4 ms·

I'm not so sure about that. Take a look at cellular automata. It's pretty trivial to screw around with them (though not as easy as with integers, I'll grant you

I'm not so sure about that. Take a look at cellular automata. It's pretty trivial to screw around with them (though not as easy as with integers, I'll grant you). Where are the theorems? There seems to be an awful lot of land, but no maps. To a lesser extent, graph theory has this problem as well. In the ~60 years that it's been a subfield in its own right, we haven't got an awful lot of fundamental new methods. Results being proven today could be easily understood by a graph theorist from 40-50 years ago transported ahead in time, perhaps after at most the equivalent of a semester-long grad course.

rocqua 9y ago
Cellular automata are much harder to screw around with. Partly that is because computation by hand is a lot harder, partly because there isn't much that one can combine. What makes the integers interesting is that addition, multiplication and exponentiation are all easy, all operate on the same numbers, and yet they behave very differently. This allows one to pose very easy questions (e.g. Can I express every prime as a sum of ...) that have no obvious solution to them.