I woke up this morning with the full intention of going back to bed. I slept just terribly, getting up 4-5 times in 7 hours and struggling to get back to sleep each time. Having already attained my goal in terms of writing this week, I decided to just loaf around today.
First, I started suiciding one of my aliens off a robot 3092 times. (Don't ask.)
Then I napped for an hour.
Finished suiciding one of my aliens off a robot 3092 times.
Did some reading.
I have been reading, "Unknown Quantity: A Real and Imaginary History of Algebra". It is one of those "pop" math books. Mostly, I enjoy reading these books for their historical content, but I have read so many math history books and popular books such as this one, I really do not find them satisfying anymore. Invariably, I wind up reading about the same people over and over because prior to the last 125 years, the number of notable mathematicians in a generation typically maxed out at about three or four. Of course, they were also working at a time when a mathematician could reasonably be expected to know all of mathematics. A feat that would be practically impossible 125 years ago and definitely impossible 80 or 90 years ago. Of course, the mathematics in these books is a bit too watered down to be satisfying as well.
Eventually, I was inspired to work on a problem that I quit working on last spring. It is likely the oldest unsolved problem in mathematics, which means I have no chance of solving it completely on my own. But a math problem is not solved all at once. Most problems are like a giant wall that must be taken down brick by brick until, finally, enough of the bricks have been removed, allowing someone to come along and smash through the rest of the way with that one great idea. It would be nice if I could remove but one brick.
The problem is regarding the existence of an odd perfect number. A google search will yield all the information you could ever want on the subject. Mathematicians do not even know if such a number exists, but I suppose the leading evidence suggests there is not. I stopped working on it last spring when all of the current research relied on proving theorems that allowed the writer to create a more efficient computer algorithm than the last guy. Where they then used the computer algorithm and a number of days of processing power to show whatever it is they wished to show. Their proverbial brick as it were.
I didn't want to attack the problem in this manner so I hung it up for some time. I started looking at the problem again this afternoon and evening and I think I have chosen a single brick to attack. We shall see if I get anywhere this time around.