Ten years ago this month for various reasons I thought to myself it might be fun to try and find simple solutions to famously hard math problems, so I went at it.

Believe it or not, I assumed that I could use modern problem solving techniques to quickly find what I figured people weren't really looking for, as from what I gathered mathematicians believe that all the easy stuff was found years ago, and they pride themselves on building only on what's known.

Like with the spherical packing problem or Fermat's Last Theorem, I thought maybe there were simple answers, but because today's mathematicians start by looking at what other mathematicians did, and trying to build on it, maybe if I just started from scratch, using modern problem solving techniques, I could find something that was missed.

After a couple of weeks I actually thought I was done. I was very, very wrong, and here now about a decade later, I wonder at how naive I was.

Still if I'd known what was ahead, would I have tried?

Who knows, but I did try and now I have mathematical discoveries that span number theory.

Possibly I can go into the journey itself in this blog, as it's been a remarkable adventure, with lots of bumps along the way, and some strange characters and misadventures.

But through it all has been the beauty of discovery and the power of logic, and thought, as I worked very hard for some years to get some answers.

And I found some.

James Harris