As a result of decades of empirical research, crime science has emerged as the leading multidisciplinary approach to develop new ways to tackle crime and terrorism. As opposed to traditional criminologists, crime scientists commonly use a broad spectrum of different disciplines and sciences to achieve their aim of cutting crime. Using knowledge from chemistry, geography and physics, to architecture, public health, psychology and information technology, crime science has been able to offer new solutions to the most pressing issues that impact on the health and security of millions of people. Among all the fields and disciplines used, applied mathematics, statistics and econometrics are perhaps the most common tools used by crime scientists. Continue reading
If spiders could count all the way up to forty, calculate angles and tensions, then perhaps we could explain why their webs all follow a similar pattern, having a similar number of strings and turns and flips… but the reality is that they (probably) can’t, so the fact that webs are similar must be because spiders are really good at minimising functions! Continue reading
Crime prediction, robotics, big data, image processing, fluid dynamics. Andrea Bertozzi, professor of applied mathematics at the University of California, Los Angeles (UCLA), has worked in all these areas and more. Her curiosity and many collaborations have made a real impact in our modern world. Continue reading
Every time I walk into an empty bus stop, I feel like I will have to wait for a much longer time until the next bus arrives. Why am I the first passenger to arrive? And, more importantly, how much longer do I have to wait, now that I know that I am the first passenger in the queue? Chances are that the last bus left the stop just seconds ago, therefore the stop is empty.
Does this person have ginger hair? Is this person a boy? Is she wearing a hat? Is your person Anita?
Maybe everyone has played Guess Who? the board game where you try to guess which character your opponent has before they find out yours. For those who have never played Guess Who?, the game goes as follows: each player picks a card at random, on which will be drawn the face of a character. In turns, the two players ask each other yes/no questions to try and guess who their opponent has picked. A board with all the images of the characters initially standing up helps the player keep track of which ones have been eliminated along the way. Continue reading
Could one ever get tired of those 140 characters of freedom? With the ability of opening a Twitter account for free and then sharing thoughts, pictures, videos and links with the rest of the world (except for some countries), will the number of users continue to grow until everybody has an account? Recent data shows that perhaps the world is actually getting tired of Twitter: the number of monthly active users of the network, at least in the US, has practically remained constant for the last year (one could even say that it decreased slightly, taking into account the 0.7% population growth of that country). This is the end of Twitter’s golden era, in which they managed to double the amount of users year after year.
Differentiating a function is usually regarded as a discrete operation: we use the first derivative of a function to determine the slope of the line that is tangent to it, and we differentiate twice if we want to know the curvature. We can even differentiate a function negative times—ie integrate it—and thanks to that we measure the area under a curve. But why stop there? Is calculus limited to discrete operations, or is there a way to define the half derivative of a function? Is there even an interpretation or an application of the half derivative?
2015 is the 100th anniversary of the Sierpinski triangle, first described by Wacław Sierpiński, a Polish mathematician who published 724 papers and 50 books during his lifetime! The famous triangle is easily constructed by following these steps:
- Start with an equilateral triangle.
- Divide that triangle into four equilateral triangles and remove the one in the centre.
- Repeat the same steps with the remaining triangles, dividing each one into four triangles and removing the one in the centre.
Every time I see a rainbow, one of those magical shows that nature has prepared for us, I can only feel amazed by such a special and colourful figure shining up in the sky. What shape is it? From how far away is it still visible? What does a rainbow look like from the side?
Sitting in a pub in Leicester Square, talking to one of the most brilliant mathematicians of our generation, is not the way one would normally expect to spend a sultry evening in early June. But it turns out that Artur Avila, winner of the 2014 Fields Medal, takes very spontaneous holidays, and is a big fan of the pub.
In the UK, Artur certainly does not conform to the stereotype of a mathematician. He is good-looking, stylishly dressed in a white T-shirt and designer jeans and asking about the best London nightclubs. However, Avila was born and bred in Rio de Janeiro, famous for its spectacular parties and beautiful beaches. He still spends half his time there, based at the National Institute of Pure and Applied Mathematics (IMPA), and spends the other half at the French National Centre for Scientific Research (CNRS) in Paris, where the nightlife is terrible, according to Avila.
It’s perhaps unusual for an exceptional mathematician not to spend all their time in the USA or Europe, where there are higher numbers of world class research institutions, but Avila believes ‘it’s significant that I studied at IMPA because it shows that Brazil has institutions that can prepare someone to do maths at a high level, and it’s not necessarily true that you always have to go to the United States or to Europe to advance.’
And, of course, Rio has many appealing features: ‘I have several times brought collaborators to the beach with me and we would just sit and share ideas with each other, with the sound of the sea in the background.’