Because we are not mathematical machines. We live, we breathe, we feel, we bleed. If your students are struggling, and you don’t acknowledge it, their education becomes disconnected and irrelevant. Why should anyone care about mathematics if it doesn’t connect deeply to some human desire: to play, seek truth, pursue beauty, fight for justice? You can be that connection.
(Francis Su, Mathematics for Human Flourishing)
Mathematicians learn from a very young “academic” age that, to thrive in our environment, we need to be confident, brilliant, fast. Talking over others is advised, together with delivering inaccessible talks — the sure sign that the mathematics you are explaining is, in fact, so difficult and hard that only you could understand it and do it. Asking “stupid” questions in seminars is ill-advised: you surely don’t want to be labelled as the one who didn’t know that basic definition, right?
When we sit in the audience of a talk, we often do it with the expectation that the talk will be completely inaccessible. We are ready to pull out our phones and start scrolling Twitter as soon as the “introductory” bit. Presentations are delivered in a style that closely follows Euclides’ Elements — definition, proposition, theorem, definition, proposition, theorem; rinse and repeat. Results are often presented without a word on what the underlying motivation is, without a hint towards the intuition for a certain object. The audience is expected to just sit in stunned silence.
It is somehow assumed, and accepted, that mathematics cannot be properly communicated. Or, even worse, that the proper mode of communication is a display of strength and confidence, weaving together obscure mathematics and concise exposition to make sure that the audience knows that you are, indeed, very smart and brilliant (and possibly hireable).
A lot of the time, none of this is done on purpose, or maliciously. It is a wicked combination of a crashing job market, our own insecurities and a culture that prizes those who can project high computational capacity. Getting outside of this nasty feedback cycle is hard, impossible even — especially for members of historically disadvantaged minorities, for which the road is already artificially uphill to begin with. No one can be blamed for their survival strategies.
The prestige that comes with obscurity
Much of how mathematics is communicated among mathematicians has a partial origin in how mathematics is perceived and narrated outside of the mathematical community. As a subject, mathematics has always been depicted somewhere on a spectrum between funny, quirky puzzles and impossibly complicated, arcane knowledge.
The effects of these narratives ripple throughout society. As an Italian mathematician, I can’t help but notice how this paints a very curious scenario in Italy’s public opinion. Whereas the public would find it inacceptable for a politician or a policymaker to be completely ignorant in language, literature or even basic science, it is considered perfectly fine to not understand any mathematics at all. In fact, it is encouraged in a way, because it turns the politician into somebody close to the public, un “uomo del popolo”.
Why is ignorance of mathematics widely accepted, even encouraged? Why do so many adults grow up wounded by mathematics to a degree that they just refuse to engage with it? How come the teaching of a subject that, especially nowadays, is essential for all matters of democracy is not under heavy scrutiny, trying to find the gaps?
And what are mathematicians doing about it? Most of us throw our hands in the air: nothing can be done about it. We have tried our best — some people “just don’t get it”. Yet, when “some people” is most of the population, one might be tempted to consider that, perhaps, the problem is not on the receiving end of this communication.
Perhaps the main problem is this perception of communication as having ends, instead of being more circular, an ongoing conversation rather than filling an empty vase. Even though this is more of a widespread problem in science communication, it evolves into a particularly nasty beast when mathematics is involved. There is prestige in being the holders of obscure knowledge. There is power in being able to get close to this horrid black hole that most people are (rightfully, due to how it was taught to them) afraid of.
Much alike priests of some cult, mathematicians are often shy of making structural changes in how mathematics is taught because of the fear that, if they did, they would lose all the respect they have “earned” by being experts in a subject that is so far away from the public’s understanding. They worry, consciously or not, that showing grace and vulnerability will lead to the loss of a certain image of the mathematician, one that is both hurtful (especially to those who don’t conform to the unwritten rules that come with it) but also prestigious for those who can hide behind it, wear it like a mask. Mathematics is widely perceived to be “objective,” and with this picture comes prestige — those who master it must be also masters of logic, of reasoning, computer-alike thinkers who know the secrets of an inaccessible reality.
If we want society’s perspective of mathematics to change, if we want people from disadvantaged minorities to thrive as professional mathematicians, if we want to equip the general population with the tools they need to defend themselves against all the ways mathematics can be used against them, we have to stop treating mathematics like something that must hurt. We have to put our foot down and decide, consciously, that mathematics is not a contest of confidence, bravado, a way to display how smart we are to others.
It’s more than that. We have to understand that cleverness, or the display thereof, is not an excuse to be despicable human beings. The mathematical community can survive if less open problems are settled in the next ten years. It will only rot and shrivel if it allows bullies to thrive because of their perceived skills and acume. What’s the point in advancing mathematical knowledge faster if, in doing so, it leaves so many people behind? If the presence of “highly-skilled” bullies pushes away people and wounds so many? What is the point of pushing for diversity and inclusion if the environment we want to open up is deeply toxic for those who enter it? If the mental health of those who try to enter the community is seen to rapidly worsen, under the pressure to always perform, to put on a façade of machismo and bravado, always doubting your own skills and comparing them to the ones of others?
Is advancing mathematical knowledge really worth all of this?
I can’t put it any other way: it is not. So many still believe that, well, that one mathematician is certainly an awful person, a bully and an harasser, but they produce such deep mathematics, surely we can’t get rid of such a smart person?
The world is full of smart people. Prioritize finding the kind ones.
And this applies to mathematical communication too. We need to embrace our own vulnerability and genuineness — we need to accept that teaching and explaining mathematics is not a confidence contest, a race to showcase how smart we are. Talks and lectures should convey meaning, help people understand. Attending a conference shouldn’t teach a PhD student to be cynical and hopeless. It should be an occasion to exchange knowledge. And this conversation cannot happen without a space where people feels comfortable asking the “stupid” questions, where explanations are tailored to the audience to make sense to them, where accessibility and clarity is favoured over stunning displays of ability.
This starts with the speakers. Not every talk is a job talk. A presentation shouldn’t have, as a upshot, “look how smart this person is”.
It continues with the audience. Nobody should be judged for what they know, or they don’t. Whether or not a person conforms to artificial standards of “professionalism” has nothing to do with the content that they are trying to get across to you. If you don’t like how somebody decides to (respectfully) express themselves, you know where the door is.
And it ends with how we write papers, how we talk to the public, how we explain mathematics to our families and friends. It is high time we get rid of the aura of mystery and elusiveness, and start ripping the veil that stops the public understanding of our topic.
I don’t believe that this is wishful thinking. I believe that this is the only way to ethically and sustainably move forward, as a community. Changing the culture, and the narratives around us, is a necessary step if we want to burn down the stereotype of mathematician that is so effective in keeping people out, or hurting them to the point that they are forced to leave.
And it’s not only because of moral reasons (even though they should be more than enough). Sooner rather than later somebody will realize that, on top of fostering an environment that is effectively hostile and discriminatory, we are also essentially self-regulating, choosing what is relevant in a completely opaque way, and refusing to effectively explain our work to the outside world (and in fact, even to ourselves).
And then not even the accumulated prestige over the centuries will protect us.