Maths

Here are some of the projects I worked on, which relate to mathematics.

Mathophilia

This is not so much my project as it is my brother’s - the idea is to experiment with better ways to teach math.

Table of Polytopes

This is a simple table to list all of regular (interesting) polytopes in 3 dimensions.

Property Table of Algebraic Structures

This project is, first and foremost, an exercise I did for myself - to better get a grasp of the many terms and concepts of group theory and category theory.

The exercise is quite simple: to fill up some huge spreadsheets, mapping each and every algebraic structure (for example, the natural numbers ℕ with the operator +) to each common property of algebra (for example, “associativity”). The goal is also to have the relevant proofs in each cell as extra annotations.

I have begun to implement all of these proofs using lean, with the valuable help of the wonderful Joseph Dimos. The end goal is to create a large database of the properties of mathematical structures, such that one may query for any example structure with the desired properties that suit their mathematical needs.

Base-Neutral Number Notation

This is a notation system for integers which I invented.

This system is not based on additions of powers of an arbitrary radix, like a traditional number base (decimal being radix=10, hexadecimal is radix=16, binary is radix=2, etc). Instead, this notation system is based on the idea of multiplication, and the concept of prime numbers (which is a natural consequence of multiplication).

Axioms and Systems table

To better understand the various systems of set theory (ZF,ZFC,etc) and the axioms they each use, I began to draw up a large mapping of axioms to all major systems of logic.