National Bureau of Standards in Washington in 1964 and running to over 1000 pages. The preface to the ninth printing in 1970 notes that sales were then rapidly approaching the 150,000 mark. 

Events are moving ahead rapidly as we plan ahead for the celebrations next year for the IMA’s 50th Birthday. This is a year which will involve all IMA members and we very much hope that you can all make it a year to remember. There are lots of ways to get involved, these include sponsoring the events, sending in photos or other memorabilia, designing a maths trail or simply turning up to the many events being organised. These events will be going on all through the year in the different IMA regions, but we would like to highlight some of the major ones. 
Education Grant Report: Maths and Motion 
The theme for this year’s Maths week was ‘Maths and Motion,’ where students got to experience a wide range of activities putting mathematics in the reallife context of things that move. This was our busiest Maths week to date, with over 700 students being directly involved in either external trips or working with visitors in school. The IMA awarded an Education Grant to cover the cost of transport for students from Framwellgate School to Shildon Railway Museum and Newcastle University. 
Talking about Shapes 
This article is based on the IMA Summer Lecture I gave on 26 June 2013. It explores how people have communicated shape in the past and how they do it now. It closes by suggesting that new methods ought to be invented to take advantage of the very large memories now typically available. Having worked in the aircraft industry, my main focus is on smooth shapes, like aircraft, ships and cars. 

Content from the June 2013 issue
Editorial 
Leadership is a tricky concept to pin down. I sit on many interview panels for senior positions and questions around leadership are invariably on the agenda. People respond in different ways. Some have a clear understanding of what leadership is all about (which may or may not correspond with mine). Others recognise its importance but aren’t particularly good at articulating what it means. A small percentage pay lip service to the concept – they expect to be asked but don’t really have a clear grasp of why it is relevant to them or to the role they are seeking to fill. But I don’t think any interviewee has ever told me that they don’t think leadership is important. 

Nearly 50 scientists, industry experts, academics and students had their first glimpse of the world leading Orion laser facility when the delegation gathered at the IMA Employers’ Forum, hosted by AWE Aldermaston on 4 March 2013. 

Mathematics 2013, the continuation of the series of annual one day conferences on mathematics and its applications took place on 14 March. It was again held at Mary Ward House in Tavistock Place, London. 

Mathematical models are useful weapons in the crimefighting arsenal. With the development of cheaper and more powerful computers, mathematical modelling of systems representing some aspect of crime or criminal behaviour and the analysis of the resulting numerical solutions is becoming more popular. Models may be used to guide decisionmaking, develop policies or to evaluate specific strategies aimed at reducing crime. This review provides an introduction to some relatively recent mathematical models of crime. 

Content from the April 2013 issue
Editorial 
I hope that some of you had the chance to see David Spiegelhalter’s entertaining programme Tails You Win: the science of chance that was broadcast originally in October 2012 on that beacon of TV excellence which is BBC4. Spiegelhalter is the Winton Professor for the Public Understanding of Risk at the University of Cambridge and, as befits anyone with that title in the modern age, he maintains an excellent blog (http://understandinguncertainty.org). 

A recent (2012) independent report by consulting firm Deloitte, commissioned by the UK government has shown that: 10 per cent of UK jobs and 16 per cent (£208 billion) of Gross Value Added to the UK economy stem from mathematical sciences research. 

The interaction between Earth sciences and mathematics has been for a long time a very stimulating one for both disciplines. Indeed, on the one hand, the phenomenology of the fluid and solid Earth and of the Earth ecological systems has provided the basic inspiration leading to the birth of entire mathematical areas such as those related to chaos, fractals, catastrophe theory (see an example of a climate tipping point in Figure 1), extreme events theory, and multiscale processes. On the other hand, mathematical tools developed in these areas, as well as in fields such as ordinary and partial differential equations, dynamical systems, signal processing, stochastic calculus, statistical mechanics, taken together with the understanding of the underlying physical, chemical, and biological processes, have immensely increased the predictive and descriptive power of Earth sciences. Since World War II, scientific calculus has been especially relevant for bridging mathematics and Earth sciences and providing tools of practical applicability for an everincreasing range of applications of great societal importance. 

Living as we do in the Rossby wave surf zone (as Professor Michael McIntyre has memorably called it) the weather of the UK is constantly a source of news and interest. As I write, warm Atlantic air is in a battle with cold polar air to decide who gets snow dumped on them and who does not! But the climate is so much more than the fluid dynamics of the atmosphere and ocean  it is affected by longterm interactions and feedback between all sorts of chemical species and factors, from carbon cycle and anthropogenic greenhouse gases to solar variability, evolution and ecology. Mathematical problems range from predicting the behaviour of coupled nonlinear systems to the problems of understanding remote sensing data. As the mother of all complex systems it is very topical as we are now several months into the year of ‘Mathematics for Planet Earth 2013’ – readers of Mathematics Today will already know from February’s MPE special issue. 

Content from the February 2013 issue
Mathematics for Planet Earth Editorial 

The year 2013 has been dedicated as a special year for the Mathematics of Planet Earth (http://mpe2013.org/), by a worldwide network of mathematical research institutes, 



We live in challenging and anxious times. Human society is ever more interconnected on a global scale and in many areas, such as health, quality of life and prosperity, the human condition continues to improve for most people. However, we are also acutely aware that there are less comfortable trends such as an unsustainable rate of population growth, increases in inequality, deterioration of the environment, a persistent billion or so people who remain in extreme poverty, increase in natural disasters, increasing scarcity of natural resources, and unprecedented loss of species and habitats. 



Ecological systems at many scales can exhibit multiple stable states and the possibility of regime shifts. These shifts are relatively well understood for a variety of specific systems which are amenable to description by simple mathematical models. Using the insights from these simple models as a bridge to understanding regime shifts in more complex systems raises substantial mathematical and ecological challenges to determine approaches which should help guide both management and adaptation in the face of global change. 



Vaccination is one of the major medical advances of the 20th century. Although vaccination was scientifically investigated by Edward Jenner in the late 18th century, it was not until the biochemical advances of the 20th century that cheap, safe vaccines could be produced in large quantities. Vaccination is a powerful tool in the publichealth control arsenal, and allows for the mass prevention of infection rather than treating the symptoms of infection. Vaccination saves thousands of lives each year in the UK alone. 


Content from the December 2012 issue
Editorial 

Pretty much at the same time as Hilary Mantel was awarded the 2012 Man Booker prize for Bring up the Bodies, I finished reading Wolf Hall, the winner of the same award, by the same author, in 2009. These two books form part of a trilogy telling the story of the rise and fall of Thomas Cromwell, seen through his own eyes. Wolf Hall charts his journey from blacksmith’s son to king’s Chief Minister, culminating in the succession to the throne of Anne Boleyn and the separation of the Church of England from the Roman Catholic Church.  


The first IMA Employers’ Forum, hosted by EDF Energy, was held on 18 September 2012. The subject of the meeting was Employability of Mathematics Graduates, and the aim of the meeting was to bring together stakeholders, including representatives from industry and academia, to facilitate an exchange of views and the sharing of good practice. 

IMA Supports Practising Teachers to ICME12 