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62 Comments
- Dinsdale77, on 11/21/2008, -1/+23I saw some pretty ugly math during my undergrad experience.
- divinediva, on 11/21/2008, -0/+20The truth of the matter is that, though mathematics truth may be beauty, it can be only glimpsed after much hard thinking.
- AmyVernon, on 11/21/2008, -2/+13Isn't math really behind everything though? Everything can be broken down into mathematics. Symmetry often is considered a type of beauty, for example.
- NathanielJ, on 11/21/2008, -0/+7The FTC is pretty, but for me it felt like watching a movie that's already been spoiled for you. Sure it's good, but you already knew what to expect, so it's hardly a surprise.
- speedk0re, on 11/21/2008, -2/+8math + beauty = http://en.wikipedia.org/wiki/Danica_McKellar
- rustintable, on 11/21/2008, -0/+5Godel's Incompleteness theorem and the the central limit theorem are also pretty sweet.
- FasterGun, on 11/21/2008, -0/+5Drinking your own blood is the paradigm of recycling.
- petterp, on 11/21/2008, -3/+8god is mathematics btw
- danj484, on 11/21/2008, -0/+5That man is an amazing balance between insightful genius and profound ***** insanity.
- TSK05, on 11/21/2008, -0/+4I don't know about the article but math is pretty awesome. They completely fail at teaching that before college. In high school, I felt like any math besides 2+2 was useless and I would never see it again (like trig functions). There is really exciting stuff in math, I am not up to theoretical levels (which I hear are really awesome) but even calculus (1,2 and 3) have their own interesting stuff - like how would you find arc length (of non-standard shapes) without integrals? Or how would you find surface area? You can't find almost anything about non-standard shapes without calculus.
- Issius, on 11/21/2008, -0/+4but you CAN prove that woman are evil...
- NotYourProdigy, on 11/21/2008, -0/+4The truth about this article: 90% fluff, 10% information
- disappointed, on 11/22/2008, -0/+4"Mathematics is the language with which God has written the universe."
-- Galileo Galilei - charlietuna, on 11/22/2008, -0/+3"Math is hard"
.... Barbie - darkhelmet08, on 11/21/2008, -1/+4I remember the first time I learned the fundamental theorem of calculus...
it was like falling in love. - lovemorgul, on 11/21/2008, -1/+4I hope that there are no short cut to those platonic realms of Mathematics, neither to the gut experience of mathematical intuition nor to the vision of its beauty.
- rustintable, on 11/22/2008, -0/+3Since godel's incompleteness theorem says that every axiomatic system has unanswerable questions which require new axioms then there may be no one most fundamental foundation of analytic thought.
- tallguyg, on 11/21/2008, -0/+3this might not fully answer your question but its long been studied that when it comes to human faces, the more symmetrical the facial features, the more "beautiful" that face is judged to be. our eyes just prefer to look at things that are symmetrical. so in order to quantify that into something they can study (and be related to math) they used a series of dots.
they are basically reducing symmetry to a very simple form - different numbers of dots - so they can measure its effect on judgment. - inactive, on 11/21/2008, -0/+3The squeeze theorem made my wander for a second . . .
- buddyw, on 11/21/2008, -0/+3what can't be represented mathematically?
- MalarkeyPN, on 11/21/2008, -0/+3Wow what a great piece of spam.
- NathanielJ, on 11/21/2008, -0/+3If you think that analysis is "baby math", then you haven't taken analysis and likely don't even know what it is.
- acetv, on 11/21/2008, -0/+2Perhaps "fundamental" is the wrong word. Math has some groundbreaking philosophical results and questions that shake the vary foundations of logic.
- Dystisis, on 11/21/2008, -0/+2Agreed, just like geometry is more complex than symmetry. Beauty is geometry and numbers.
- thegrantman, on 11/21/2008, -0/+2How the hell do you equate symmetry and beauty?
Symmetry may assuage your notion of balance but beauty is far more complex. - inactive, on 11/21/2008, -1/+3Stats/prob is ugly. Analysis is much more elegant. imho. P(X=2)=0.3 just doesn't seem like 'real' math to me. (not that i'm a real math nurd or anything)
- inactive, on 11/21/2008, -1/+3women
- dithyrambica, on 11/22/2008, -0/+2I envy those of you that Math comes easy for.
Math gives me anxiety in a very serious emotional way. Like ya know, tears and stuff.
I consider myself to be a fairly intelligent person.
Yet Math makes me feel like a Big Stupid Dummy Head.
- acetv, on 11/21/2008, -0/+2? Analysis is beautiful, man. Dedekind cuts to construct the real numbers? Brilliant.
- digitalArtform, on 11/22/2008, -0/+2Euclid alone has looked on beauty bare.
- Edna St.Vincent Millay - kernel16, on 11/22/2008, -0/+2Linear algebra isn't complicated, but it's really interesting above all else IMO, plus looks good on paper.
- rustintable, on 11/21/2008, -1/+3Predicted specific events in a uniformly random system.
- wearestars, on 11/22/2008, -0/+139 comments and not a single reference to Keats? Ode on a Grecian Urn? You people make me sad.
- TheMoniker, on 11/23/2008, -0/+1Also, calculus opens up doors to many branches of physics. You can cover most of classical physics using only multivariable calculus (with some differential/partial differential stuff necessary for things like fluid mechanics). Heck, if you add in the differentials (and some linear algebra), you can cover basic quantum mechanics as well. Not to mention, you could make inroads into relativity (though if you don't use tensors and summation conventions there, things would probably get horribly ugly really fast).
It's a little like reading the language that the comprehensible universe is written in: a point that Roger Penrose makes in his book, The Road to Reality. (I think that both Plato, Galileo and a bunch of others have said the same, or very similar things, about math in general). - digitalArtform, on 11/22/2008, -0/+1And no reference to Star Trek?
'Is There in Truth no Beauty?'
That was the one with the alien ambassador in a lunchbox that makes you crazy if you look at him. - TheMoniker, on 11/23/2008, -0/+1For calculus moments, I'd have to list variational calculus and Lagrange's equations as a huge moment. When you first see how they explain physics problems, that are essentially huge Rube Goldberg setups, with such ease and elegance, it's almost like black magic. (They--or an equivalent formalism, like Poisson Brackets, Hamiltonian notation--form the basis of field theory, which is pretty fascinating.)
- inactive, on 11/21/2008, -0/+1Technology is like living with the eyes of a shark.
- Gary Busey. - undershirt, on 11/22/2008, -0/+1Let me tell you my background. I have just finished my bachelor's degree in math and cs and have long thought that math is at the core of everything. But after checking out this topic, I'm starting to see how theoretical computer science actually goes deeper to explaining the behavior and complexity of things. Math is actually on the surface explaining how things work. But this seems to answer the question of why things are so complex. I think that's more fundamental. Check it out.
- rustintable, on 11/21/2008, -1/+2The proof that there are 5 fundamental solids in 3 space, 4 in four dimensions and 2 in all higher dimensional euclidean space is also good.
And the fundamental theorem of algebra.
And the proof that a heptagon can not be constructed with a ruler and straight edge.
Incomensurability.
And the proof of the distribution of the primes is 1/log(n).
The many proofs of Pythagoras' theorem.
The proof of e^(ip)=1.
Alan Turing's computability. - StarThrower2, on 11/22/2008, -0/+1You gave me the incentive to look for that quote! Beautiful!
- TheMoniker, on 11/23/2008, -0/+1What I like about linear algebra is that it ties into quantum mechanics all over the place and it's generally where people cut their teeth on their first math proofs. That said, I'd have to go with calculus (specifically multivariable and partial differentials) as being the most interesting for the intuition they give into so many physical phenomena. That said, I wish that I understood algebraic topology for all the upper-level physics that it opens up (strings and branes).
- quickgold192, on 11/21/2008, -1/+2paradoxically, it's not a beautiful website
- TheMoniker, on 11/23/2008, -0/+1Math (informed by a few observations) tells us a lot about the world: from the basic algebra of first year physics, to fluid mechanics and the mind-bending subtleties of relativistic and quantum physics. With that said, I have always liked the candour and depth of this quote by Bertrand Russell:
"Physics is mathematical, not because we know so much about the physical world, but because we know so little: it is only its mathematical properties that we can discover. For the rest our knowledge is negative." - metalclay, on 11/22/2008, -0/+1-that is all
Ye know on earth, and all ye need to know. - NathanielJ, on 11/21/2008, -2/+3Physics doesn't count.
- StarThrower2, on 11/22/2008, -0/+1lol . . . when I googled the line by St. Vincent Millary, it asked me if I meant the "quote by Edna St. Vincent Millay: Euclid alone has LOGGED on beauty bare."
Google being a smartass? - disappointed, on 11/22/2008, -0/+1http://en.wikisource.org/wiki/Jordan_(I)
- StarThrower2, on 11/22/2008, -0/+1The sad thing is that students at a very early age are conditioned to dislike math -- or be intimidated by it, which makes them dislike it. At any rate, it was something I found fun, like playing games, until I was taught that math was supposed to be a drag. THAT was a drag! I'd like to be able to read Euclid while waiting for mundane things like doctors' appointments . . .
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