I suppose one could say that mathematics is an of interpretation of reality, especially if one subscribes to the idea that the "fundamental reality" is ultimately unknowable due to our human limitations, but again, the intent is to represent something in such a way that it is independently verifiable by other agents. As for beauty, I don't think that beauty is necessary for art. I certainly think that a lot of art deals with beauty, but just as much has been created that revels in the ugliness of things, or in some other aspect, which I understand that people often characterize as "beauty". Personally though, I think that particular word works against art of all stripes because by and large, the casual consumers of art tend not to understand the difference between "beautiful" and "pretty." Similarly, most approach the arts with an expectation, not of enjoyment, but entertainment. For example, I might enjoy feeling a particular sadness or feeling a well-crafted loathing for something-- that is, I don't always look for artistic experiences that will leave me feeling good about what I've just experienced, if that makes sense.
Mathematician/engineer here. This discussion of art and its relation to mathematics is very common among mathematicians. Less so among engineers in my experience. I think you've struck on an important point: that aesthetics is not the only element of art. This is why I think using the term "beautiful" is not always appropriate to describe the way a mathematician feels about a particular piece of work. My opinion is that art (a very hard term to define) is intimately related to sharing perspective. I think that our attraction to various kinds of art is the connection it provides with the artist, the story they tell us and the emotions they share with us. For example, a photographer understand and manipulates light in order to convey a view on a frozen moment in time. Similarly, an impressionist painter exhibits his process without being tied so close to a single physical scene. Even comedy works best by making a connection to the audience while providing a fresh and maybe unexperienced perspective on a topic. This is the context I use while discussing the art of mathematics. The formulas and proofs used often do provide satisfaction to the practicing mathematician, in the same way an inspiring painting, photo, musical piece, or comedic bit provides pleasure while inspiring new work. However, I don't think they're "beautiful" in and of themselves. Rather, it's the new perspective that comes with a deeper understanding of the underlying structures you come across. It's the "ah, look at that" aspect that can sometimes be very striking and even emotional. Made all the more powerful by its timelessness and transcension of humanity.
I'm glad to get a perspective from the other side of the discussion! I see what you're saying and I do agree. It wasn't so very long ago that math, science, the arts, religion and magic were all one and the same and it's easy to forget that shared history. I also think that the way that knowledge is divided into subjects is somewhat harmful to public education. For example, some understanding of earth sciences and chemistry is very useful in arts such as sculpting and painting and of course, history ties those subjects together in yet another way. The ideas of revelation, understanding, mastery and transcendence are common to all disciplines, so I have a hard time understanding why practitioners of those many varied areas of endeavor are sometimes quick to dismiss the works and efforts of others. I could be very wrong, but I suspect that while we are now in an era where the artistic and scientific are fairly well delineated, that in time the two will once again mutually inhabit certain spaces in the human experience.The formulas and proofs used often do provide satisfaction to the practicing mathematician, in the same way an inspiring painting, photo, musical piece, or comedic bit provides pleasure while inspiring new work. However, I don't think they're "beautiful" in and of themselves. Rather, it's the new perspective that comes with a deeper understanding of the underlying structures you come across.
It's the "ah, look at that" aspect that can sometimes be very striking and even emotional. Made all the more powerful by its timelessness and transcension of humanity.
It does. I like works like that (And hate it when people don't value something because it doesn't make you feel good), but I suppose like you said, I just clump it all together under "beautiful", knowing the distinction between the words beautiful and pretty. I suppose maybe beautiful isn't the best word for it either since it leads to that kind of misunderstanding.I don't always look for artistic experiences that will leave me feeling good about what I've just experienced, if that makes sense.