Mathematical daisies

Mathematical daisies.

I am having a bad week.  This is not on account of a vicious encounter with plantar fasciitis, and not entirely to be blamed on the spirit of doom and gloom that pervades every department of every university in the land, though it is not unrelated to work.  It does indeed have a great deal to do with work, but to understand the subtleties of present evil temper, something must be understood about the nature of mathematical research.

Few people outside of mathematics have any very accurate idea of what mathematical research entails.  I've always rather wanted to have a secondary school work experience kid posted to tail me in my days activities.  I would like to observe him or her observing me.  What would she make of the long hours staring at a blank blackboard?  The corridors in our shiny new department have thoughtfully been made circular, presenting the pacing mathematician no obstruction and no need to reverse direction.  If I please, I can be counter-clockwise all day (actually, I prefer clockwise).  I believe they design homes for the demented on the same plan. Would she follow me loyally through the day as I pace out the circumference, many times, as if to multiple check its measure?

What would she make of the hours of feverish excitement, when she is pressed into service as listener, who understands nothing, not that that would reduce the effectiveness of her role, of sympathetic ear that doubts nothing of what it hears.  The celebratory mug of tea, with extra chocolate biscuits, when the conclusion has been reached that the last link in the chain of logic holds firm, that the theorem which depended on the proposition which depended on the lemma is intact, proven beyond reasonable doubt (subject to re-checking the calculations of course).  A fairy pink paints the sky of the late afternoon winter sun, surely there must be a god in his heaven as all is right with the world.  That last lemma effects a deification: god-like I see the shape of the mathematical universe spread out below me as from satellite height, each bend and ripple according to the laws which I have just demonstrated on paper.  I am not totally devoid of earthly ambitions too, I must acknowledge.  The clarity of my vision and the elegance of my arguments, the wit of my prose will certainly win me the honours that have been so curiously lacking in my career.  I will accept them, though tardy, with gracious magnanimity.

What would she make of the following morning, when, shaking the rain off my coat, I come in, late, moody, uncommunicative.  These days come with the predictability of Singaporian thunderstorms; you don't know when, you don't know where, you just know for sure it's going to happen.  The hapless work experience student must imagine me crossed in love, so evil is my temper.  It is not an inapt metaphor; we understand what we see from the point where we are at; we go further, the view changes, understanding grows, sometimes bringing delight, sometimes distress. We are no more able to guess what tomorrow's understanding will bring than sweethearts are able to see tomorrow's heartache on the horizon.  He loves me, he loves me not, it's true, it's false it's true.  How many petals does a daisy have?

But today's vile spirits arise from a source beyond the spectrum of true or false.   The pernicious daisy representing the elegant theory I have laboured long to describe possesses yet another petal that has no parallel in the annals of the affairs of the heart: a deformed brown and shrunken petal labelled Useless.  The whole of the structure is built upon a dream, an M.C. Esheresque contradiction in spite of the local elegance, and the dream itself without point or conclusion, the So What? of judgement without reply beyond the query's own echo.

The wise work experience student would best model her behaviour on that of the hound, who observes with one raised eyebrow and then quietly slinks off to a distant room to wait until the atmosphere has cleared. The student should perhaps consider seriously a career in the City.  Perhaps the hound does.

Today, banned even from venting my temper on my trainers by the pernicious PF, I can only scowl in stationary silence.  But this is our life.  I'll be back at it tomorrow, sifting through the shards of my elegant but shattered structures, trying again and again, most patient of suitors, to win the way to the heart of the matter.  I've done this all my adult life.  I can't see me stopping now, but shall persevere until the mathematical daisy bald of petals proclaims my day is done.

I've known runners like us.  From this perspective, the training schedule stretches invitingly before me.  Plantar fasciitis is but a minor complication which will melt away like last year's snows.  The long runs marked in pencil on the calendar I imagine to be as good as run. Shedding the extra weight is easy - just exercise restraint.  It's as good as done. So my grand theory looked in its youthful stages, the lemmas obviously true just needing careful statement, the whole standing up clear, bright, evident, and above all, important.  Just waiting for the passage of weeks to proclaim it so.  And then it fails.

But we're runners.  Put yesterday's defeat in the past, and find the trainers.  Begin again.  It's what we do.

Training today? No way. Foot not right.