What is THE HARDEST topic in mathematics

saminator910

In your opinion, what is the hardest topic in math? I don't really know many high high levels of math, maybe differential topology, or K theory, idk, what is it in your opinion? Oh, and don't say "some people think Calculus is hard" or other stuff like that, think of a high level math topic.

mathwonk

the one you don't know yet.

Number Nine

Why not? It's the only reasonable answer.

saminator910

You guys did exactly what I didn't want you to do, just pick a topic in your opinion that you think is the hardest topic in math, I realize that "The one I don't know" will be difficult for me, but what was difficult for YOU.

micromass

Every topic is hard once you learn enough about it. If we can't give you an easy and straightforward answer, then that is because an easy and straightforward answer does not exist.

Evo

You don't get to choose the answers you get. *WE* choose.

Pythagorean

I don't know about hardest, but Abstract Algebra has always given me trouble. The more abstract the mathematics, the harder it is for me to get.

My applied analysis (fourier/laplace transforms of differential equations) teacher had a B.S. in physics and had a teaching style that always referenced some intuitive physical system. Made it a lot easier for me to understand the mathematics.

symbolipoint

That quote suggests another topic: A picture interpretation can allow understanding, but some people do not look for nor accept a picture as part of an explanation or as part of reasoning.

Anytime something in a mathematical topic can be given a picture for its representation, this should make the topic much easier... It SHOULD.

Pythagorean

I understand the picture is not proof, but it helps make sense of the symbols when you're first learning it. Once you have it in your head, then the symbols invoke those images and notation becomes second nature.

But for me, the kinetics are important too. Velocity and acceleration really helped me to understand derivatives.

DiracPool

The hardest topic topic in mathematics is the one where you have a lame, out of touch instructor who doesn't know how to communicate the operations of abstract symbols to an adequate variance of unlearned pupils. That is the general answer. I would say, however, all things being equal as as far as instruction, most mathematical physicists would probably say that the tensor calculus of general relatively is the toughest to navigate. At least as far as mainstream mathematics.

Pythagorean

I've never even touched Riemannian geometry; I can't imagine. Precession is tough enough (as far as book-keeping goes, anyway). In my undergrad modern physics course, at the end of the second semester (after QM and nuclear) we had the choice between general relativity and nonlinear dynamics and we unanimously chose nonlinear dynamics.

DiracPool

It turns out that, for the most part, the mathematics used in GR and nonlinear dynamics are somewhat similar. Both involve coupled, nonlinear DE's and typically cannot be solved analytically and have to be solved numerically by computer. GR analysis reduces to huge sets of coupled, partial, hyperbolic nonlinear DE's. I study brain mechanics using a model for coupled oscillators that uses coupled, nonlinear ODE's, which are simpler than the partials of GR but still require numerical analysis.

Pythagorean

Interesting. That's my area of research for graduate studies (brain mechanics).

DiracPool

Wow, cool. Check out the CLION website at U Memphis under Kozma and Freeman's research. They've developed a model called the KV model where they lay out the equations. They even have a Matlab toolbox that you can download for free to play around with the oscillators.

Pythagorean

Ah yes, large scale integration. Wasn't able to find the actual KV model on their site so far. I'm currently using a single neuron model (the Morris-Lecar model) of which I couple like 50-100 together. I'm guessing large scale integration involves something on the order of million-neuron-networks.

Evo

Thread is off topic.