Federico Ardila is a mathematician working in combinatorics and its connections to geometry, algebra, topology, and applications. He is interested in fostering an increasingly just, equitable, and welcoming community of mathematicians, one that benefits from members’ differences and serves the needs of all. In “Todos Cuentan: Cultivating Diversity in Combinatorics,” published in 2016 in the Notices of the American Mathematical Society, he wrote four axioms that have formed a useful foundation for his educational and outreach efforts: 

• Axiom 1. Mathematical talent 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. 

“These statements should not sound revolutionary,” Ardila wrote then, “but considering the current practices of the mathematical society, they are a pressing call to action.”

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