What is so beautiful about Euler's Identity?

[joelio36]

I'm a pretty novice Physicist/Mathematician, but I've got a few offers for good universities, to show you my general level of knowledge.

Could someone please explain in terms I will understand why this equation is considered so perfect and beautiful?

 

[HallsofIvy]

What is so beautiful about the Mona Lisa?

Euler's equation, $e^{i\pi}+ 1= 0$, which can also be written [itex]e^{i\pi}= -1, combines five fundamental constants, 0, 1 (or -1), e, i, and $\pi$ into a single, simple, equation. Simplicity and depth make for beauty.

 

[mathman]

What is so beautiful about the Mona Lisa?

Euler's equation, $e^{i\pi}- 1= 0$ combines four fundamental constants, 0, 1, e, and $\pi$ into a single, simple, equation. Simplicity and depth make for beauty.

Error! Should be + 1 = 0, not -1.

 

[Dr. Lady]

'Tis true... both of the above.

 

[Fredrik]

I think that the "beauty" is in the fact that the constants are from very different branches of mathematics. 0, 1 and i are from algebra, e is from calculus/analysis, and $\pi$ is from geometry.

 

[Integral]

What is so beautiful about the Mona Lisa?

Euler's equation, $e^{i\pi}+ 1= 0$ combines four fundamental constants, 0, 1, e, and $\pi$ into a single, simple, equation. Simplicity and depth make for beauty.

And in combining those fundamental constants it uses each of the 4 fundamental math operations: Addition, multiplication, exponentiation and equality.

All to arrive at a result that seems impossible.

How can that be anything but beautiful?

 

[Denton]

Why does no one mention the i, is there nothing special about imaginary numbers or something?

 

[maze]

Am I the only one who isn't in awe of this equation?

When I first saw it, it seemed random and just didn't make any sense, like those infinite sum formulas of Ramanujan (...one over pi equals WHAT?). But then after I studied complex analysis, and the more I learn in math, the more pedestrian and booring it becomes. It seems to just be a random consequence of much bigger ideas, and it doesn't lead to any insights by itself.

I've thought about this a few times and tried to "see the beauty" but as far as I can tell all the awe is based purely on shock value and nothing deeper.

 

[Tac-Tics]

It's easy to remember and makes a lot of otherwise tough math easy.

 

[mathwonk]

why so hung upon the word beautiful? try unbelievable, or wacky, or unexpected, or sexy, or what ever, but at least it ain't boring.

 

[WarPhalange]

I've never seen an equation that put me in "awe", but this is a pretty cool one. And it only gets better when you find uses for it.

 

[Doodle Bob]

I've never found anything in mathematics to be beautiful. The concept of beauty in mathematics traces back to Hardy's A Mathematician's Apology and is based on a more-or-less Late 19th/Early 20th Century sense of aesthetics.

Nevertheless, this equation has always intrigued me, since it gives us a sneak peek into the structural integrity of Mathematics as an academic discipline.

 

[Primitive]

I always don`t get it. To me, if it can solve problems, and extend new ideas, then i like it. I don` t bother with 'beauty'.

 

[daytripper]

If you ask me, something is beautiful when it's stimulating and seemingly simple (women excluded of course! eyo!)
Euler's identity is, to me, a 7. $$A\; =\; \pi r^{2}$$ is like a 3. $$e=mc^{2}$$ is about a 9. The Lorentz factor is a perfect 10, if you ask me. =]
Simplified complexity... mmmm...