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One of thc most note-worthy features of the mathematics of the late
1980s and early 1990s is a renewed contact with science, and a two-way trade
of ideas. This is a sign of health and vigour, and deserves encouragement.
Five recent books show what can be done.

I’ve always felt we need at least as many ‘X for Mathematicians’ books
as we get ‘Mathematics for X’. Peter Lorimer’s The Special Theory of Relativity
for Mathematics Students is a case in point. ‘Okay, you guys: I don’t need
to tell you what the chain rule is, but let me fill you in on magnetic fields’.
(I paraphrase. The author’s prose is more conventional.)

Most group theorists would be astonished by what happens to their pets
when a physicists gets his hands on them, as in Groups, Representations,
and Physics by H. F. Jones. I’m not suggesting we teach quantum field theory
to every alge-braist, but they could learn an awful lot from the group-theoretic
treatment of the vibrational modes of the water molecule.

That leads to another area of science: chemistry. My selections here
are a bit more advanced, but they are full of marvellous examples of nonlinear
dynamics that would breathe new life into a final-year course on differential
equations.

The first book in this area is Patterns and Waves, by Peter Grindrod,
an exposition of how patterns arise from the competition between reaction
and diffusion.

The second of my choices is Steve Scott’s Chemical Chaos, which is definitely
postgraduate material, but again contains some wonderful applications of
new ideas that could easily be imported into an undergraduate course by
an imaginative lecturer. I recommend it also to those scientists who think
that chaos theory is nothing but pretty pictures and hot air.

The same goes in spades for Bruce. J. West’s Fractal Physiology and
Chaos in Medicine. As its author says: ‘We are now in the position where
clinicians with their stethoscopes poised over the healthy heart, radiologists
tracking the flow of blood and bile, and physiologists probing the nervous
system, are all, for the most part unknowingly, exploring the frontiers
of chaos and fractals.’

If this seems a sweeping statement, then I suggest that you wait ten
years.