For whatever reason, I practiced the piano three times yesterday. I’m annoyed by my inability to play the Grieg Piano Concerto. I suppose it’s probably quite difficult, but I don’t consider that an excuse. I suppose I’ll learn it eventually. I just keep forgetting how difficult it is to learn new pieces on the piano.

It occurred to me yesterday that to prove the Twin Prime Conjecture it is only necessary to prove that Brun’s Constant is irrational. That’s really obvious, but for some reason, I never thought of it before. I don’t imagine that it’s easy though — I don’t think Brun’s Constant converges quickly enough by partial sums to use Liouville-Roth irrationality measure easily. Since we only know about 9 digits of Brun’s Constant, I don’t think this method will be usable.

Does anyone know of any good books on algebraic number theory? The time has come to learn some.

The world is so boring. Only classes are enjoyable. My outlook on life seems to be returning to its state five years ago, when I couldn’t stand school breaks because I would learn less. I’m glad that it’s returning.

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## About Simon

Hi. I'm Simon Rubinstein-Salzedo. I'm a mathematics postdoc at Dartmouth College. I'm also a musician; I play piano and cello, and I also sometimes compose music and study musicology. I also like to play chess and write calligraphy. This blog is a catalogue of some of my thoughts. I write them down so that I understand them better. But sometimes other people find them interesting as well, so I happily share them with my small corner of the world.

Algebraic Number Theory — the ones I’ve used are the Dover Algebraic Number Theory by Pollard & Diamond and Algebraic Number Theory and Fermat’s Last Theorem by Ian Stewart and some other guy. Both of them go as far as ideal factorization with some other stuff (of course the Stewart book has extra FLT-related stuff). I’m not sure how much that will help — a friend of mine was working through an advanced graduate-level book on it which used topology and other stuff, but I don’t recall the author.