3.3

1. As the chapter said, this stuff isn't too hard with manageably-sized sets but as the sets grow, so does the problem of finding isomorphisms/homomorphisms by hand (or so it seems to me). This seems like a job well-suited for a computer: it is rigorously definable and really just symbol manipulation, which is what the Turing vision of a computer entailed.

2. Mathematics is for me often intriguing in that I wonder if a lot of math is developed (or discovered, but let's not start that debate...) but with no real purpose and is simply discarded. On the one hand, real world problems serve as motivation for mathematical (or any kind of) discovery that can lend itself to the solution of the problem. On the other, I could see many well-educated and well-read mathematicians with nothing really new to offer but who still develop some kind of consistent system and declare it new math. I wonder if Fermat knew the implications that prime numbers would have on our "futuristic" society (where almost all security is based thereon, etc.).