I really enjoyed this TikTok video about the difference between real math and what's taught in schools. It's probably not what you think - it's not, for example, the suggestion that there should be more 'practical' math taught in schools. Quite the opposite. Instead, what you don't learn "until after you've completed your PhD" is that the math we learn is one of many different ways math could be, and that ideally, what you should learn in math is how to create these mathematical systems for yourself. This was something I was lucky to learn about in my philosophy of mathematics classes, and it does indeed change your perspective of what counts as 'foundational' knowledge.
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