The Historical Context for Modern Mathematics

Most people do not understand the history or context of modern mathematics. They do not realize just how many assumptions were made around the turn of the 20th century, as mathematics was undergoing a foundational crisis.

Instead, your average PhD has a strong opinion about the rigor of modern mathematics and has never conceived of alternative structures of math. They passionately believe the very first thing they were taught - no different than a religion.

Euclidean geometry served as the foundation for mathematics for nearly two thousand years, with the supposed "best minds" considering it indubitable. Until it wasn't. When non-Euclidean geometries were discovered, they shook the literal foundations of mathematics - a crisis that has never been fully resolved.

In this video, I go through some of the attempts to re-found higher mathematics. Different philosophies will yield different mathematical structures - especially with regard to the notion of "completed infinities."

Comments and corrections welcome. I don't expect this story is 100% accurate, as it's just a brain dump to get it out while working on other things. When editing, I already know I misspoke. Still, this should be a good enough story to serve as a starting point to learn about the context for modern math. I do intend to write significantly on this topic.

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