Can someone tell me what's the most advanced thing you know in any field of mathematics?

Question

amistre64 · Answer

addition

myininaya · Answer

I think some people might find some knowledge more advance then others.
i think the word advance is almost an opinion.

hero · Answer

nothing

myininaya · Answer

for instance addition is advanced for amistre, but hero finds addition to be not advanced

hero · Answer

Well, it isn't ;P

myininaya · Answer

and see amistre would disagree with you

hero · Answer

You still haven't told us your advanced knowledge of math Ms Computational

myininaya · Answer

it does depend on what we are adding

myininaya · Answer

what if we adding an infinite amount of numbers together

jamesj · Answer

I know some rather beautiful things in algebraic topology and non-Riemann manifolds.

Why?

hero · Answer

In that case the sum is $$ \infty$$

myininaya · Answer

sometimes the sum is convergent though

hero · Answer

That's 8 sideways

anonymous · Answer

I just want to see some cool equations

anonymous · Answer

What's your favorite equation. Like if you were to show someone 1 equation so that they would be impressed by how cool and advanced it looked, what would it be?

myininaya · Answer

$$e^{i \theta}=\cos(\theta)+i \sin(\theta)$$

hero · Answer

I've seen cooler ones

jamesj · Answer

Hmm.  Sometimes big complicated things are not that interesting.  But simple looking things can often be deep.  For example, this equation is rather thorny.

Let p be positive integer greater than 2.  Then what are the characteristics of
$$x^p + y^p = z^p$$

myininaya · Answer

$$curvelength=\int\limits_{a}^{b}\sqrt{1+(f')^2} dx$$