By Luna Lomonaco
Mathematics is a perfect world; it's up to us to create it or discover it
A few years ago, I was in a bar in Toronto listening to a band. When the performance was over, one of the instrumentalists came to my table, the only full one besides that of the musicians' friends. I was the only woman at the only occupied table, and the guy started hitting on him. Smiling, he asked me who I was, where I was from. The third question was what I was doing in the city. I said it was math, and I was there for a conference at the Fields Institute. Before I even finished the sentence, the guy turned around and left.
This was the most extreme reaction I ever provoked when I introduced myself, but I'm used to facing a dose of skepticism, incredulity, I would even say disappointment, when I say what I do. Often, after the interlocutor of the time confesses to me how good or bad he was in mathematics at school, and especially how much he hated or loved the subject (I don't know why this confession always appears, but the fact is that it always appears, and surprising by this subject that many consider “cold” to arouse so many emotions), the questions that follow are of the style: “Are you math? You mean you teach math classes? ”, And I:“ Well, I teach math classes, but I also do math ”. “Do what? Do you count? ”. "No, actually I don't even see many numbers in my day to day, I try to demonstrate theorems". At this point, the interlocutor usually says "Oooh", sometimes mentions Pythagoras, but in general he doesn't ask any more questions – and sometimes he starts looking for a delicate way to turn around and leave.
What do I do while math? I try to understand what we have done so far, more precisely a part of the math that has been done so far, and I try to create (or discover) more. Why?
I have been doing math for sixteen years, and I have been asking myself this for seventeen (because I started in the last year of elementary school, when I opted for the discipline instead of studying philosophy or anything else). I think the answer is: "To try to discover the truth". When we demonstrate a theorem, what is written in that theorem becomes true, absolute truth: there is a demonstration, this means that there are logical steps that can be followed to arrive at that. And anyone can go through these steps – just study to understand them.
The truth does not change by changing person, gender, race, country, continent, culture. The truth is true, and it will always be true. This fascinates me, and besides fascinating me, it summons me. Because there is something in me that makes me try to be absolutely sure of what I think is true, and tries to define it, demonstrate it, and separate it from what is a lie. There is something about me that seeks a perfect, coherent, consistent world. And then he creates it: a wonderful parallel world where everything makes sense. For that aspect, I think of mathematics as an art form, the expression of a perfection that something within us yearns for.
On the other hand, I consider mathematics a part or a kind of platonic hyperuranium: the world of perfect ideas (we, here in the real world, experience copies of these ideas, and try to understand the world through science, which uses mathematics). And in that sense, this perfect and exact world is not created by mathematicians, but discovered. The theorem I'm trying to demonstrate, others have tried to demonstrate it, and if yours doesn't get there, someone else will. The theorem exists independently of me. In this way, mathematics is a perfect world that exists independently of us, already existed and will always exist, it is just waiting for someone to discover it and map it: demonstrate it through logical steps that anyone can follow, if want to visit it.
Why do I do math? Because I don't know if we create or discover, but I know that, in one case or another, for me, it's worth it: if something perfect can exist, I want it to exist.
Luna Lomonaco is a researcher at the Institute of Pure and Applied Mathematics (IMPA)
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