Ok this has be bothering me for a bit, I understand that a bitcoin can be traded like any normal currency. What I don't get is how they are created, I mean I understand the creation of the coins by solving mathematical problems (which are geared to make sure there is a "steady supplier of coins"). But aren't problems they are solving is just busy work? They don't seem to be performing any useful calculations, when I first heard about bitcoins I thought it was more along the line of the SETI project where the free processor time was used to process massive amount of data, but with anyone able to buy processing time (I get the worry about criminals buying time).
Have I missed something? Because at the moment the creation seems like a waste of time and electricity, where it could be used for so much more.

Any insight on this would be appreciated.

AFAIK it is "useless work". The reason, as far as I can tell, is that it's really hard to think of a problem that is both useful to solve and has the cryptographic properties required by bitcoin.

The waste will not last forever though. At some point all possible bitcoints will have been created, unless the system is changed. This is by design. After that, existing bitcoints will just have to be divided into small enough parts. Bitcoin is designed to be divisible into very small pieces, much smaller than our usual cents and pennies.