I have never looked at math and saw this beauty people describe. Math to me is as beautiful as an angle grinder, it’s a useful tool that hates you and plots your demise.
See that seems like the kind of thing Matt Parker would make a video about, “Someone noticed a weird pattern in some numbers.” Like how 2 pi or the fibonacci sequence keep turning up in nature, and I just can’t muster up much more than a “…huh” about it. I mean I understand margesimpsonpotato.jpg but if you want me to do calculus you’re gonna have to bring me more than “I just think they’re neat.”
Just in to say, I know exactly what you mean, and I love the subject, to the point I did a PhD in pure maths. The whole “golden ratio” in nature, and a lot of other adjacent stuff, leaves me indifferent at best, and really irritates me at worst. It’s often cheapo mathy wank to feel clever when you talk to your friends. There is nothing wrong in being interested in it, but I’d hope someone into maths would eventually go beyond that.
I also am not a fan of several very useful branches of maths, like calculus, but it’s a tool you need to have. Some people love it though, and I scratch my head at it as much as you do, if not more probably, because I have had to use it so much.
There are probably as many reasons to find maths beautiful (or ugly) as there are people, but for me it boiled down to the fact that:
with relatively few assumptions, we can logically and iteratively build an abstract machinery that is consistent (well, with caveats…);
a lot of these abstract theories provide good enough frameworks for other sciences to base theories on and be successful at explaining the world with these (I could talk about the fifth axiom of Euclid, non-euclidian geometries, and how we eventually arrive to something that is a formal setting for the theory of relativity for hours, it’s fascinating);
it provided me with abstract objects that I could reason about, explore in different ways, and with different points of view, until something clicked and I got to understand the objects better;
some proofs, even of quite complex theorems, have such a simple and elegant initial idea (when others can feel quite forced), that it is hard not to marvel at how things fall neatly into place (sometimes…).
So to me maths provided a setting in which things worked and made sense, and you could essentially just enjoy an endless supply of puzzles in that setting, whose solutions you could formally prove.
Unlike a lot of maths nerds, I don’t necessarily think that that’s totally limited to maths though. I think most people do their abstract thinking and puzzle solving on whatever it is that they find beautiful. Or I hope they do, it’s a wonderful feeling. The formal aspect of proofs though (and I don’t necessarily mean computations), that’s the unique thing that can set it apart.
Fair lol. IMO you kinda gotta be fucked in the head to like calculus. But I am fucked in the head, so it works for me 🤷
Personally, calculus is really where I fell in love with math. I had 0% interest in math at all until I took calculus. And also, I’m in one of the few positions where I actually use calculus all the time (PhD student in electrical engineering).
But also, I do music production as a hobby. And music production is, under the hood, real-time math. For example, audio equalizers are basically just doing real-time integration for you. You can absolutely do music production without calculus, in fact 99.9% of people do, but it’s been so helpful for my creativity to actually understand at that level what filters (and other things) do. So to me, at least in my autistic brain, math, calculus in particular, is part of everything I do, even my hobbies and free time and dreams and everything.
Oh, and computers can do calculus now, even with symbols. If you install its symbolic toolbox, GNU Octave will do it for free on a potato. So even if you don’t want to slog through the algebra, it’s super easy to just fuck around with calculus and a computer.
I have never looked at math and saw this beauty people describe. Math to me is as beautiful as an angle grinder, it’s a useful tool that hates you and plots your demise.
IMO math is fun when you choose to study it.
Also, if you want some classical “beauty” results, look into complex numbers and complex analysis. E.g., Mandelbrot sets are absolutely gorgeous.
But personally, I’m more partial to stuff like Borwein integrals, i.e. when you make “weird stuff” happen with “not very weird” ingredients.
Basically, the above pattern “works” for exactly the first seven iterations, but then it “breaks” for some reason on the eighth!
See that seems like the kind of thing Matt Parker would make a video about, “Someone noticed a weird pattern in some numbers.” Like how 2 pi or the fibonacci sequence keep turning up in nature, and I just can’t muster up much more than a “…huh” about it. I mean I understand margesimpsonpotato.jpg but if you want me to do calculus you’re gonna have to bring me more than “I just think they’re neat.”
Just in to say, I know exactly what you mean, and I love the subject, to the point I did a PhD in pure maths. The whole “golden ratio” in nature, and a lot of other adjacent stuff, leaves me indifferent at best, and really irritates me at worst. It’s often cheapo mathy wank to feel clever when you talk to your friends. There is nothing wrong in being interested in it, but I’d hope someone into maths would eventually go beyond that.
I also am not a fan of several very useful branches of maths, like calculus, but it’s a tool you need to have. Some people love it though, and I scratch my head at it as much as you do, if not more probably, because I have had to use it so much.
There are probably as many reasons to find maths beautiful (or ugly) as there are people, but for me it boiled down to the fact that:
So to me maths provided a setting in which things worked and made sense, and you could essentially just enjoy an endless supply of puzzles in that setting, whose solutions you could formally prove.
Unlike a lot of maths nerds, I don’t necessarily think that that’s totally limited to maths though. I think most people do their abstract thinking and puzzle solving on whatever it is that they find beautiful. Or I hope they do, it’s a wonderful feeling. The formal aspect of proofs though (and I don’t necessarily mean computations), that’s the unique thing that can set it apart.
Fair lol. IMO you kinda gotta be fucked in the head to like calculus. But I am fucked in the head, so it works for me 🤷
Personally, calculus is really where I fell in love with math. I had 0% interest in math at all until I took calculus. And also, I’m in one of the few positions where I actually use calculus all the time (PhD student in electrical engineering).
But also, I do music production as a hobby. And music production is, under the hood, real-time math. For example, audio equalizers are basically just doing real-time integration for you. You can absolutely do music production without calculus, in fact 99.9% of people do, but it’s been so helpful for my creativity to actually understand at that level what filters (and other things) do. So to me, at least in my autistic brain, math, calculus in particular, is part of everything I do, even my hobbies and free time and dreams and everything.
Oh, and computers can do calculus now, even with symbols. If you install its symbolic toolbox, GNU Octave will do it for free on a potato. So even if you don’t want to slog through the algebra, it’s super easy to just fuck around with calculus and a computer.
Borwein is incredibly interesting. Thank you for sharing