## 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)

Academia provides a sandbox for the advancement of society.

The first axiom does not contradict the laws of probability only if the density of mathematical talent is a delta function, I mean, it is zero everywhere.

The earth is a compact set, so there is no contradiction. If you’re going to be pedantic at least be correct.

I didn’t get it. How the compactness helps here?

Feel good axioms notwithstanding, here is a somber analysis of what is going on on the ground:

https://quillette.com/2021/08/19/as-us-schools-prioritize-diversity-over-merit-china-is-becoming-the-worlds-stem-leader/

Dear Sasha, thanks! I don’t think the issue here (in Ardilla’s approach) is “diversity over merit” but rather “merit through diversity”. I hope mathematics will flourish everywhere.

Dear Gil,

We all hope. Pesky reality, however, may be out of touch with our hopes. One can argue that the destructive policies described in the article by Deift, Jitomirskaya and Klainerman are just some unfortunate distortions of noble and virtuous ideas. Perhaps. Shouldn’t one ask then, why some ideas get distorted so easily and so frequently (and some other nice sounding ideas, such as communism, for example, seem to be distorted with terrible consequences every single time they are implemented on any sizable scale)?

This is not to question the work Federico is doing. It is the “sloganeering” component of the post that worries me.

(Revised, and much shorterned) Wow, until you mentioned it is I didn’t even notice that the paper is written by Percy Deift, Svetlana Jitomirskaya, and Sergiu Klainerman (DJK)! My initial reaction is that I agree with the efforts to improve K-12 mathematical education, and I don’t share the authors’ concerns regarding diversity.

Clearly nobody can literally believe Axiom 1. Really, *equally*? In *all* groups? The Ashkenazim included, for instance? What about, say, “the children of mathematics professors”? It’s preposterous for any interpretation of the term “mathematical talent” that doesn’t trivialize the phrase by equating mathematical talent with the potentialities encompassed in Axiom 2. It’s very frustrating that people with laudable goals and interesting projects can’t seem to stop themselves from saying things that make no sense, without even feeling the need to defend them. It is counterproductive to talk nonsense to mathematicians.

Hi Kevin, Sure “Ashkenazim” (namely Ashkenazic Jews) form a large group of the Israeli population and I firmly believe that they are not more talented (nor less talented) in mathematics compared with other groups in the Israeli society.

As for children of mathematics professors, this goes beyond the scope of Ardilla’s axioms. It is reasonable to think that on average they are more talented in mathematics compared to the general population but less talented in mathematics compared to their math professors parents. (By regression to the mean).

It looks like science won this round.

News

The first axiom is not plausible in running.

https://www.unz.com/isteve/fastest-running-times-by-distance-by-race/?highlight=100+meter