Frederico's Axioms

Doug Watson

24 Nov 2025 — 2 min read

You may have never heard of Federico Ardila-Mantilla, but let me just introduce you to his four axioms from the project he calls Todos Cuentan. This approach really resonates so strongly with us. We didn’t create the axioms, but we admire them and see them as a thoughtful foundation for how mathematics and all academic disciplines might better serve people.

Here are the axioms he proposes:

Axiom 1. Mathematical potential is equally present in 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.

They’re straightforward principles, but they speak to real gaps between what mathematics, as well as science and philosophy, could be and what they often are.

How These Axioms Shape Our Work

For us, these axioms aren’t slogans—they’re a practical guide for how we want to operate.

In mathematics, they remind us to challenge assumptions about who “belongs,” to design programs that lower barriers, and to encourage forms of engagement that are actually enjoyable and meaningful.
In science and philosophy, they push us to think about who benefits from our work, whose perspectives are included, and how our disciplines can adapt to meet the needs of different communities.

For me personally, these axioms line up with the values that already guide my research and outreach: that everyone’s potential should be taken seriously, that joy matters, and that respect is the starting point, not an optional extra.

Continuing the Conversation

Federico emphasizes that these axioms are a work in progress, and I appreciate that honesty. No framework for community or education is ever final. But these principles give us something clear to return to as we try to build a more welcoming and thoughtful environment—whether in mathematics specifically or in the broader scientific and philosophical worlds we engage with.

We admire these axioms, and we aim to carry their spirit into all areas of our work at the Science and Philosophy Institute!

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