A generating function is a clothesline on which we hang up a sequence of numbers for display.
In Mathematics it is always best to cheat.
Induction makes you feel guilty for getting something out of nothing, and it is artificial, but it is one of the greatest ideas of civilization.
The full beauty of the subject of generating functions emerges only from tuning in on both channels: the discrete and the continuous.
For every epsilon, there is a delta.
The research reported on in our book "A=B", has moved a whole active field of mathematics from the province of human thought to the realm of computer-fodder. It is quite exciting to think about what other fields of pure mathematics, hitherto thought to be reserved to human intelligence, might be moved to that realm next. The goal is to put ourselves out of business completely, and the work is well underway.
