What's the hardest mathematical thing you know?

nydryl said:
I don't mean to be rude, and I'm sure you're a better mathematician than I am, but I tend to find that the people who resort to an explanation like this are the very same people who don't fully understand their work.

I may be wrong, but it's an observation that tends to be fairly close to the mark.
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Its a lazy answer rather than one that indicates a lack of understanding. I've used it myself once or twice when I don't have the time to explain everything, but lots of things can be discussed qualitatively with non-mathematicians if you have a little patience
 
Judgeneo said:
As to Castiels question, have a read of this http://en.wikipedia.org/wiki/Axiom
Everything is based on the axioms of mathematics, as for the incompleteness theorem, well thats beyond my expertise. Essentially you can't have a system of axioms that prove themself, and define the natural numbers? I just assume the axioms are true :)
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Thanks, I knew what an axiom was and the limitations therein, I found some good sources which have given me what I wanted.

Thanks though. :)
 
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complex analysis is currently making my brain melt as i try to revise for my 2nd year uni exams, however i nailed my real analysis exam today so it evens out :P
 
Probably vector calculus. Nothing too tricky. There should be a lot more stuff listed here but I didn't attend any of my lectures this semester so don't even know what the topics were.... yeah resits in august for me. :(
 
nydryl said:
I don't mean to be rude, and I'm sure you're a better mathematician than I am, but I tend to find that the people who resort to an explanation like this are the very same people who don't fully understand their work.

I may be wrong (there are obviously exceptions), but it's an observation that tends to be fairly close to the mark.

As for the hardest mathematical thing I know? Whatever I'm trying to learn at the time.
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I think it says more about my explanation skills than anything else. Having said that, I'm only a first year undergrad doing mathematics - so I'm no expert in mathematics.
 
Judgeneo said:
Its a lazy answer rather than one that indicates a lack of understanding. I've used it myself once or twice when I don't have the time to explain everything, but lots of things can be discussed qualitatively with non-mathematicians if you have a little patience
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I use it too when I'm trying to explain my research, but it's probably an equal split between laziness and realising I haven't understood something fully myself.
 
Spherical polar integration, and integration involving more than 2 variables. Ie dx, dy, dx. Also, proving the taylor series in its valid form for more than one variables is annoying.
 
Fluid mechanics, perturbation theory, complex analysis, pdes

Some other physics areas that use some decent maths as well
statistical physics, quantum mech, langrangian + hamiltonian mechanics
 
I did a fair amount of discrete maths when at university, last time I looked back on my notes which was probably 10 years ago I couldn't make head nor tale of it, god knows how I used to understand it all.
 
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