Prior to my previous blog entry, wishing my a Level students good luck in their exams, I wrote about two books that I had recently read, and thoroughly enjoyed; ‘Why does E=mc2? (And Why should We Care?)’ by Brian Cox and Jeff Forshaw and ‘Not Even Wrong’ by Peter Woit. what was special about these two books is the way in which they place mathematics at the heart of their discussion of modern science. a third such book is ‘it Must be Beautiful: great Equations of Modern Science’ edited by Graham Farmelo.
This book is a collection of eleven essays, each of which takes as its core theme an important equation of modern science. the essays are written by a variety of authors and the equations they focus on are drawn from a variety of disciplines, including maths, physics, chemistry, astronomy and biology. As the very nature of this book suggests, the equations – and hence mathematics – lie at the very heart of this book.
Since physics is the subject that is most mathematical in its nature, it is no surprise that equations of physics are common in this book; including Einstein’s famous equation E=mc2 (which is the central focus of the book ‘Why does E=mc2? (And Why should We Care?)’ by Brian Cox and Jeff Forshaw). There is also an excellent essay by Frank Wilczek, a Nobel prize-winning theoretical physicist, on the Dirac equation, the equation, discovered by the British physicist Paul Dirac, that describes the behaviour of an electron (an electron is one of the fundamental particles of theretical physics; to find out more about electrons you could do far worse than read either Frank Wilczek’s excellent essay or ‘Why does E=mc2? ’, amongst others).
Not only is this essay particularly well-written – I have read many accounts of the Dirac equation and none describe the consequences and meaning of this equation anywhere near as clearly and as entertainingly as Wilczek’s essay – it is also a wonderful essay to read because of the way in which Paul Dirac arrived at his famous equation; Dirac is said to have placed a high value on mathematical beauty and used this as a guiding principle to help him derive his equation. This is an extraordinary episode in the history of modern science – and an important chapter in the interconnecting story of maths and physics – and well-worth reading; and I could try to recount this story myself, but it would not be worth it – Frank Wilczek’s essay is so good you should just read his account instead!
I also thoroughly enjoyed John Maynard Smith‘s essay on the use of mathematics in biology and the mathematical tools used to analyse biological processes and structures. what is so fascinating about this essay is that it is comparitively rare to read such an essay, where the mathematical aspects of biological strategy are celebrated and explored. As a mathematician I found this essay particularly interesting because it examined a relatively new branch of mathematics – the application of maths to biology – and because I very nearly applied to do my PhD in this branch of mathematics (before opting for a PhD in fluid dynamics, I considered applying to CoMPLEX – the Centre for Mathematics and Physics in the Life Sciences and Experimental Biology – a research group at UCL). In mathematics it is very easy to feel as though you are building on the work of thousands of years of earlier mathematical work; and hence to do anything new or novel means you have to work through thousands of years worth of results and progress before you yourself can create something original. hence the appeal of a new branch of maths like mathematical biology as a field of research and as reading material; it makes you feel like you can already see the boundaries of the subject – and that makes it feel like you yourself are closer to being able to discover something new!
Another essay I especially enjoyed was ‘a Mirror in the Sky’ by Oliver Morton, an essay written about the Drake equation. the Drake equation – named after the radio astronomer Frank Drake – deals with the probability of other advanced civilizations existing within our galaxy. taken only as an equation, the Drake equation is rather plain and uninteresting however that is not what makes this equation special. Quite recently I saw a TV documentary on the Drake equation, which I must confess I thought was rather dull and uninteresting; hence, when I realised that one of the essays was about this equation I thought I’d skip over it and read the other essays first!
Having done so I decided to give the Drake equation a second chance and read Morton’s essay – and I’m really glad I did. it was an excellent and entertaining essay that reminded me of the importance of mathematical equations and mathematics in general; we use maths because it is a precise, efficient means of expressing complex ideas – and that’s important because that enables us to work with those ideas and order our thoughts and ideas in a precise, concise way. and that’s exactly what the Drake equation achieves. it is not mathematically elegant and it doesn’t offer any mathematical appeal; neither is it beautiful like the Dirac equation or simple like Einstein’s E=mc2. and it doesn’t even make you think ‘wow’, I wonder how someone came up with that equation! yet despite all those failings the Drake equation is still wonderful – as Morton’s essay has persuaded me – because it does what maths is supposed to do; it gives you a means to describe problems that can’t be handled any other way, and in doing so, brings focus and clarity to a complex problem that might otherwise have seemed too daunting to even begin with!
This collection of essays has been a delight to read and I would sincerely recommend this book to anyone with an interest in maths and science. it is well-written, entertaining, varied and inspiring – and I hope Graham Farmelo compiles a second compilation!
Related articles
- ‘Why does E=mc2? (And Why should We Care?)’ by Brian Cox and Jeff Forshaw (getaheadinmaths.wordpress.com)
- Mathematicians are everywhere! (getaheadinmaths.wordpress.com)
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