50 Visions of Mathematics

"This book, appropriately, has 50 articles in it. It was edited by a number of people in the IMA. Sam Parc is not a person. It is a pseudonym for the editors, constructed from their first names, which are listed on page six of the preface. What’s really nice about this book is the wide range of topics and the fact that the articles are all very short, typically three or four pages. It’s a fantastic book to just dip into. There’s a whole variety of articles—from biographical and autobiographical articles, which I particularly like— through to topics like “Motorway Mathematics,” which explains how you can use modelling to understand traffic jams. On the motorway, you slow to a crawl, and then a little later you think, ‘Why did I slow down? There’s no obvious accident or problem.’ Mathematical modelling helps you understand the wave effect of that slow-down through the traffic. That’s why we’re getting these smart motorways now. Ultimately, they will be able to adjust the speed limits with the aid of—hopefully—mathematical theory to minimise traffic jams. There’s also a good article about how if you’re at a murder scene and look at the blood stains on the floor you can find out what happened by working out where the body was when the blood started spurting out. Just using elementary mathematics, sines and cosines—it’s almost ‘A’ Level maths in a way—to try and work backwards . This is by somebody who has a job doing this kind of thing: Graham Divall, independent consultant forensic scientist with 35 years of bloodstain examination experience. There’s also one by Simon Singh on Simpson’s rule. Of course, Simon Singh has published an entire book on the mathematics behind the TV series The Simpsons. This is just a short article relating to one aspect of that. I’ve never watched The Simpsons so I don’t particularly connect with that one. The editors did a really good job of finding interesting articles. The members of the IMA are teachers at schools all the way through to university researchers and people in industry. It caters for all those. It organises conferences, it has journals, and it has a nice magazine that comes out every month. Yes, the IMA is very strong on outreach, on showing the importance of mathematics to the general public. I think one aim of this book was to do that. So, yes, this is very accessible. It is published by Oxford University Press and they’ve clearly gone to a lot of effort to make it read well and be widely accessible. When I was doing my ‘O‘ Levels, I would have said my best subject was English. But I somehow knew that I’d be better off going into science so I did maths, physics, and chemistry at ‘A’ Level. I never really regretted it. In general, scientists are not very good at writing. It’s not hard to be a better-than-average writer as a scientist, especially as a mathematician. So, if you have an interest in writing and you’re reasonably good at maths that’s a great position to be in. There’s no point in doing great science if you can’t explain it to other people. You won’t even get published if you can’t explain your work to your peers and write it in a compelling way. So I’ve always been interested in maths but liked writing as well. I actually spend more of my time writing. Probably every scientist would say the same, because you have to write emails, write lecture notes, write papers, write referee reports, and somehow you spend more time doing that than doing the actual science. Well, always, yes. But the act of writing is not something you can hand over to somebody else, because writing is part of understanding. Quite often I’ll write something up and realise that I don’t fully understand it. I’ll have to go back and look at the maths again. It’s an iterative process. It’s not what many students think is the process when you’re doing a PhD — spending three or four years doing the maths and then, at some point in the last year, saying ‘I’ll write it up and then I’ve got my thesis .’ That’s certainly not the way I work with my students. I get them writing immediately. If you leave it to the end then (a) you’ll run out of time and (b) you’ll have forgotten some of the work you did three years ago — you can’t understand it anymore and it probably contains flaws. Writing in maths has to be part of the process."