Math seems to me a bit like love, you have to experience it to understand it. Definitions and discussions like the OP might help a little, but don't get at th

Math seems to me a bit like love, you have to experience it to understand it. Definitions and discussions like the OP might help a little, but don't get at the essence. No-one who reads such a definition will suddenly come away knowing what mathematics is. I had a few epiphanies in my life that made me understand what mathematics is. One of them was understanding why it is that there are infinitely many primes - I think I learnt more about what mathematics is in the moment that proof clicked than I have from reading hundreds of discussions of "what is mathematics". The experience was, simply, miraculous.