Here is a set of axioms proposed by Federico Ardila:

Axiom 1. Mathematical potential is distributed equally among different groups, irrespective of geographic, demographic, and economic boundaries.

Axiom 2. Everyone can have joyful, meaningful, and empowering mathematical experiences.

Axiom 3. Mathematics is a powerful, malleable tool that can be shaped and used differently by various communities to serve their needs.

Axiom 4. Every student deserves to be treated with dignity and respect.

What follows from these axioms? Let’s prove it!

I conduct mathematical research on several different topics, overlapping the traditional boundaries of geometry, topology, group theory, combinatorics, and probability.

My main interest at the moment is tilings of a square.