Why this blog?
The main objective of this blog is that I want to understand the Riemann Hypothesis, starting from Riemann’s 1859 landmark paper, and then progressing to other topics concerning prime numbers and analytic number theory. Why make it public then? Well, for one thing, it helps to write things down and express them in your own words. Docendo discimus. For another thing, I’m sure there are plenty of people out there just like me: Fascinated by prime numbers, but unable to follow the vast mental leaps most mathematical authors demand from their readers.
To put it another way: If you enjoyed reading Marcus du Sautoy’s The Music of the Primes or John Derbyshire’s Prime Obsession, and were missing more mathematical background; if you tried to read H.M. Edwards’s Riemann’s Zeta Function, but got discouraged by all the technicalities, then this blog is spot-on for you. If you expect lengthy explanations why primes are beautiful or prolonged repetitions of the usual anecdotes, I would refer you to the aforementioned books. They’ll get you hooked. If you expect exciting breakthroughs in prime number research, you’ll probably be bored.
Since my declared goal is to make the Riemann Hypothesis accessible to myself, I shall freely assume knowledge that may not be obvious to everyone in one area, and in another one, I may dwell on certain points that are commonplace. I’d prefer the latter to be the common case, and encourage you to make use of the comment function in case anything is unclear. Also, I shall frequently appeal to intuition when it comes to technicalities. I would like to keep the reader focus on the big picture.
As we are on the topic, whom do I hope to reach? Since I shall freely include as many formulae as I please, according to what we may refer to as Hawking’s Law my audience would quickly tend to naught: Assume that my potential audience would be the entire world’s population (yes, I do have ambitions!), how many formulae would it take to have an audience left of less then one?
\[ 7.114\cdot10^9\cdot0.5^n<1 \]
This indeed holds for as little as \(n>33\), a number we will quickly exceed – and yet you are here, reading this blog, thus defying Hawking’s Law. Q.E.D.
Expressed in a less geeky way: Any contribution is highly appreciated.
One last word to the format: I explicitly chose to write a blog for the lack of structure. This is not a “proper” textbook, it’s merely a collection of interesting facts that will help develop an understanding of the Riemann Hypothesis, in no particular order. I shall write an article whenever I stumble across some curiosity that is worth writing about. And I hope you will enjoy reading it, and learn something new along the way.