This short excerpt started off an essay which will never see the light of day. I hope to eventually have a suitable way to complete this idea, but until then, maybe somebody will find it good food for thought. (You may also substitute “mathematics” for the theoretical subject of your choice, with varying degrees of success.)

In mathematics, a proof is no more than a convincing argument of a statement’s validity. But as justification for a theorem, a proof alone is wanting. Why state one theorem over another?

The metric of real-world utility seems not to apply. After all, the very objects of study are, in some sense, artificial.

But the allure of mathematics–to me, at least–is how well those objects fit together: the degree to which mathematics unifies apparently different concepts is staggering. Perhaps nobody said it better than G.H. Hardy in A Mathematician’s Apology: “The ‘seriousness’ of a mathematical theorem lies in…the significance of the mathematical ideas it connects.”

If research mathematics is about connecting ideas, surely math education ought to convey that interconnectedness. On the contrary; until reaching senior-level courses, mathematics appears an amalgam of essentially disparate concepts.