Having posted an earlier essay, and calmed down a bit, I bethought me: perhaps I have been too harsh, in attacking the cultural relativists such as Raymond Wilder. For at least he (like his fellow-subjectivist Reuben Hersh) is still within the camp of genuine mathematics. All in all, it isn’t so bad. But, caution! If you move mostly in Cantorian and Apostolic circles, you seldom come in contact with the actual howling-gibbon lunacy that exists -- well, not really in the fields and forests outside the groves of Academe, but mostly within the Academy, in those parts that have fallen prey to multiculturalists, and are thus a lost cause.
(One must say, proponents of the latter made a singularly unhappy choice, since, of all the objects of knowledge, towards which we poor bipeds strive, mathematics is surely the least flavored by race or indeed by species: a mathematical pachyderm, or a thinking cloud, faces exactly the same problematics as any earthling reckoner whether Alsatian or Zulu.)
I’ll not polemecize against those trends, any more than I would engage in debate with Donald Trump. After all, the people whose good sense I respect (mostly carpenters and electricians) and on whom the health of our nation depends, are unlikely to be seduced by such twaddle. But let us summarize the subject thus: Although no part of mathematics proper, the study of the acquisition and imparting of mathematical knowledge is a legitimate pastime among others, ranking as somewhat more important than the rehashing of yesterday’s sports scores (and other activities that serve mainly to keep the molecules moving), and somewhat below the latest brownie recipe (since you can eat the brownies). Further, if you choose to engage in this pastime, your time will be better spent tracking the thinking of such men as Riemann or Cantor, than in celebrating how Mbobo of Gboko learned to count on his fingers (an actual activity of cultural studies -- really, this stuff is beyond satire). And finally, we must sharply distinguish between, on the one hand, the truth and proofs and applications of (say) the Urysohn Metrization Theorem, and (on the other), how you personally feeeeel about the theorem, as a person (as a gay person; as a retarded American; as a transgendered Albanian).
All in all, the actual practice of genuine mathematics, at whatever level you can handle, is a stern and sterling antidote to the idols of the tribe now cluttering the agora.
Oh and -- Mathematical knowledge? how does it come to us? => By a mysterious mixture of insight (read: Revelation) and hard work.
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