You still have to tell the computer what to prove.
Indeed. Generating proofs is a bit like generating code. I can picture a computer generating proofs or code, but at least in the foreseeable future, I can't see a computer thinking of interesting conjectures (things to prove) or program designs (things to code).
Because most people encounter math as a tidy collection of Big Theorems and their accompanying proofs --- after all, even those who take math at university aren't likely to see anything remotely new unless they're math graduate students --- and because math usually only makes the news papers when someone has solved a really hard problem (like proving Fermat's last theorem), it's easy to get the impression that what mathematicians do is basically trying to come up with proofs for More Or Less Big Theorems. I'm only a budding math major myself, but I get the impression that the problem most mathematicians (well, the researchers anyway) face is rather that of finding interesting things to prove. Software can definitely help, but only as the tool of a mathematician.
So far most places I go start at a certain place, like Wolfram's site, and go up. If you don't know exactly what they mean it is basically useless. I even know the general ideas of stuff but then they add more. E.g. they give a page on conic sections. We all know that. But then they add stuff like R and sets and other things but miss the stuff in between. It's like they have high school stuff and doctorate stuff with nothing in between.
First let me say that however much mathematics you learn, you'll never completely get rid of the phenomenon you describe. The stuff you understand will always be but a drop in the ocean of stuff that's way over your head. The more you learn about a particular branch of math, the more unanswered questions you will find, and the more connections you will see to other branches of math that you know nothing about. It's a bit like trying to learn to know people: you could spend a lifetime studying just one person, but there are six billion of them, and they interact with each other. You might as well learn to enjoy the feeling of cluelessness, because it's not going away.;)
That said, there is probably no individual subject that you can't understand if you have the time, inclination and resources to study it. What you seem to lack at the moment is a part of the resources, namely the 'basic higher math' that serves as your map and compass on the above-mentioned ocean of stuff that's over your head. It's hard (at least for me) to compile a list of everything that should be included in 'basic higher math', and that's probably one of the reasons it's hard to find one book or even a few books that would cover all of it. The "stuff like R and sets" you mentioned is definitely a part of it, though.
Another, related reason why you probably won't find one book that covers everything is the interaction between different branches of mathematics that I mentioned above. 'Basic higher math' contains the basics of the few most important branches, and they all depend on each other to some degree. You can't just learn everything (all the basics) about one branch and then move to the next one. You'll start with one branch, but at some point you'll hit a wall that you can't get past without studying some of the other branches. So rather than first learning everything about calculus and then moving on to everything else, you'll learn a bit about calculus, then a bit of everything else, then a bit more of calculus, then a bit more of everything else, and so on. It would be hard (though perhaps not impossible) to write one book that would have everything you need to know presented in the order you need to know it.
It would probably be easiest if you could take math at a university somewhere. That's what I did.:) If you can't, you could try to look at some of the introductory math courses (ie., ones that don't have other courses as prerequisites), and buy the books they use and plod through them on your own. That route will probably feel more difficult, at least at first, but it can certainly be done.
Sidenote: I don't think Al Qaeda would be trying to kill people if they had a way to move away from the influences they dislike.
I'm not so sure about that. As far as I understand, they're not fighting because they're desperate, but rather because they're fanatic. If they really see the West in general, and the US in particular, as a manifestation of evil, I don't see why they would want to run away from it, at least not as long as they're still winning.
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You still have to tell the computer what to prove.
Indeed. Generating proofs is a bit like generating code. I can picture a computer generating proofs or code, but at least in the foreseeable future, I can't see a computer thinking of interesting conjectures (things to prove) or program designs (things to code).
Because most people encounter math as a tidy collection of Big Theorems and their accompanying proofs --- after all, even those who take math at university aren't likely to see anything remotely new unless they're math graduate students --- and because math usually only makes the news papers when someone has solved a really hard problem (like proving Fermat's last theorem), it's easy to get the impression that what mathematicians do is basically trying to come up with proofs for More Or Less Big Theorems. I'm only a budding math major myself, but I get the impression that the problem most mathematicians (well, the researchers anyway) face is rather that of finding interesting things to prove. Software can definitely help, but only as the tool of a mathematician.
I'm afraid you won't find a book like that; see below for a lengthy attempt at explaining.
That said, one book that could shed light on "stuff like R and sets" and some other basic building blocks is Daniel Velleman's "How To Prove It": http://www.amazon.com/exec/obidos/tg/detail/-/052
It won't tell you everything you need, but it's a start.
First let me say that however much mathematics you learn, you'll never completely get rid of the phenomenon you describe. The stuff you understand will always be but a drop in the ocean of stuff that's way over your head. The more you learn about a particular branch of math, the more unanswered questions you will find, and the more connections you will see to other branches of math that you know nothing about. It's a bit like trying to learn to know people: you could spend a lifetime studying just one person, but there are six billion of them, and they interact with each other. You might as well learn to enjoy the feeling of cluelessness, because it's not going away.
That said, there is probably no individual subject that you can't understand if you have the time, inclination and resources to study it. What you seem to lack at the moment is a part of the resources, namely the 'basic higher math' that serves as your map and compass on the above-mentioned ocean of stuff that's over your head. It's hard (at least for me) to compile a list of everything that should be included in 'basic higher math', and that's probably one of the reasons it's hard to find one book or even a few books that would cover all of it. The "stuff like R and sets" you mentioned is definitely a part of it, though.
Another, related reason why you probably won't find one book that covers everything is the interaction between different branches of mathematics that I mentioned above. 'Basic higher math' contains the basics of the few most important branches, and they all depend on each other to some degree. You can't just learn everything (all the basics) about one branch and then move to the next one. You'll start with one branch, but at some point you'll hit a wall that you can't get past without studying some of the other branches. So rather than first learning everything about calculus and then moving on to everything else, you'll learn a bit about calculus, then a bit of everything else, then a bit more of calculus, then a bit more of everything else, and so on. It would be hard (though perhaps not impossible) to write one book that would have everything you need to know presented in the order you need to know it.
It would probably be easiest if you could take math at a university somewhere. That's what I did.
Whatever you decide, good luck!
I'm not so sure about that. As far as I understand, they're not fighting because they're desperate, but rather because they're fanatic. If they really see the West in general, and the US in particular, as a manifestation of evil, I don't see why they would want to run away from it, at least not as long as they're still winning.