>[!abstract] Abstract >I understand and define mathematics not as an *invention*, but as a *discovery* process of taking a set of axiomatic premises (the ZFC set theory) to their logical limits. That process was historically constrained by the cognitive abilities of humans to reason at increasing levels of abstraction; however, that constraint is being lifted as generative AI and formal proof languages (such as Lean) act as a force multiplier in exploring the search space. >[!tip] Motivation >I am *not* a mathematician by any stretch of the imagination; not even a hobbyist one, except perhaps in the most casual sense. I am, however, drawn to math for two reasons. > >The first is its *unreasonable effectiveness in the natural sciences* ([[Wigner (1960)|Wigner, 1960]]) which might, in the limit, elegantly explain our perceived reality as an emergent property of a [[mathematical universe]]. > >The second is that I admire (and envy) the seemingly-alien abstract reasoning prowess of the greatest mathematical minds, even as I will never truly grok the full breadth of the intellectual legacy they bestowed upon us. > >In my spare time, I enjoy exploring mathematical concepts at the edge of our human understanding, such as the [[notes/Riemann hypothesis]] or the [[Langlands program]], and taking small steps to understanding them better through the consumption of lay publications, LLM self-tutoring, and science videos. The notes below are the ones I have kept to teach myself during that exploration. ## Metamathematics ```base views: - type: list name: List filters: and: - categories.map(value.toString()).contains("[[Mathematics#Metamathematics]]") order: - file.name - description separator: ": " ``` ## Riemann hypothesis ```base views: - type: list name: List filters: and: - categories.map(value.toString()).contains("[[Mathematics#Riemann hypothesis]]") order: - file.name - description separator: ": " ```