Why is math considered beautiful?

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SUMMARY

This discussion centers on the subjective beauty of mathematics, with participants expressing varied opinions on different branches of math such as Real Analysis, topology, and differential topology. Many contributors agree that while math can evoke strong emotions, including tears of joy or frustration, the beauty lies in its abstract concepts and rigorous proofs. Notable expressions of admiration include the equation e = -1 and the elegance of topology. The conversation highlights the dichotomy between the perceived beauty of math and the challenges faced in understanding it.

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  • Understanding of Real Analysis concepts
  • Familiarity with topology and differential topology
  • Basic knowledge of complex numbers and Euler's formula
  • Experience with abstract algebra and linear algebra
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Students, educators, and mathematics enthusiasts interested in the philosophical and emotional dimensions of mathematical beauty, as well as those seeking to deepen their understanding of advanced mathematical concepts.

beautifulmath
hello all and i just want to say that math is beautiful. the beauty of math can only be described in one word: stunning. Many shed tears of happiness during first Real Analysis lecture we had and many always gasp and stunned by beauty of proofs and conjectures in class because math is beautiful and I hope you see the beauty as well.
 
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I think those were tears of desperation.
 
Uh? Sure maths is indeed beautiful and interesting, but shedding tears during a lecture? The only time I heard of people weeping during a lecture was when the material was too difficult and they didn't understand it from start to end.
 
I do think that math is beautiful, but I'll admit (as one who prefers discrete math) that I didn't see much beauty in Real Analysis.
 
I'm studying every bit of advanced math I can, now, just for fun. Same reason people climb mountains, I guess.

And I will admit, I was actually awestruck the first time I saw e^{i\pi} = -1
 
math is beautiful, but not in a way to shed tears. Well, I still agree I love that e to the i pi equals -1
 
CRGreathouse said:
I do think that math is beautiful, but I'll admit (as one who prefers discrete math) that I didn't see much beauty in Real Analysis.

Likewise; I find linear/abstract algebra much nicer.
 
Yeah, analysis is awesome. It makes all those epsilon expansions in physics meaningful.
I think topology is more awesome though... Seeing how one can prove a sheet with a hole is different from a sheet is incredible.

Now, combine the two, you get differential topology... that's double the awesomeness!

And I agree that math is beautiful... It's cold and rigid, with hard facts like a solid block of ice; yet, it can be abstract and soft, with twisting ideas and imaginative connections. But still, physics is more beautiful with it's deep intuitions and astonishing predictions of actual reality.

That's enough I think before sounding like an English major...
 
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I have absolutely no idea what anyone is trying to say here!
 
  • #10
I see no meaningful dissucssion of math in this thread... Off to GD.
 
  • #11
Eww, math. Lol

I see beauty in math, but only higher math which I will never use/understand/etc. The rest of it, yuck.
 
  • #12
I see no meaningful dissucssion of math in this thread... Off to GD.

OOoh...demoted to GD!

Errr...math is beautiful, but the process of learning it is pretty ugly (I say the same thing about physics).
 
  • #13
Math haz a ugly.
 
  • #14
tim_lou said:
Yeah, analysis is awesome. It makes all those epsilon expansions in physics meaningful.
I think topology is more awesome though... Seeing how one can prove a sheet with a hole is different from a sheet is incredible.

Now, combine the two, you get differential topology... that's double the awesomeness!

And I agree that math is beautiful... It's cold and rigid, with hard facts like a solid block of ice; yet, it can be abstract and soft, with twisting ideas and imaginative connections. But still, physics is more beautiful with it's deep intuitions and astonishing predictions of actual reality.

That's enough I think before sounding like an English major...

True, math is cold and rigid. Its pure, there's nothing unnecessary present, its clean. If only real life were that way. It would be a LOT simpler, though I think that might take the excitement out of it.
 
  • #15
"Math is beautiful" makes as much sense as "english is differentiable".
 
  • #16
Dragonfall said:
"Math is beautiful" makes as much sense as "english is differentiable".

What makes you think that it isn't?
 
  • #17
Because it's discontinuous at every point.
 
  • #18
lol tears of desperation indeed
 
  • #19
There was once a lecture about statistical physics, and I had no idea what the lecturer was explaining. I was merely sitting there, staring at the blackboard, wondering why I'm sitting there, staring at the blackboard. It seems that there was some other student who wasn't understanding anything either, and he started laughing in the middle of the lecture. I cannot be sure of why precisely he started laughing. Perhaps he believed that it was quite common for students in that lecture room to stare at the blackboard without understanding anything, and he then found the entire situation highly ridiculous? Whatever the reason was, he started laughing, which naturally draw attention from everybody else, including the lecturer. Then he got embarrassed, but could not stop laughing, and eventually he escaped out from the lecture room so that the lecture could go on.

IMO it was funny incident.
 
  • #20
beautifulmath said:
Many shed tears of happiness during first Real Analysis lecture

Jesus.
 
  • #21
Dragonfall said:
Because it's discontinuous at every point.

That's why your english teachers try to get you to make your essays flow. It makes the calculations that much easier.
 
  • #22
jostpuur said:
There was once a lecture about statistical physics, and I had no idea what the lecturer was explaining. I was merely sitting there, staring at the blackboard, wondering why I'm sitting there, staring at the blackboard. It seems that there was some other student who wasn't understanding anything either, and he started laughing in the middle of the lecture. I cannot be sure of why precisely he started laughing. Perhaps he believed that it was quite common for students in that lecture room to stare at the blackboard without understanding anything, and he then found the entire situation highly ridiculous? Whatever the reason was, he started laughing, which naturally draw attention from everybody else, including the lecturer. Then he got embarrassed, but could not stop laughing, and eventually he escaped out from the lecture room so that the lecture could go on.

IMO it was funny incident.

I saw a similar incident last year, which was my first year of grad school. In quantum mechanics one day, our professor was having his postdoc substitute. Anyway, the guy started deriving the differential scattering cross-section for a particle with a given momentum scattering off of a potential. Basically this turned into over an hour of mathematical calculations (the class is 1 hour and 20 minutes long). Towards the end I asked him, "so I got lost in the math...what exactly were we doing?" Everyone seemed to find this hilarious, and several people burst out into laughter.

Anyway, I agree that math is pretty cool. I majored in it back in college. Not sure I'd want to do it for a living, though.
 
  • #23
jostpuur said:
There was once a lecture about statistical physics, and I had no idea what the lecturer was explaining. I was merely sitting there, staring at the blackboard, wondering why I'm sitting there, staring at the blackboard. It seems that there was some other student who wasn't understanding anything either, and he started laughing in the middle of the lecture. I cannot be sure of why precisely he started laughing. Perhaps he believed that it was quite common for students in that lecture room to stare at the blackboard without understanding anything, and he then found the entire situation highly ridiculous? Whatever the reason was, he started laughing, which naturally draw attention from everybody else, including the lecturer. Then he got embarrassed, but could not stop laughing, and eventually he escaped out from the lecture room so that the lecture could go on.

IMO it was funny incident.

You just described 90% of my lectures. I was asking a professor a question once, and the guy next to me made me laugh while I was asking the question. That was embarrassing. Leads to a lot of funny looks.
 
  • #24
Transfinite mathematics. That has a spooky beauty.
 
  • #25
Michio Kaku made crying at the sight of equations fashionable.

I must admit that having never been a very serious student until my last year of high school, and having first attended college in any real sense in my late twenties, the early part of my college career was intellectually dramatic... even traumatic at times. All good really, but as my wife Tsu can vouch, every day was an adventure. The perpetual explosion of new ideas left me in thrill overload much of the time. And there were certainly a few times that I got a bit emotional about it. Math and Physics were the classes most cherished, of course, but I even fell in love with classes like A History of Great Britain - perhaps the most surprising of all in some ways, and my very first class [taken during the summer session].
 
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  • #26
Awesome thread haha - I'll admit it, there have been a few times that I've shed a tear due to the beauty of math.
 

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