Plato suggests mathematics and love of beauty as doors to the transcendent. Most mathematicians are Platonists, I think—they believe mathematical objects exist independently of human thought and action and even physical reality—but mathematics today is too closely connected to measurement, analysis and prediction of natural phenomena, and the tendency to resolve it into arbitrary axioms and formal logic is too strong, for it to serve the educational function it did in Plato’s time, at least for most people.
That leaves beauty. So far as I can tell, people don’t pick up on it as readily as they once did. The world, maybe in the form of TV, video games and careers, is too much with us. The popular or rather commercial arts get a lot of their appeal from other sources—sensation, emotionalism, fashion, eroticism, sentimentality, moralism and what not. The fine arts seem to be in decline. People don’t care about them much, and they often seem to rely on shock, politics, pretence, snobbery and the like to boost interest. None of those things leads us out of ourselves.
Even so, beauty is a perpetual possibility that can still subvert the technological claim to completeness and omnipotence. It’s certainly present in remnants of the past, and I’m always struck by the amount of good unpretentious art I run into by local artists near where I live. Life goes on even in troubled times.
Probably people today see beauty mostly in nature. Nature is independent of us, that’s what defines it as nature, and that, I think, is a key point. We are drawn to beauty, and can promote it in various ways, but we can’t simply contrive it and get it whenever and however we want. If we could then any competent artist could produce masterpiece after masterpiece. Beauty is independent. It appears when it wants, it is what it wants to be, and it rewards us only when we accept it as it is. For that reason it trains us in disinterested contemplation of something other, and perhaps better, than ourselves. It tells us that there are rewards other than those of getting our own way, and so helps cure or at least soften arrogance, narrowness and overreaching.