The trouble with integers is that we have examined only the very small ones. Maybe all the exciting stuff happens at really big numbers, ones we can't even begin to think about in any very definite way. Our brains have evolved to get us out of the rain, find where the berries are, and keep us from getting killed. Our brains did not evolve to help us grasp really large numbers or to look at things in a hundred thousand dimensions.
It would be very discouraging if somewhere down the line you could ask a computer if the Riemann hypothesis is correct and it said, "Yes, it is true, but you won't be able to understand the proof."
Juggling is sometimes called the art of controlling patterns, controlling patterns in time and space.
Math is sometimes called the science of patterns.
Well, as you know, there are 24 hours in every day. And if that's not enough, you've always got the nights!
A rule of thumb for any good math talk is that it should have one proof and one joke and they should not be the same.
Martin has turned thousands of children into mathematicians, and thousands of mathematicians into children.