Held Accountable

A few weeks ago, I asked my fellow graduate students to give their list of the “Top N Mathematicians of All Time.” In return, I was publicly shamed by my good frenemy, K¹.

K believes that asking “who is the best mathematician” of all time is exclusionary. No matter how you cut it, you will leave out women who were barred or discouraged from math, historical figures whose discoveries we gloss over, and so on. K was incensed enough to give a talk to the graduate students entitled “A Clapback Talk: what a recent Slack thread reveals about inclusivity in math,” where K intended to “hold me accountable for my actions.”

Well, consider me held accountable.

K’s arguments fall in two main directions.

1. Mathematics is not a competition, and we shouldn’t rank people.

2. Mathematics has historically excluded women, and by not acknowledging this we perpetuate that exclusion.

MATHEMATICS IS A COMPETITION

K’s favorite phrase is “mathematics does not exist in a vacuum.” I agree, it does not. It exists in societies with finite resources. We can’t hand over infinite amounts of time and money so that very privileged people can sit in lecture halls all day thinking about “mathematical truth.” It is lovely that mathematics is a boundless ocean of knowledge or whatever, but we have houses to build, bridges to repair, and doctors to train.

We have finitely many dollars to do mathematics. How do we allocate them? We can only afford to accept so many graduate students, hire so many professors, fund so many postdocs, and so on. It would be stupid to make these choices at random, so we have systems to decide who gets money. You’re welcome to pretend that these systems don’t exist, but most people will work to put themselves in the “funded” category. This is competition.

Unless you think we should put limitless funds into mathematics (and we probably literally can’t), mathematics as a social activity will not exist without competition.

In many mathematics departments around the country, graduate students are privileged enough to ignore competition. You have to compete to get there, but after that you’re basically safe. You don’t have to apply for grants or fellowships or anything like that. Just pass your exams, don’t harass your students, and you get money for five to seven years. Everyone is allowed to do more-or-less whatever they want and poor performance has few consequences. (If I hear “grades don’t matter” one more time, I will lose it.) We sit in a cushy ivory tower and talk about how “it’s not a competition.” Nonsense.

Compare this state of affairs to sports. Despite what your closed-minded academic friends might think, sports are an art form. They reflect the extremes of humanity: Camaraderie. Rivalries. Triumphs. Falls. Determination. Pettiness. All of human nature on display, driven by superstar, larger-than-life figures.

At first glance, athletes at the highest levels seem like special people. They want glory, to be champions, to be one of the greats. Michael Jordan takes everything personal? Inject it into my veins. Tom Brady counting off all six quarterbacks picked before him? Captivating. After winning two gold medals at the 2016 Rio Olympics, what was Elaine Thompson-Herah’s goal for Tokyo 2020? “Get three gold medals.”

We love athletes because they are not special. They are like “funhouse mirror” reflections of ourselves, distorting our natural features almost beyond recognition. Competition, envy, and greed are normal. They drive us to be better.

Richard Hamming says as much in “You and Your Research”:

At Los Alamos I was brought in to run the computing machines which other people had got going, so those scientists and physicists could get back to business. I saw I was a stooge. I saw that although physically I was the same, they were different. And to put the thing bluntly, I was envious.

Chess grandmaster Bobby Fischer said that the greatest pleasure of winning a game of chess is “when you break [your opponent’s] ego. Hardy wrote “A man’s first duty, a young man’s at any rate, is to be ambitious.” Even Obama is competitive:

Mr. Obama’s obsession with virtuosity and proving himself the best are remarkable. … More than a tic, friends and aides say, it is a core part of his worldview, formed as an outsider child who grew up to defy others’ views of the limits of his abilities.

If you are, by nature, less competitive than your peers, or find it distasteful, that’s fine. No one is forcing you to be as intense as Michael Jordan or Tiger Woods. However, do not expect to be funded to prance around academia forever. There is no “right” to be an academic. If you want to be one, accept competition.

EVERYTHING IS EXCLUSIONARY

We can all agree: Mathematics was grotesquely exclusionary until like, twenty years ago. There are probably ways that it still is. We should look into that. But what does this have to do with how great Euler was?

Again, I wish more of us were sports fans.

When I look at the greatest basketball players of all time, I don’t find a lot of 5’9” Whites from South Carolina. I don’t see a lot of Asians, or Hispanics, or anything else. Just Black men. And that’s…fine? I don’t see how this takes anything away from me. Of course, I’m White, so maybe I’m just “letting them have one.” Then why is the NBA the biggest sports league in China, despite having only one good Chinese player ever? What would K’s objection in this context even look like? I walk into a pickup game and ask everyone to stop yelling “Kobe” when they take a shot?

No one is excluded from mathematics by being left off the list of “best mathematicians.” They are excluded because of things that people did in the past. That’s a shame. We shouldn’t do those things anymore. But we also can’t change what was done in the past.

Maybe there would have been dozens of incredibly influential female mathematicians if we were more welcoming to them. Maybe Frederick Douglass would have been a legendary president if America were not suffocated by racism during his life. Maybe every poor kid in Missouri on food stamps could be the next Einstein if they had the resources.

Maybe maybe maybe maybe. Maybe this, maybe that. We don’t know. We can’t know. There are infinitely many “maybes,” and every choice produces infinitely many more. We cannot refuse to talk about the past because someone was excluded. All we can do is make choices now based on what happened.

If you want to discuss “most promising mathematicians which were not allowed to do mathematics,” then go for it. I love “what if’s.” But this is simply a different discussion than “most influential mathematicians,” not a better one. To suggest that either is “unsafe” is just as naive as saying that “mathematics is not a competition.”

The really sinister thing here is that the charge of “being exclusionary” is too vague to answer. How could you possibly prove that you are not being exclusionary? It’s a rhetorical flourish to combat a deeper problem: There are not enough women in mathematics Ph.D programs.

Roughly 40% of mathematics and statistics undergraduates are women, but that drops to around 25% in Ph.D programs. That’s a big gap, and it’s not clear why it’s there. This gap is not present in many other fields. In fact, women make up a majority almost everywhere but in STEM fields.

K, like many of us, thinks that there are “bad things” dissuading women from joining Ph.D programs, and would like to fix them. But K, like most of us, doesn’t have much control over the situation. You can only attend so many conferences for women, run so many woman-focused organizations, and lobby so hard for your graduate director to accept more women before you realize that changing demographics is very slow. So, if you’re really driven to bring in more women and secure their place in academia, you have to find something else to do.

In this case, the “something else” was dragging us all into a reeducation session. Was this the appropriate response? Well, academics should say what’s on their mind. That’s the whole point of being one. On the other hand, since there is clearly stiff debate surrounding inclusivity, giving a talk “holding people accountable” for their views seems like an overreach.

Either way, it was a fun few weeks. Happy Thanksgiving!

[Note: In an earlier version of this post, I used K’s name and insinuated that they were a “bully” in some deleted paragraphs. After reflection, the former felt like airing dirty laundry, and the latter was just mean-spirited. Both are gone now.]