> For the complete documentation index, see [llms.txt](https://mandober.gitbook.io/math-debrief/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mandober.gitbook.io/math-debrief/900-index/980-hierarchy/hierar.md).

# HIERAR

1. Elements

* About Mathematics (What is Math)
  * abstraction
  * history
* Mathematical method
  * rigor, Euclid
  * formal system
  * axiomatic system
  * primitive
  * definition
  * axiom
    * consistency
  * conjecture
  * inference rules
  * theory, theorem, lemma
  * expressiveness vs provability
* Foundations of Mathematics
  * Crisis in the Foundations of Mathematics
  * Hilbert's program
  * 24 Hilbert's problems
  * Axiomatization of Mathematics
  * Logicism
  * Tarski's undefinability theorem
  * Kurt Gödel's Incompleteness Theorems
* Philosophy of Mathematics
* Division of Mathematics
  * Subject matter
    * change, space, quantity, relation
  * Branches of Mathematics
    * discrete vs continuous
    * pure vs applied