Using mathematics to understand AIDS better

The relationship between the applications of mathematics and rigorous proofs is something which I find mysterious. For many non-mathematicians proofs probably seem superfluous and a kind of fetish of the mathematicians. At the same time the endeavour to develop such proofs lies at the heart of the subject. I feel that it is here that the ultimate strength of the subject lies. My starting point in writing about this here is that, rather than having a well-formed opinion on the subject, I am trying to develop one. I want to try to get useful input from whatever source. The basic direction is to concentrate on the way that mathematics can be used in practise rather than on building philosophical theories on the subject. It would be nice to have some positive examples of what mathematics can contribute.

An example of this kind is the development of multi-drug therapy for AIDS. Some relevant information can be found in an interview with David Ho for the Academy of Achievement. He was one of the key contributors to this breakthrough and his work was recognized by his being chosen as Time Magazine’s Man of the Year in 1996. He started out his scientific career as a physicist before going into medical research. He says in the interview, ‘…this is where my physical science background really came in useful, having a strong background in mathematics and applying it to biology…’. In the highly cited paper by Ho and collaborators related to this development (Nature 373, 123-126) mathematics plays a rather low-key role. There are numbers and graphs of data but the only equations are confined to the captions of the figures. A lot of background about the applications of mathematics to AIDS and related problems can be found in the book Virus Dynamics by Martin Nowak and Robert May. On the first page of this book there is the following interesting quote: ‘ … mathematics is no more, but no less, than a way of thinking clearly’.

First steps

Here I am, taking my first steps into the blogosphere. I feel that I am supported by a good title, Hydrobates. This comes from the scientific name Hydrobates pelagicus of the Storm Petrel (as it was called in my youth) or European Storm Petrel (as it is known in these times of globalization). This is a small bird which is about the size of a swallow and spends most of its life on the open ocean. It normally comes on land only at night and only to nest.

There are two reasons why I have chosen this name. The first is that I find the character of this bird inspiring. For me it symbolizes what I regard as an ideal of how a human being can be. It is intrepid. It is confronted with difficult conditions, wind, waves and storms, and turns them to its own advantage. I wish I were more like it. A picture of the bird showing its typical appearance can be found on a Wikipedia web page.

The other reason comes from my experiences as a schoolboy. At that time I got involved in ringing birds. One of the most memorable experiences I had at that time was travelling to small, sometimes uninhabited, islands to ring Storm Petrels. We would put up mist nets during the night to catch them. As a defence mechanism the birds spit a strong-smelling fluid. In handling many of them over the course of a week we found that our clothes became impregnated with the smell of this oil. I came to like the smell but for anyone else confined with one of us in a small space it was overpowering. I still have a vivid memory of the softness of the birds feathers and their curiously shaped foreheads which have something slightly alien about them. The best island for Storm Petrels we visited was Auskerry. On a clear day the lighthouse of Auskerry can be seen from the main island of Orkney where I grew up and before I had been there it was a kind of mythical place for me. In a way it still is now. I have very strong positive associations with the Storm Petrel.

Why have I started to write a blog? Just the other day my first book was published. It is called ‘Partial Differential Equations in General Relativity’. Now that that task has been accomplished I have the urge to communicate in a different way with a wider audience. My enthusiasm has been fired by the blog of Terence Tao. I do not hope to do anything remotely comparable but that example has created in me the wish to do something with this medium.