Excited about mathematics?...

[short]

Math is indeed quite better after programming. Math is simple to me now, where at least %25 of the class is failing, me and my friend Kevin have high 90's.

[rant]Only thing I still see no purpose for is proofs. Seriously, they're pointless. Unless you're gonna be a scientist or a hardcore mathematician, I don't see why they're useful. I see no use in writing out every step with definitions and theorems(together they easily make up %50 of my homework). I'm pretty sure they aren't in the curriculum, but the teacher is making us do them anyway.[/rant]

Agreed. I wrote four epsilon delta proof's last semester, in calc 1.

If I remember correctly, they were for proving the limit laws.

I have to say, after writing them, I did feel smarter.

[MarauderIIC]

Proofs are either 1) So you know how things work or 2) So you can show that your own stuff is right. Also, don't forget about 3: The scientist asks "Why does it work?". The engineer asks "How does it work?" [<-Proofs go here(?)]. (The artist asks "Would you like fries with that?")

Of course, 2) assumes that you do the proof correctly...

The thing you have to understand about math: case-by-case basis means absolutely nothing, since mathematics is infinite. So there can be infinitely many cases that make your theorem look correct... even though it's not.

But no, I'm not sure that you'll design many mathematical proofs. Maybe logical ones (in AI, for instance).

As for what the mathematician says...
Two guys were in a balloon. They went very high, above the clouds. When they came down through the clouds over a field, they had absolutely no idea where they were. But they saw a man in the field. So they went down and they asked him, "Where are we?"
The guy in the field thought for a while, and he said

"...You're in a balloon."

So the guys in the balloon left. And as they were leaving, one of them said to the other,
"You know, he must have been a mathematician."
"Why?"
"Well, first, he thought about his answer. Second, he was completely right. Third, his answer was totally useless."

[dandymcgee]

As for what the mathematician says...
Two guys were in a balloon. They went very high, above the clouds. When they came down through the clouds over a field, they had absolutely no idea where they were. But they saw a man in the field. So they went down and they asked him, "Where are we?"
The guy in the field thought for a while, and he said

"...You're in a balloon."

So the guys in the balloon left. And as they were leaving, one of them said to the other,
"You know, he must have been a mathematician."
"Why?"
"Well, first, he thought about his answer. Second, he was completely right. Third, his answer was totally useless."