SworDsy

check out the animation

Teaching advanced math, on the other hand, is really hard to do when you're interacting with a person because there are so many pitfalls and if you hit even a single one you can't usually continue until you've tracked it down. Khan Academy has material on all sorts of non-math stuff, like economics and other sciences, and they seem to be gearing the math stuff more towards a younger audience, not an older one, which is probably more important anyways to be honest. smart move, mr.Khan, smart move.

Consider carbon dating. Since it's been observed, we should assume it's observational. carbon dating indicates that dinosaurs existed hundreds of millions of years ago instead of mere thousands. but that's historical and therefore this is a contradiction, so we can't assume the distinction.

the only logical conclusion is that we have a false premise.

I think sometimes mathematical definitions, especially advanced ones that rely on simpler definitions, are too complicated/long to recant every time you use them, which you have to. If I want to prove something relating or relying on uniform continuity I don't want to state the definition every time both because its repetitive and because definitions often use the same notation, so I don't want my uniform continuity deltas and epsilons getting confused with my normal continuity epsilons and deltas. Try proving advanced things about field extensions and galois theory using induction like that and you may actually run out of symbols.

That being said it is hard to read real math writing/research which can be both dense and obtuse even if you're used to it. Maybe that's why you need a PhD to consider entering the field.

if you shame someone like that, they won't feel good and it probably won't make them perform better at work. you have to be reasonable with them too, if you're too mean they won't like you which doesn't foster good teamwork. except here the company is the country and deadlines are economic achievements and such.

that being said i appreciate the sentiment here, you have to feel responsible to the team because you're a part of it, upon doing that you'll get the best out of people i find, although thats never an easy balance to find either.