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Why Mathematics is Lonely


Jun 22, 2024··[thoughts][mathematics]

Kutay gives insights into why mathematics may be "lonely" and why that might not be the case.

After a really long time, I am finally writing a post that is essay-esque, which will be about why I think mathematics is lonely. I watched a video about on this, and I wanted to write about it too (maybe in more depth). Note that I am not a maths student (I will be majoring in computer science next year), but I think I can give some insights around the topic. I found a couple reasons to why mathematics is lonely—around our culture and even between mathematicians—and why there is some hope.

Specialisation

Mathematics is a very old subject (it has been around since Egyptians and Mesapotomians, nearly 4000 years ago) and the amount of mathematics known (and the amount of science known, in general) has grown to incredible amounts in the past couple of centuries, with no end to see. This has resulted in researchers needing to be really specialised in a field (or even a subfield) to create new knowledge most of the time. Therefore, the best mathematicians alive now know only very limited amounts of "mathematics." The amount of mathematics today can be visualised by looking at the Mathematics Subject Classification System, where it tries to list EVERY item of interest in mathematics. That document is 224 pages long—reiterating, it is two hundred and twenty four pages long. As a result of the sheer amount of mathematics in today's world, many mathematicians studying, for instance, number theory or algebraic geometry may specialise in totally different subfields and may not able to understand what others are researching. And, the reason that one's paper may not be read that much is not because that person is a single unknown mathematician, but it's because only so many people can read and understand what you wrote. In other words for a mathematician,

Only a handful of people can understand the thing you devote your life to. (Some random person on the internet)

Esotericism

The video linked above argues that mathematics is a body of knowledge that is hard to understand as an outsider, and that it takes a really long time and a lot of effort to become an insider. By contrast, this is not the case for music and art, since "outsiders" to them (the general public) can understand what musicians and aritsts create by just listening to or looking at the piece. Like when my friend composes a piece on GarageBand, I can listen to it and easily see the beauty of the thing they created and worked on without understanding (or even knowing) the theory behind it, which I'm sure that he hammered away at learning it.

However, this is really not the case for mathematics, the general public cannot "just" look at a theorem and understand its beauty in mere seconds (which was the case for, such as, paintings and sculptures). As a kind-of-an-outsider, I cannot just understand the following one-sentence proof that every prime p=4k+1p = 4k + 1 is a sum of two squares1:

One Sentence Proof

This proof is actually a condensed—and I mean, REALLY condensed—version of another quite elegant proof of the same problem by Roger Heath-Brown. The proof is said to be a Book Proof and is in Proofs from THE BOOK. Even if I look at this proof for hours, I still wouldn't understand much and wouldn't be able to see the beauty, because one needs to be a mathematician to understand a mathematician.

One might think that this is also true for more science-y areas of knowledges, such as physics or computer science. While it is true to some extent, since the techniques in those areas may be esoteric, the things they are about are not. So for those researchers, their technique serves their art, but for mathematicians, their art is their technique. You just can't share you study as a mathematician.

People just don't get it/hate mathematics

As I was researching and thinking under this subtitle, I found lots and lots of things to say, but unfortunately I don't have enough space and time to discuss all of them here. So, I'm only going to mention a couple things here, but I'll write another post probably under the title "Why People Just Hate Mathematics."

In high school, I was not bad at mathematics and seemingly passed exams without any effort, which resulted in me being the "smart" one in class and even being told to "shut up, you're good at mathematics, you don't have a say in this" when discussing the questions in the mock that we just took for IB Mathematics AA. I don't agree with this stereotype that being good at maths is equal to being smart. Logic is inherent for some people, but not for others. It can be hard for someone's ego to fail at something repeatedly, and it can sometimes be easier to hate the external thing or the thing that is different from you (the ones that are "good" at maths) than face one's own limitations. And, developing these feelings towards mathematics can lead to a lifelong dislike for it, which results in people just not getting why we love mathematics or feeling distant to people that are good at maths, studying maths, or doing mathematical research (even when we don't feel the same way towards them just because they have problems doing maths). Another example is that after we took the university entrance exam here, many of my friends that I talked mentioned that they were finally able to leave mathematics behind their backs. I kind of get this because they won't need mathematics in their future careers/lives, since the ones said that were mostly going to study medicine, law, or something that isn't related to or not closely related to mathematics. But, even then, if the mathematics education were not this atrocious and allowed people to learn the intitution and the "why" of the concepts of mathematics, then maybe people wouldn't be this biased towards mathematics and maths people.

This isn't the whole picture

While mathematicians seem to be "lonely" and "alone" from the outside—working in the basement and coming out only when they solve a famous problem (this is a joke)—I do believe that mathematics is one of the most social sciences. I know this might appear as impossible, but most mathematicians talk to each other a lot. They talk about problems that they are trying to solve using a pen and some tissue paper on a coffee table in a random café. Because they have something—just a single thing—common between each other: deep obsession about mathematical problems. This is also true for computer science and physics too. I remember discussing competitive programming problems on whiteboards during an olympiad in informatics camp—and remember that we are programmers, coders, and to-be-computer scientists; we are as anti-social as it gets. But, this "fever" towards a common ground is what makes us not anti-social (yeah, I just can't say "social").

Being social in this field is a necessity too. The human brain is so small while mathematics is so big and complex, so cooperation is a must for advancing in the field. Even if the conversing mathematicians are specialised in very different fields, it is always a possibility (which is higher than what one might think) that one of the people that you are discussing with listened to a conference or read online about a similar problem that you are trying to solve, and without you even know it, you are collaborating with researchers all around the world to solve that problem.

So start collaborating. Make sure that you tell all your mathematical friends about all the things that you are working on, especially the things that you are having trouble with. Don’t worry about competition or ideastealing. Mathematics is a giant—indeed, universe-sized—commons, where everyone can and should plant crops; sharing, creating, struggling, and sharing some more. And don’t forget to have fun! (Paul Zeitz)


Footnotes

  1. https://www.jstor.org/stable/2323918



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