I have been trying to understand a few elementary results about the zeta function during the past month. I have learned enough about Riemann's original 1859 paper and its importance to become officially addicted the Riemann Hypothesis. I will occupy part of my time for the next several years trying to understand the dense mathematics, beautiful equations, and esoteric proofs associated with the problem. It usually takes at least two years for my math addictions to run their course.
I recall why I majored in mathematics. I literally could not help myself. I kept wanting to learn a little bit more about math even though I was not particularly good at it compared to my brilliant and hard working peers. The odd thing is that I have probably learned more about math after leaving college than I did while I was there. I have spent my whole life wanting to learn a little bit more.
I have found a way to understand some mathematics in my own way. That is so hard to explain. I suppose it is a little like reading a great writer that you love. You read her the first time, become bewitched even though you only get the gist of what she is saying. Then you return to her over and over again. Eventually you understand her based on your own terms, terms that have meaning for you, metaphors that fit the way you frame the world.
Of course, mathematics is creative, creative in the sense that it too is built starting from basic metaphors and blending them into complex metaphors. I learn the math behind the Riemann Hypothesis based on the metaphors that work for me. That is the fun part of the math for me, creating my own metaphors.
Much has been written about the aesthetics of math. To me math really is beautiful. I am not artistic, but I can do some amateurish math. Math is my paltry artistic outlet.
I recommend "A Mathematician's Apology" by G. H. Hardy. It is a literary classic. You don't need to know any math to appreciate it, for it has only a little in it, and even where it does, anyone who understands arithmetic will understand his two mathematical illustrations of what math is all about.
Hardy worked on the Riemann Hypothesis all his life. He proved infinitely many zeros lie on the critical line. That is a big result, but still far away from proving the Riemann Hypothesis.
A spectacular full moon rose over the lake at the end of the first day of summer. What else happened? Darned if know.