Maths is vast. Sometimes, looking at how
much has been done, I wonder at the mathematical Universe that has been created
by the collective endeavour of all Man’s generations of mathematical thinkers.
Now, this vastness has consequences which Ainan discovered recently.
Some time ago, Ainan drew what seemed to
him a very interesting shape of tangential circles within a circle, echoing
fractally on. He drew it because the form of it appealed to him, aesthetically.
He liked its mathematical beauty.
Some time later, Ainan stumbled on
something on Wikipedia: the Apollonian Gasket. It was the figure Ainan had
drawn...the fractal shape of tangential circles. Ainan had rediscovered
something invented, initially, by Apollonius of Perga, the Greek Mathematician.
How odd...and how revealing of the vastness of mathematical creation, that a
random creation of a child, playing with mathematical ideas, should, itself,
have already been the random creation of an adult, long ago, in Greece.
Ainan is inventing much mathematics these
days. He invents mathematical problems, schemas, conjectures, propositions and theories, for himself to play
with. No doubt, on occasion, they will be something that has been done before –
like the Apollonian Gasket – yet, at other times, I am sure, they are something
that has never been done before. The problem with that is that I am not a
mathematician and so I am not in a position to advise Ainan as to the merit,
utility or value of anything he does. So, he just creates in mathematical
isolation, playing with maths, as other children might play with the sand, at
the beach: happily, joyfully, for the very purpose of immersing oneself in the
environment – in his case, an abstract one – in the other’s, the beach.
Ainan is presently alone in his
mathematical pursuits. There is no-one to share them with – though I listen to
him and watch, with a sprinkling of wonder, at what he does. Yet, I cannot be
the perfect audience to his mathematical work, because my primary domains are
elsewhere, other than this.
Ainan spins on, growing, becoming,
morphing, each passing year, into a being, ever more rarified, ever more
unexpected. My role is to do what I can to foster that growth – even if it be
in areas that are not my primary strengths. I enjoy it, but I wish, for his
sake that I could be all the differing intellects he requires to be properly
supported. I can be most of them – and am – but I cannot be all of them. Yet,
what I can be, is appreciative of his intellectual growth, in whichever
direction it meanders, no matter how far it wanders...I can appreciate it...and
I hope that is enough.
Posted by Valentine Cawley
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Labels: Ainan Celeste Cawley, Apollonian Gasket, Apollonian net, mathematical creativity, mathematical serendipity, mathematically gifted, rediscovery, the beauty of mathematics