A selection of epigrams:
It may be legitimately objected, that in beginning with a grubstake of mere integers, and proceeding stepwise to full mathematical Platonism, I am here sneaking past the goalposts via the fallacy of the sorites.
[For the full essay, click here.]
He demystified the notion of the obscurely named “imaginary numbers”, the “square root of minus one” which, thitherto, had seemed some sort of deliberate paradox, like the “sound of one hand clapping” or the “difference between a duck”.
[For the full essay, click here.]
It is in the first instance odd, that the idea of infinity should ever have occurred to anyone, since everything we have ever actually met with is quite finite.
[For the full essay, click here.]
What does it mean for a space to be metrizable, and why should we care?
[For the full essay, click here.]
Mathematics itself might be defined as the science of matching patterns; so there is a certain appropriateness that it serves as a link between such superficially disparate phenomena as the pattern of spots on a leopard and the subject of reaction-diffusion equations (pioneered by none other than Alan Turing), or floret patterns and Fibonacci series.
[For the full essay, click here.]
For the truth of the theorem resides, not in the cloaca which these gentlemen are pleasured to inspect, but in the realm of Invisibilia, the kingdom of the Lord of Hosts. And the valid mathematical moves made by this or that fallible incarnated creature, in their groping attempts to approach the truth, gain their validity, not from thermodynamic or statistical considerations, but from our miraculous harmony with such abstract truth itself, which stems, we know not whence; though some of us have an inkling.
[For the full essay, click here.]
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