> I don't know how to do this on a small scale in a practical way, but I do know that computing machines are very large; they fill rooms. Why can't we make them very small, make them of little wires, little elements – and by little, I mean little. For instance, the wires should be 10 or 100 atoms in diameter, and the circuits should be a few thousand angstroms across.

You don't study mathematics just to improve your mental arithmetic. If mental arithmetic were the point, you'd just practice mental arithmetic for your whole mathematical education, rather than progressing to more advanced topics.