Ah, well, you wave your arms because you're communicating with them. Like, in my experience:
Palm up, contracting fingers quickly like you're squeezing something: fundamental system of neighborhoods, nets, filters, particular neighborhood that is "nice"
Hand from A to B, then B to A: bijection/isomorphism
Arm from behind you to a quick jab upwards: embedding
There's all sorts of hand signals I've seen math people use, and they tend to be big so that they're completely unambiguous that you're signaling. When you're talking quickly, they can be a real godsend. Talking loudly is also partially about enunciation. When you're discussing something with a lot of letters in it, it has to be very clear that you're talking about a homomorphism vs. a homeomorphism, or an isomorphism vs. an automorphism. Your letters and pronunciation have to be completely unambiguous. This often means that you get pretty loud, and you'll speaking extra-loudly on certain syllables and letters to make sure that the listener knows you're changing what you're talking about. For example, if you have "s and s prime," you'd say the "prime" about twice as loudly, with a pause.
This isn't like angry yelling and screaming, though, it's just
loud. Chalk gets all over the place because you'll be writing on the board as you illustrate your points with two other media simultaneously, and you have to be writing a. rather large b. fairly darkly and c. quickly. Why? Because you have more than 10 different alphabets you're going to be picking the letters from, and the difference between script N and capital letter N without serifs can seriously change the meaning your reader will receive.
Furthermore, saying "but you are wrong!" and refusing to budge after you've explained your argument three times and written it all out for the other person to read is just plain reasonable. Remember, it's not something either of you has an opinion about, or emotions invested in other than a sort of austere artistic appreciation. If you're wrong, then you really want to close your mouth as soon as possible.
It's not about posturing, it's about doing whatever has to be done to communicate, and even though I say argument, a better word might be "shared explanation process."
Getting
actually angry would just be pointless.
I read somewhere that while Japan is pretty deferential, Korea is the most deferential culture in the world towards authority. Before they started training them to speak up, Korean co-pilots used to let planes crash because they didn't want to correct their superiors.
You read that in Malcolm Gladwell's book, Outliers =)
And yes, the Korean language has 7 politeness levels. As a friend said, it's like Japan taken up to 11.