Back in 2009 I began keeping a log of the books I read. It's a mixture of Science Fiction, Fantasy, Thrillers, Murder Mysteries and a few computer science books. Some are in danish, some in english. As you can see, I didn't include the start and finish dates at first, but I quickly realized that it would be a good idea to include that information as well. I wish I had started this back when I was still studying at the university — back then I used to buy around 20 books each summer because the local book store was selling 5 books for 100 DKK (which is less than what one book usually costs), and now I have a hard time remembering which ones I've read.
One of the important – indeed central – aspects of mathematics is the idea of abstracting out interesting structures in order to study those structures in general. The study of groups, rings, fields, vector spaces, category theory, and so on, are examples of this. Other types of abstractions are general methods and principles, such as proof by induction or the Pigeonhole Principle. One such principle caught my attention recently, namely the Inclusion-Exclusion Principle.
I became interested in making music back in the good old days of the Commodore 64 home computer. I listened to the wonderful music of Rob Hubbard, David Whittaker, Ben Daglish, Martin Galway, Fred Gray and all the other musicians who composed for the C64 (I still sometimes find myself whistling the tunes from Spellbound, Master of Magic, Street Surfer, Krakout, Parallax, Shadowfire and other games that I haven't played for at least 20 years).
The first two mathematical conjectures that I describe in this post go back to the days when I was studying math at the University of Copenhagen. At that time I always had several "mathematical pet projects" that I was thinking about whenever I could find some free time. Usually my projects were generalizations of math problems from my classes, and most of them involved number theory, group theory or combinatorics.
I have a Roland JW-50 Music Workstation, and I've been worried about what would happen to all my music (stored on old 3.5" disks) when the keyboard (or the built-in floppy drive) dies one day. The JW-50 actually lets you save your songs in MIDI format, but I have had problems with that function — I have at least one song that crashes the keyboard if I try to save it in MIDI format.