Note. Foundations and Flora [index]

Foundations and Flora

Hello! I’m Gael Penha, and this is Foundations and Flora, an attempt at creating a corpus of mathematics that I plan to keep updated as I learn math.

What this is

The goal of this project is to use some foundations for mathematics to prove as much as possible, in a somewhat formal environment that will ideally be intuitive to understand. In doing this, I will be taking some approaches to mathematics that are (or at least I believe to be) fairly radical, such as a complete disregard for set theory, since I find sets unintuitive as mathematical objects.

Who this is for

If you are looking at this page, you are probably already the intended audience, but if you aren’t sure yet, take a look at some of the links below. I hope that the way I will be presenting ideas will keep them accessible to any audience that may be reading my ramblings. Ideally, though, this will be accessible to anyone who is interested in math.

Organization

Since math is fairly non-linear, and results from many fields can be used in other fields, the mathematics here will be presented in a sort of wiki. The purpose of taking this approach is to allow separate fields of mathematics to be developed concurrently. If you wish to see the full wiki, click the full graph button above the graph to the right.

Where to start

Currently, the only place to look is Foundations. Other interesting places to begin looking through this will be added in the future.

Feel free to check out the graph of this site here.

Status

This project is in its beginning phase and is thus incomplete; any updates will be posted here, so check back later if you are interested!

If you see any mathematical errors, have interesting examples, or math you would like me to explore, email me at gael@gaels.garden, and I’ll respond ASAP.