What's the big deal about Euler's Identity?

Answer 1

Euler's identity links the complex numbers with exponential functions.

Since it relates different areas of math in an unexpected, but non-superficial, and fundamental manner, it can be called a "deep" result.

Since it can be stated very briefly and simply, it is also an example of a mathematically "elegant" result.

To a mathematician, these qualities are aesthetic values.

I would describe my experience of deep results as similar to the experience of standing next to Niagara falls, and feeling the sheer power reverberate through my body.

Elegance is similar the contemplation of the quiet austere beauty of the Milky Way filled sky on a quiet chilly night while alone during a summer camping trip.

Besides, that the formula can be handy in a pinch.

Answer 2

I assume you are referring to:

e(i*pi) + 1 = 0

This link might give you some insight:

http://mathforum.org/dr.math/faq/faq.euler.equation.html

As a footnote: Euler, in my opinion, may have been the most competent and proficient mathematician of all time.
His great contributions are often unknown to university math students, and of course the man in the street has no idea who he was.

2nd footnote: Good answer Triple M!

Answer 3

e^(i*[pi]) + 1 =0

Right?

It's amazing because it combines the most important constants in mathematics: e, i, pi, the unity and zero. Feynman used to call it "Euler's jewel".

Answer 4

Which identity are you refering to?