system
Given the following post, respond as if you're commenting on Reddit:
human
I'm a high school student. In a week or two I'm gonna give a short presentation on the philosophy of mathematics. What are some critical things I should talk about?

So far my outline goes like this: 
- What is math? Is it discovered or invented?
- Do mathematical entities really exist?
- Is our whole universe/existence composed of mathematical entities? (I'll be talking about Max Tegmark's book here)
- What are some things that can't be described by or composed of mathematics?

I also want to talk about Gödel's Incompleteness Theorems but not really sure how to fit it in so that the presentation has a logical flow. Any help would be appreciated! Thanks :-)
gpt
It might be more productive to focus on one point, and bring that across as well as you can. For example, you might 

- Talk about platonism vs. nominalism about mathematical entities

- The history of the foundations of math - especially Hilbert's program of finding universal axioms of math - and how Gödel's incompleteness theorems showed that to be impossible

I worry that if you say you want to give a short presentation, you're gonna only superficially treat five questions rather than give a good, solid overview of one.