Is It Flowers You’re After?

After many years of trying to understand and teach this stuff in multiple seminars and a few lecture courses in Prestigious Universities, my textbook Mathematical Phyllotaxis is now ready. Why should you care?

Well, the biomathematical theory of why we see Fibonacci numbers in plant structure is mathematically elegant, has scientific explanatory power, and is still generating novel testable hypotheses. More than that, it is an existence proof that the programme of twenty-first century molecular biology, which is to move from the ‘list of parts’ of twentieth-century genomics into the functional understandings of ‘systems biology’, will require at least some LaTeX.

The two little mathematical in-jokes (*) of the last paragraph are shibboleths: if you don’t recognise them this book is PROBABLY NOT FOR YOU. I don’t mean this subject is not for you. In fact one of the real attractions of mathematical phyllotaxis is that it can showcase the power of mathematics to pretty much anyone with an interest in why living things have the forms they do. It’s just that this book is not that showcase.

Instead it is aimed at someone who thinks of themself, or would like to, as a person who teaches mathematical biology. Despite what seems to me being a brilliantly good example of what maths can bring to science, and moreover one that can appeal to students who think of themselves as only interested in ‘pure’ (**) mathematics, phyllotaxis has been available as material for undergraduate courses for decades, but as far as I can see no-one teaches it. (If you are outraged that I am traducing your up-to-date mathematical biology course please let me know.) So this is an intervention intended to change that. These are not lecture notes or classroom examples, but an example of doing mathematics, with Theorems and everything, reaching through families of dynamical systems which are the subject of current research, through to the endless puzzles of knowing when to stop creating mathematical structure and when to start exploring biological structure. If you want new material to add alongside SIR models and the Turing instability, this book is meant to reassure you that this area, too, is Proper Maths. You have to work out how to teach it yourself (or ask me for the slides, but be warned I use Powerpoint).

This is not, like an alarmingly large number of books on the subject, a key to all the mysteries of flowers, complete with wonderful insights that only I have seen, nor is it an uncritical guide to Turing’s remarkable work in the area (which is what first got me interested). It is a textbook and guide to decades of peer-reviewed literature: almost everything in it is a retelling of other people’s work.

After all that. if you are likely to use this text in a classroom setting or want to review it, contact me.

(* Existence proofs and LaTeX. See, not funny if you explain.)

(** This is not the place to explain why I put scare quotes here; but let’s say I have found purity sometimes toxic in these contexts.)

(The title and image are not from the book, but from a Squarespace default template, but they get us in the mood)