In part four we see how Bombelli used \(\sqrt{-1}\) to solve Cardan's problem. This was cutting edge mathematics at the time - but these days can be completely understood by strong algebra students. I tend to move at a pretty quick pace through the derivations - but I assure you, the math isn't so bad - and you can always pause the video to check it out in more detail. Keep in mind that you may need to change your playback settings on YouTube to HD to see everything.

What strikes me about this part of the story is how unimpressed Bombelli was with his own work - we see this type of behavior with a number of scientists and mathematicians - Newton comes to mind. This makes me wonder how many folks are out there sitting on amazing discoveries, but haven't shared them yet because they don't think their work important enough.

It's interesting to me as well that doing quality work not only requires the ability to do the work, but the ability to gauge what work is important and what work is not. The later seems to be more of an art than a science.

Enjoy!