Professor Johnson said: “Baubles are notoriously fragile and Christmas decorations have a nasty habit of taking up too much space. So what’s the most efficient way of storing festive spherical objects, which also applies to the Chocolate Orange, walnuts, Brussels sprouts, and even snowballs? While there is uncertainty about the potential for bird flu to infect humans, investing in new vaccines now could avoid the ruinous cost of another pandemic. Photograph: Ian Forsyth/Getty Images

I have recently been working on the group testing problem. This is a combinatorial search problem, which acts as a prototype of a wider class of sparse inference problems in estimation and statistics. I have developed the idea of rate and capacity of algorithms, and proved a range of theoretical performance guarantees for them in this sense. I am also interested in the idea of converse bounds: that is to show what performance is optimal. This has included recent work to extend the standard Fano-based bounds in statistical inference problems to a sharper criterion based on Renyi entropy. Regarded as ‘the perfect introduction to the power of mathematics – fluent, friendly and practical’ by Tom Harford,author of How to Make the World Add Up.David Spiegelhalter, author o f The Art of Statisticsalso referred to it as ‘A fine and valuable read. Johnson applies careful analysis and great common sense to an extraordinary range of applications of mathematical ideas, from football to filter bubbles – explaining formal ideas with minimum technicalities, and weighing their relevance to the real world.' What you'd like is a nice spread of baubles, without too many of the same color next to one another. It seems natural to try decorating the tree 'at random,' but this won't lead to a good effect. Suppose you have 100 baubles and 100 branches: if you just put each bauble on a randomly chosen branch, then more than a third (about 37%) of the branches will have no decorations at all, whereas some might well have as many as four baubles. The perfect introduction to the power of mathematics - fluent, friendly and practical. * Tim Harford, author of 'How to Make the World Add Up' *Lucid and entertaining. With barely an equation in sight, Numbercrunch makes a passionate case for how just a little bit more numeracy could help us all' - Tom Whipple, The Times'The perfect introduction to the power of mathematics - fluent, friendly and practical' - Tim Harford, bestselling author of How to Make the World Add UpIn our hyper-modern world, we are bombarded with more facts, stats and information than ever before.

Similarly, there will be bare patches, just by random chance. In the same way, placing different coloured baubles randomly will tend to lead to two or three baubles of the same colour close together more often than we’d like. That means in fact, the best way to decorate your tree might be using a so-called quasi-random strategy, which lies somewhere between the very random and very structured extremes, and can be more pleasing on the eye.” Professor Johnson explained: “While it may be powerless to sweeten the pill, maths can certainly help you understand what’s going on. For example, what are the chances that the last chocolate left in the box is a nasty one? It’s actually very simple: if our box has 24 nice chocolates and 6 nasty ones, there’s a simple way to see the likelihood of the last one being nasty is 6/30, or 20%. That’s the same chance that the first one is nasty, because you could imagine randomly pulling out all the chocolates and putting them in a long line – and then deciding which end of the line to start eating from. What you’d like is a nice spread of baubles, without too many of the same colour next to one another. It seems natural to try decorating the tree ‘at random’, but this won’t lead to a good effect. Suppose you have 100 baubles and 100 branches: if you just put each bauble on a randomly chosen branch, then more than a third (about 37%) of the branches will have no decorations at all, whereas some might well have as many as four baubles.Professor Johnson explained, "While it may be powerless to sweeten the pill, math can certainly help you understand what's going on. For example, what are the chances that the last chocolate left in the box is a nasty one? It's actually very simple: if our box has 24 nice chocolates and 6 nasty ones, there's a simple way to see the likelihood of the last one being nasty is 6/30, or 20%. That's the same chance that the first one is nasty, because you could imagine randomly pulling out all the chocolates and putting them in a long line—and then deciding which end of the line to start eating from. As a result, it can be wise and necessary sometimes for governments to follow strategies that may well seem wrong in hindsight. For instance, it feels prudent to invest now in the capacity to manufacture H5N1 vaccines even if a bird flu pandemic in humans may well not occur, because we know that the potential outcome would be so severe if it did happen. Expected goals According to the publisher, Numbercrunch equips readers with the mathematical tools and thinking to understand the myriad data all around us.

Oliver Johnson, Professor of Information Theory at the University of Bristol, helped explain the constant stream of statistics during the pandemic. He has also been busy writing his debut book Numbercrunch, out next year with Heligo Books, which reveals how numerical thinking can help resolve some of life’s biggest conundrums. No Christmas is complete without a rootin'-tootin' singalong of The Twelve Days of Christmas. Well done if you can remember all the lyrics but top marks are reserved for those who know the secret significance of the number of presents received each day.Oliver Johnson is professor of information theory and director of the Institute for Statistical Science in the school of mathematics at Bristol University To whet your appetite for his wizardry, Professor Johnson has turned his mathematical mindset to the equally challenging problem of number crunching Christmas. Oliver Johnson, Professor of Information Theory at the University of Bristol, helped explain the constant stream of statistics during the pandemic. He has also been busy writing his debut book "Numbercrunch," out next year with Heligo Books, which reveals how numerical thinking can help resolve some of life's biggest conundrums. I am interested in the relationship between properties of entropy and limit theorems, such as the Central Limit Theorem and Law of Small Numbers (Poisson convergence). This includes trying to understand relationships between information-theoretic properties such as the Entropy Power Inequality and maximum entropy theorems and probabilistic ideas such as log-Sobolev inequalities and transportation of measure. I have a particular interest in developing discrete analogues of these results.