Obiter dicta by Professor Gavin Brown AO

Roots

17 September 2004

We all need a break from the excitement of elections and football finals. Revising and compressing a paper on "Approximation on two point homogeneous spaces" prior to publication lets me return to my roots. Many unkind things are said about mathematicians. Indeed, whenever vice-chancellors are especially on the nose I give myself some shock therapy by admitting to be a mathematician at the odd party or two. This is akin to wearing a headband marked "Serial Killer".

It is true that the personality type is special and I recommend Mark Haddon's bestseller The Curious Incident of the Dog in the Night Time to give some flavour of what lurks below the surface. Curiously, the mathematics that appears in that book is clumsy and sloppy but there is insight into thought patterns.

It is no accident that I am a first class proof-reader -– not because I have a high tolerance for boredom -– but because, generally, I see what is written on the page an instant before I engage with its meaning. There is a tendency to observe what is there rather than what is expected to be there. Perhaps this trait of many mathematicians extends to body language and to interpersonal engagement. There is certainly a popular joke which asks how to identify an extrovert mathematician -– she looks at your shoes when talking to you. That is why Adam Spencer and I find public performance so draining.

One fact must be admitted. Although mathematicians love complex word puzzles they are also suckers for weak puns. That reminds me that, in the spirit of the title, I should issue a gentle challenge. In order to save our printer stress let's use the command sqrt to replace the usual square root sign. Thus sqrt 4 is 2 and sqrt (sqrt 4) is the square root of 2. What, in that case, is the simplest way to write the number x, defined by:

sqrt(2 + sqrt(2 + sqrt(2 + sqrt(2 + …where the pattern goes on for ever?

A simple way to check mathematical propensity is to evaluate how much pleasure someone takes in the following argument to show that a triangle ABC with equal sides AB and AC has equal angles at B and C. Pick it up, flip it over and put it down again as ACB. Because of the sides it fits exactly on ABC so the base angles are equal.

There is concern approaching panic in the United Kingdom about the state of high school mathematics. A recent study at the University of York claimed that a B at A–level guaranteed a readiness to fail necessary university mathematics. There was also a startlingly poor comparison of the achievements of those with the top grade today with the standard competencies of a few years ago. Dangerously, one remedy suggested is to cut out some of the hard bits and make the course more socially relevant. Dangerous too is the notion that vastly increased computer power relieves the need for mathematical skills. This is because skill and understanding can never be totally separated.

Some old skills, like extracting square roots by hand, are now fully redundant, which reminds me that x equals 2 because x squared = 2 + x.