I have a lot of respect for all you have achieved! Your work at IBM sounds fascinating, and sounds like you are applying your knowledge more than just researching further. I think it is balancing that you also took time to hike and explore, and build human relationships.

One question -- it's been ages since I studied math for my engineering degree, but possibly, there is a zero missing in this:

If you remember the quadratic equation (Ax^2 + Bx + C = 0), the discriminant is B^2 - 4AC and is precisely when this system has a double root.

Precisely zero when the quadratic equation has one real double root?

I had to look it up here: https://en.wikipedia.org/wiki/Discriminant and still too rusty to know if you left anything out (zero) or if I am not reading what you wrote correctly!

I am having fun getting into the math and coding involved with steem and steemit, and it is good to be refreshed in things I once knew and move forward to learn new things. Thanks for helping with that!