School children often say maths is their most-hated academic subjects.
But this is probably because they just don’t understand how amazing maths can be.
Mathematicians find maths to be profoundly beautiful and incredibly exciting.
Redditor EulerANDBernoulli asked Reddit’s mathematicians about this beauty, which started a very interesting conversation.
Here were some of the notable contributions to the conversation that help get at why mathematicians find the subject to be so moving.
Mathematicians feel a rush when, after a long struggle with a concept, understanding finally dawns:
- IamAlso_u_grahvity: “For me, it’s the ‘Aa, ha!’ moments when you gain insight into a problem. It’s like staring for hours at the streaming green text in The Matrix and suddenly it’s a beautiful woman in a red dress.”
- jsmooth7: “There is also the related, and much less enjoyable moment when everything you thought you knew about a problem crumbles to pieces, all because of one counterexample you didn’t consider. But later, when you finally are able to put everything back together and at last solve the crux of the problem, the ‘Ah ha’ moment is that much more beautiful.”
Learning maths entails a gradual buildup of knowledge, going from having no idea how something works to feeling like it is a part of you.
Maths undergraduate student burne114 asked “I feel like this stuff would require me studying for at least three times as long as I have been to begin understanding. As a professional mathematician, did you have a similar experience as a student?” And he got some great answers:
- gammadistribution: “Everyone has this experience because mathematics is hard and your professors and everyone that came before you has felt the same way. You will always have the notion that you know nothing, because in the grand scheme of things you do in fact know nothing. But that’s ok. That means that you are learning that there is more out there than you could ever possibly learn in a lifetime and can begin to contribute to humanity’s knowledge base in your own way.”
- Pit-trout: “Every now and again, I look back and realise that something that I felt this way about a few years ago, I now not only understand but feel like I’ve always known. Each day, each week even, it feels like I learn almost nothing, compared to how much is out there that I want to learn, or compared to colleagues who are faster or more diligent readers than I am. But somehow, over months and years, it mounts up much more substantially than I always expect!”
Many Redditors appreciate the universal and fundamental natures of maths:
- Byzantine279: “The maths, that is the relationships between things, are there. They have always been there. They exist regardless of us, regardless of the Universe, they simply ARE. All we are doing by proving new concepts is bringing to light immutable ancient truths.”
- beccccca52 puts this very succinctly: “It’s the same in every country.”
Others argued the opposite — maths is a human creation, akin to art or poetry:
- beejiu: “I strongly disagree with this. Mathematics is an art in much the same way that language is an art. Our minds work by recognising pattern. Mathematics is not discovered, it is created. The fact that we have created a Mathematics that is quite useful in the physical world is for one reason: that is is quite useful.”
It might be possible, though, to synthesize these viewpoints:
- Pit-trout: “Philosophers debate endlessly, and sometimes fruitfully, how real and absolute the landscape of mathematics is; but I think hardly anybody would dispute that in a practical, social sense, it’s real. Groups of mathematicians working independently often discover the same techniques and ideas — sometimes almost verbatim the same, sometimes from multiple, illuminatingly different viewpoints. And then — the thing that really reassures us we’re not just a group of conceptual artists scamming society — mathematical ideas often end up having such crucial unforeseen applications in science or technology.”
The ability of maths to concisely and clearly describe relationships is elegant:
- Flame2walker: “Physicist here: I love maths since it allows you to describe the whole phenomena just in one equation/ set of equations. And no word is required. You look at the formula and understand what’s going on.”
Pure maths often has unexpected applications:
- HeartBalloon: “That any mathematical discovery is made by pure curiosity, but find amazing applications.
- Take the Quaternions: Hamilton wanted to answer to himself while studying them and now we fly in space with this system”
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