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It’s been said that a degree in mathematics opens many doors, but to many this might seem a slight exaggeration. Bernard Silverman, however, is an excellent example of a mathematics graduate who has indeed done it all. Silverman is currently the chief scientific advisor to the Home Office, a statistician, and an Anglican priest. These are just a few examples of his many achievements, starting from the gold medal he won at the 1970 International Mathematics Olympiad—the only person to do so from the western side of the iron curtain—at the beginning of his mathematical career. He went on to read mathematics at university, and eventually obtained a PhD in data analysis in 1977. “I was always interested in maths, but as time went on I became keen on doing it in a way that has applications in different things, and that is what drew me to statistics.” He jokingly adds that he felt he was never good enough to be a pure mathematician. In the course of our conversation with him, he took us on a journey through the diverse areas in which he has applied his statistical approach.

Data analysis

With a PhD in data analysis, we felt that Silverman was the perfect person to ask about how big data has changed the landscape of statistics. At the start of his career, “the towering figure was John Tukey, who wrote a book called Exploratory Data Analysis. At the time of its publication, it was an enormous advance because it had the idea of letting the data tell us the story, instead of fitting it to completely specified parametric models.” These ideas are still present in big data, he says, but “of course the challenge has gone from dealing with just a small set of numbers to enormously large data sets”. Silverman describes some of his work as seeking needles in haystacks or, in other words, “dealing with the problem of understanding when what we see is real, rather than just noise. All of this arises from handling these enormously large data sets: that is something that wasn’t there before.”

During his academic career, Silverman has written several books. His work varies from the theoretical to more practical applications of statistics. His work, described in his book Functional Data Analysis, enabled advances in spatial statistics and image recognition. “In functional data analysis,” he says, “the data is not just numbers but curves and surfaces, and this will continue to be the case in the future, with our data consisting of a lot of pictures or sounds, which we need to make statistical sense of.” Understanding this more complicated statistical situation is something we should look forward to, along with machine learning. Silverman predicts a “closer melding of machine learning and big data. The data will set its own questions as well as answer them.”

Calculator development & the next technological breakthrough

Although Silverman has always been interested in computational statistics, when he began his statistical journey during his master’s at Cambridge, there were no computers as we know them today. This meant that it would take him “weeks to write a simple programme to draw a density curve from some data”. His desire to develop the technology that would overcome this difficulty led him to move into industry, working for Sinclair Radionics on the Sinclair Cambridge Programmable calculator. First released in 1975, it was marketed as an affordable pocket programmable calculator and Silverman proudly recalls that “you could keep 36 programme steps in its memory”. At the other end of the spectrum, he expects the next technological development to be in quantum computing, which “if quantum computers ever get going—which is an ‘if’, we don’t know for sure—would be a complete game changer”. And, on a more immediately practical day-to-day level: “you just turn on your new computer and it recognises you and logs you in. This is again an application of functional data analysis, using your face as the data.”

Climate change and genetics

Silverman’s attitude is to take a statistical approach to many different subjects, especially those of enormous global importance. For example, some of his collaborative work is in climate change with the Smith School of Enterprise and Environment and in human genetics with the Wellcome Trust Centre for Human Genetics. Climate change modelling is different from standard statistical modelling: “it is not done by conducting experiments or taking measurements, because the models are all computer models. Rather, it is a question of making sense of all the different trajectories of temperature that you can possibly get under given scenarios.” In genetics, however, the challenge is different. In genomes and DNA, the idea is to “use data analysis to see what information there is in the very high-dimensional data that is generated”.

Home Office

When people say that “all the evidence points in this direction”, you should be worried.

Silverman leads a team of researchers at the Home Office. The Centre for Applied Science and Technology is a branch of the Home Office that focuses on serving a range of the government’s national interests: anything from crime prevention and community safety to security and identity assurance. Protective security is an example where maths, specifically finite element analysis, plays an important role. Finite element analysis is a method used to simulate complex physical systems: how explosions and earthquakes affect infrastructure, or the effect of wind on skyscrapers, among many other things. Take, for example, a model of an explosion in a building. We first consider the structure of the building as being fixed. The structure can be split up into units, and the blast will move back and forth through these units. When the explosion is triggered, waves propagate outwards, and initially the pressure of the system is very high, but as time goes on the range of pressures decreases.

This work, carried out (some years ago, now) at the Centre for Applied Science and Technology thus involves modelling data, without actually carrying out experiments with physical resources—rather problematic in this example!

It is not surprising that political decisions are not based solely on science, although it plays an important role: ultimately, a politician’s job is not the same as that of a scientist and priorities sometimes differ. However, on issues that really require scientific input and where evidence is needed (for example, when a policy is to be drafted regarding driving under the influence of drugs), it is the role of scientists to determine how to carry out any experiments or surveys that may be required. And, of course, although policies may be based on politics, underneath it all is how they will actually be carried out: this is where science decides what will and will not work.

Silverman emphasises the importance of “making sure that policymakers are aware of evidence and the objective”. Presenting this evidence is very different from presenting a research paper: simplicity is often preferred over detail (although presenting detail in a simple manner is even better!) and information needs to be incredibly clear. “It should empower your audience and make them feel comfortable about understanding it”. After that, though, “what they do is up to them”.

Modern slavery

There are between 10,000 and 13,000 victims of modern slavery in the UK.

Silverman is part of the prime minister’s task force on tackling modern slavery. In particular, he managed to work out a way of using the techniques of multiple systems estimation and generalised mark and recapture to estimate the size of a hidden population: the slaves of today’s society. He explains the basics with a simple example from his paper Modern slavery: an application of multiple systems estimation . Suppose that we want to estimate the number of fish in a pond. You first catch 100 fish, mark them and release them back into the pond. After letting the fish swim around for a bit, you catch another batch of 100 fish and count how many are marked. If, for example, 20 are marked (one fifth of the second batch), the natural estimate for the whole population size would be $100 \div 1/5 = 500$. This is the approach of mark and recapture. Multiple systems estimation extends that idea to situations where there are more than two lists. You can use it to estimate the number of individuals that are not on any list, giving what is known as the dark figure.

By using this approach, Silverman concluded that, for a confidence of 95%, there are between 10,000 and 13,000 victims of modern slavery in the UK. To underline the importance of research in the decision-making process of the Home Office, he adds that “the whole government strategy was built on this analysis. The paper was launched at the same time as the Modern Slavery Act was launched, but we are still trying to understand the scale and nature of this problem.”

Improving the image of maths and science

As a man who has always been interested in science, Silverman believes that “people are very odd about it. On the one hand, everybody wants all the latest gadgets; but on the other, they are suspicious about scientists and don’t like them very much.” As someone who has had first-hand experience of science in both academia and public service, why does Silverman think that people perceive science in the way they do? He notes that science isn’t perfect, but the way it is taught at school does not suggest this. At school, we are only taught facts, ideas and methods that have been around for centuries, which have been perfected time and time again before they have reached our blackboards. Modern science, however, is experimental and, for those who have not yet understood this, “it feels either very boring or irrelevant”. The truth is that it is neither: “it is very exciting. Communicating the excitement is important.”

Women in mathematics

In recent years, there has been an increased awareness of the lack of females in mathematics and science. We were interested to hear Silverman’s opinion on why that is so, and what we can do to reduce the gender imbalance. He admits that “it has been an enormous struggle to get girls interested in science. I have always wondered to myself why that is. We have to say what it is about the way we do science that women find off-putting. Because I don’t think women are any worse at it or men any better.” He believes that the culture of science is “still very macho and very male-dominated”, which is why some women might find it off-putting. To move forward, our research into how to fix this needs to be more subtle than the current penchant for asking women in the system why they stayed in it.

Priesthood

The observations of modern science are incontrovertible. They are the world that we live in; they are the world as we have it.

What people may find surprising about Silverman is that aside from his extraordinary work in science, he also takes an interest in religion. He earned a bachelor’s degree in theology from the Southern Theological Education and Training Scheme, and is currently a practising Anglican priest. So what about his views regarding the relationship between science and religion? He says that although he is not always certain about his faith, it remains an influence on everything that he does.

However, “any view of religion that doesn’t take into account modern science must be wrong, because the observations of modern science are incontrovertible. They are the world that we live in; they are the world as we have it.” He ends with the comment that “it is not a way of thinking I’ve always had, but it is what makes sense to me. It is part of your whole existence”.

Something, we suppose, that could also be said about mathematics and statistics.

Nikoleta Kalaydzhieva Niki is a PhD student at UCL, working in analytic number theory.

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