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.