What's the difference between math and poetry?

Is that a silly question? If so, let's indulge in some silliness. (Indulgence seems to me the basis of both math and poetry, whether it's called an axiom or an occasion.)

How does language find traction on the world rather than existing purely in abstraction? People hear words and things happen. People put words together and things become possible.

My younger self would have said that math has provability, rules, rigor. That these things are distinct from poetry.

Now I am not so sure. First, I am no longer certain of the rigor of mathematics. Nor am I sure that poetry does not have these things, so much as, to the extent that it may have them, the ability to perceive them is not taught in school.

It's tempting to say that math is the language of what can be understood purely from inside itself while poetry requires an experience of the world. Or that math is concerned with providing models which can be applied to the world, poetry with the movements of the self. Yet these views immediately encounter their dual: math must be grounded in something in order for understanding to exist at all while poetry creates experience anew; math produces conception irrespective the nature of the world and poetry moves the people around us.

They each possess tools for reflecting upon their object, from meta-logic to the "I". Yet at times they are each absorbed in their own context, in the production of language and nothing more.

I seem to have asked about difference and found nothing but similarity.

They are each an expression of unity. They both generate the infinity of divisions.

Math is math. Poetry, poetry.