## Todos Cuentan (Everybody counts)

In a beautiful NAMS 2016 article Todos Cuentan: Cultivating Diversity in Combinatorics, Federico Ardila put forward four thoughtful axioms which became a useful foundation for Ardila’s own educational and outreach efforts, and were offered as a pressing call to action for the academic community as a whole. (See also here, and here.)

Here are the axioms

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

Of course, these axioms extend even further when you replace “mathematics” with other academic areas and also with “art”, “music”, “sport”, “literature” “business” “politics”, etc.

My view is quite close to Federico’s view.

Two remarks: First, I learned from Ardila’s paper, interesting mathematical results that I did not know about. One result is by Anastasia Chavez and Nicole Yamzon about Dehn-Somerville’s relations that we mentioned here several time (I, II, III, IV). Chavaz and Yamzon’s paper is The Dehn-Sommerville Relations and the Catalan Matroid. The Dehn-Somervilles relation asserts that the affine dimension of *f*-vectors of simplicial *d*-polytopes is *[d/2]*. We can ask which *[d/2]* coordinates of the *f* vector determine the other coordinates. (If I had to guess I would have said that every subsets of *[d/2]* coordinates spanned the other coordinates; but this is incorrect.) It turns out that the answer is related to very interesting combinatorics.

Second, I was quite surprised that I came across Ardila’s paper and axioms only now, almost five years after the paper was published. I could certainly referred to Ardila’s axioms had I known about them in a few tedious (while important) discussions on the matter, and in a short (here, shortened further) letter to the NAMS editor that I wrote on the subject in 2019.

Dear editor,

In my opinion, diversity is an important social and academic value, the pursuit of which can also be an important means for academic excellence. One reason we need to pay special attention to diversity is that there are various mechanisms against it, which in and of themselves are harmful to academic life and excellence, such as dominance and, at times, even bullying by members of majority/power groups. On this and other issues, academic institutions have the right and duty to form academic policies and pursue them, and also the obligation to allow free debate about these policies.

—Gil Kalai

Hebrew University of Jerusalem and IDC, Herzliya

(Received November 28, 2019)