# Mathematics Is the Subfield of Philosophy That Humans Are Good At Originally published: 2012-08-10 Canonical URL: /2012/Aug/mathematics-is-the-subfield-of-philosophy-that-humans-are-good-at/ By _philosophy_ I understand the discipline of discovering truths about reality by means of thinking very carefully. Contrast to science, where we try to come up with theories that predict our observations. Philosophers of number [have observed](http://www.maa.org/editorial/mathgames/mathgames_10_18_04.html) that the first ten trillion nontrivial zeros of the Riemann zeta function are on the critical line, but people don't speak of the [Riemann hypothesis](http://en.wikipedia.org/wiki/Riemann_hypothesis) as being almost certainly true, not necessarily because they anticipate a counterexample lurking somewhere above ½ + 10²⁶i (although "large" counterexamples [are not unheard-of](http://en.wikipedia.org/wiki/Skewes%27_number) in the philosophy of numbers), but rather because while empirical examination is certainly _helpful_, it's not really _what we do_. Mere empiricism is usually sufficient for knowing (with high probability) _what_ is true, but as philosophers, we want to explain _why_, and moreover, _why it could not have been otherwise_. When we try this on topics like _numbers_ or _shapes_, it works really, really well: our philosophers quickly reach ironclad consensuses about matters far removed from human intuition. When we try it on topics like _justice_ or _existence_ ... it doesn't work so well. I think it's sad.