A Math Lesson

I was reading an article in the Wall Street Journal today that was a little depressing in that it really made me wish I hadn't avoided math so successfully when there was another option. This article discussed the fact that the prime number theory, called the "Reimann Hypothesis" was getting closer to being proved. This was advanced in 1859 by Bernhard Reimann and is now considered the most important unsolved problem in mathematics. There is even a $1 million prize to whomever proves it. Well, I am no threat to get the million since I can't even understand why they care if it is proved or not and I am also unable to understand the theory and the significance of prime numbers. One thing I read largely prevented me from studying the problem further. In her discussion, Sharon Begley made the point that there is an infinite number of prime numbers. O.K., I can accept that. But then she said the problem is "how big is that infinity?" Whoa. So now she is telling me some infinities are larger than others? Yes, and as an example she says the number of numbers divisible by 2 is infinite and so is the number of numbers divisible by 9. The first infinity is larger than the second. Furthermore, there is an infinite number of squares (4,9,16, etc) and cubes (8,27, 64, etc), but there are more primes than either of these infinite numbers. Here I am 66 years old and now they are telling me infinity is not just one big number out there somewhere. I pause here to think about all this.