I have an issue. I love mathematics, i enjoy it as one of my favourite past times. I enjoy exploring ideas and reasoning. Over the past few years it has been an ideal of mine to be a mathematician, but over time i have become slightly disenchanted with the field of PURE mathematics. I have begun to question why i must play with groups, fields and rings. I want to find a deeper meaning and TO ME mathematics does not give answers to the fundamental questions of the universe, in fact i challenge anyone to tell me how mathematics alone is anything more than a game. Where mathematics becomes the most wonderful of all subjects, is only in conjunction with physics. The two go hand in hand. But i digress. When i was 15 (only a few years ago) i was obsessed with the idea of becoming a great mathematician, and to that extent exploring mathematical beauty. I had read of this beauty in the books of E.T Bell and listening to conversations with the great mathematicians. Yet when i explored mathematics i did not find beauty, i only found truth, truth such as a wading through pure binary would provide. You see, what mathematics provides is truth, truth in the platonic realm of mathematics. I argue that truth is not beautiful. Truth is just so. To express it as beautiful is to gain pleasure from it. To a large extent i believe you can gain pleasure from mathematics, but i do not agree that that makes it any more beautiful than breathing or eating. Some claim that mathematics is the IDEAL subject, that it is more fundamental than ANY other subject, be it physics, chemistry, law, history, medicine, art. That Mathematics is somehow reading the mind of god. I disagree. Mathematics is a game we created. Some claim it is an art. To a large extent i agree, but it lacks the creativity of art (AHHHHHH i hear you shout, an Unbeliever), i define creativity as the ability to think outside the box. To a large extent you must do that in mathematics, but you can never truly step outside the box and question the axioms of mathematics. That is where i lose the beauty of mathematics. Math is useful, but it is not beautiful. If it was beautiful it would be robbed of its function to be useful. If it were beautiful we could express our very feelings in it. We cannot do that. Beauty is subjective and mathematics is not. I believe there is a cult surrounding mathematicians today. A cult of some percieved genius. Firstly they seem to believe that their field alone is important and secondly they believe that you have to be the cream of the crop to persue PURE mathematics. What if it begins to bore you, all this talk of hilbert spaces and metric spaces, which have nothing to do with space, or you question the deeper reasons for something? You are labelled as to stupid to see the beauty of mathematics and forever seen as an uneducated moron. Well the time has come to face the music. Mathematics is not the queen of science, she is the handmaiden of physics. Anything more than that is playing a game. A game with rules that have no justification. A game which i do not deny is enjoyable, and this is where i suppose the "beauty" is, but that is often labelled as the intellectual jewel in the crown. Despite all i have said i still enjoy some aspects of pure mathematics. I will not be surprised if you all hail me a fool and a moron, just don’t do so without providing reason. For without reason there is nothing.
I can sort of understand what you mean, I think. But I fail to see the logic of what I just quoted. Beauty is indeed subjective, and mathematics is not. That doesn't logically imply that objective mathematics can't be subjectively beautiful to some. To me, there's something truly beautiful about Cantor's diagonal proof. The elegance and simplicity of the argument astounds me. To me, it's truly beautiful. And beauty is subjective, so who can argue that I shouldn't find it so? Who can argue that you must find it so? And if it's a game, then so be it. That the results of that game so often find applications later is great. Can there not be beauty in something merely because it's game? Is it less beautiful because it has no immediately obvious use? I don't see that. I wouldn't say that at all. I'm surprised that you don't see much in the way of beauty in it, but everyone's different. Maybe pure math just isn't your thing. That certainly doesn't make you a fool. Beauty is subjective. Of course, in my opinion, if a great many people see beauty somewhere and I don't, it makes me wonder if I might be missing something. One might interpret your post as such.
If anything Grep, i wish i could find the beauty in mathematics again. Is it common to go through phases of disillusionment? As for your quote. you are indeed right you may find mathematics elegant or simplistic, but that does not make it beautiful. Infact if mathematics were so beautiful then why is it so simple? Or is the beauty in the simplicity. To be honest i am only just discovering my mathematical philosophy and i was hoping you guys could help me learn more about the beauty of mathematics, if there is any at all. (i hope so).
i use space in a philosophical/metaphysical relation. Obviously metric spaces take into account our notion of distance, but they are not abstract forms, like i imagined them to be. Then again feel free to prove me wrong. Infact i would be quite happy to be wrong on this occasion.
I think you should first define what you mean by abstract since your definition doesn't coincide with that of anyone else.
What i mean is that we can somehow visualise these spaces. Instead we must use parameters to describe them.
I would think it's not totally uncommon. Certainly, someone dealing with depression would likely feel that way (and I'm not suggesting you are, but it's something to consider as a possibility). I'm not a mathematician, myself, though sometimes I think I missed my calling. I do it for fun, because I want to. Perhaps that's part of it. If I had to stress out over "is this productive?" or such questions, maybe it would ruin the magic for me, I don't know. I do it because I love poking at the Universe to find out what comes out. All I know is that it's fun for me, so I do it. I don't have to feel guilty about it, because it's a valued skill. I also adore physics (being cursed with boundless curiosity), and I need the math for that. Funny how some part of math suddenly becomes fascinating when I need it to solve something that interests me. I didn't mean simplistic or simple. In fact, though the basic stuff is really simple, I'd say some of it is really quite complex. But I find the proofs and parts of math I find truly beautiful are also usually simple in their essence. Always hard to describe reasons for subjective things like this. I do think that math requires a great deal of creativity. Look at Cantor's diagonal proof. That required quite a lot of creativity, I think. Looking at it like a great piece of visual art, one might find great beauty in how a painter can say so much with so little. That takes creativity and grasping the essence of the thing, and representing it in as simple a manner as possible. People might say something like "He says so much with a single line!" I can understand that reaction. And Cantor's proof is like that. It allows you to grasp the essence of the thing, and does so in a way that's not more complicated than necessary. And in so doing, it allows you to understand some small part of eternity. It's almost poetic. Speaking of poetry, here's an example from Shakespeare's Romeo and Juliette: "What's in a name? That which we call a rose By any other name would smell as sweet." So much said with so little! Elegant, simple, and truly profound. And really beautiful. To me, it's beautiful in much the same way as Cantor's diagonal proof. An almost identical aesthetic response, for me. I'm not sure it's entirely possible to describe why one sees something as beautiful to someone, and have them really get it. But I suppose it can't hurt. I hope you find what you're looking for.
First of all, if you knew any logic such as model or set theory you would understand immediately why math is not just a "game". In fact it surprises me that since you are interested in philosophy that you would not find results such as Godel's Incompleteness Theorems to be extremely meaningful. And you cannot just lump mathematics together with "breathing and eating" as just different forms of truth. Math is beautiful precisely because it is constructed using the rules of logic alone, created within the human mind rather than the outside universe. Everything in mathematics is rationally motivated. Its truth isn't just a set of arbitrary facts. The reason why everyday phenomena such as eating and breathing are not beautiful is because these things ARE arbitrary - there may very well be no rational motivation for why these things happen to be the way they are. For this same reason experimental sciences are often ugly. There is far less "cult of genius" surrounding mathematics than physics. Being a mathematician gets you very little recognition from the public, no matter how successful you are. No one wants to write a news article about math research because you can't just give a half-baked description of results like you can for physics, so the layperson wouldn't be able to understand. Plus physics is far flashier and superficially impressive than math. I completely disagree with your claims about math being less creative than visual arts, literature, etc., but I don't want to take the time to refute them at the moment. As Hilbert said of one of his students who decided to leave math to become a poet, "Good - he did not have enough imagination to become a mathematician." Your various misinformed statements such as "metric spaces have nothing to do with space" and your complaints of math being boring and lacking in depth demonstrate a fundamental misunderstanding of mathematics. Not just a misunderstanding of the technical aspects, but of the motivation and intuition behind concepts such as metric spaces. Understanding the motivation and intuition is the key to appreciating beauty. It seems to me that what you need to do is put more effort into thinking long and hard about the motivation behind what you are studying. You can be certain that almost everything in math has an extremely nice piece of intuition behind it, and you shouldn't dismiss things as boring before you feel like you have a very solid grasp of this intuition.
I have often wondered this aswell. My reasoning for pure being beautiful is that subjects (such as math, physics, biology, etc.) are like people. Just because I find someone to be beautiful doesn't meen my best friend will agree! Like wise, when my friend says "she has beautiful hair" (physics is beautiful) I may disagree, "her hair is ugly!" (physics is not beautiful). all-in-all: beauty depends upon the person and to me math is a beautiful girl. (also i do enjoy physics, it's not ugly)