Introduction

I was never very good at math, but I have always loved it for the way it all fits together so nicely. Fortunately, it is a peculiarity of human beings that we can love that, perhaps only that, which we do not fully understand. And in this you and I are perhaps more like than unlike the very greatest of mathematicians, men whose thoughts represent some of the highest and most profound we human beings have had.

All of us face a universe in which mathematics has forever unfolded in directions we—and even the greatest mathematicians among us—cannot begin to visualize. Thus, our humility is maintained by the knowledge that, possibly as opposed to the physical universe, the universe of numbers goes on everywhere forever in every possible direction and dimension. These numbers contain unimaginably more mathematical truths than we now know, more even than our universe, even if it has eternity at its disposal, can ever know.

In the mathematical universe, any knowledge of truth we will ever have is insignificant compared to all that is true. Facing such a universe, we realize that the difference between us and the very greatest mathematicians virtually evaporates—sort of. These fellows were a tad better than we are at finding mathematical truths. And it is the glory of mathematics that many of the deepest truths can be discovered by looking through the tiny window at the tiny portion of the mathematical universe provided by our little world. It is the mathematicians who look through the window and tell us what they see.