>[!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: ": "
```