Sort of a math-tech question: What is the current state of electronic blackboards, Math OCR technology and connection to mathematical databases and equation solvers?

There is certainly software that can read simple expressions like x^5 - x + 1 and translate it into your computer algebra language of choice. But as the domain of discourse grows the usefulness of this kind of thing vanishes. Something like y^2 = 1 can easily be scanned by OCR but it could possibly correspond to any extremely large set of assertions. Is y a commutative variable? Is y a matrix? Is y a quaternion?

Specifying any mathematical structure in software typically is very difficult and doesn't resemble what you'd find in a textbook. Isabelle has one of the most readable formal libraries of mathematics, and even then it takes a large amount of additional annotation to specify even the simplest of assertions.

Has someone seen the last big bang theory episode? :D

Equation solvers: see Wolfram Alpha, that is a pretty good example (it is actually smarter than many people, because it can solve even short word questions pretty accurately). And it's database is vast.

Worked in a company that does AMS (Analog and Mixed Signal Modeling), those solvers probably even surpass Alpha, but are very specialized. See e.g. Cadence Virtuoso platform, which is kind of "industry standard".

EDIT: electronic blackboards: if there were a market for it, somebody would be producing them. IMHO projector is better.

I've seen electronic blackboards, but they mostly seem to be a waste of time/money. There's some cool stuff where you get like a small tablet and hook it up to your computer wirelessly (like with bluetooth) and you can hook the computer into a projector so you can write on the board while being far away from it. Kinda neat, though not really math-specific.

Wolfram Alpha/Mathematica have reasonable equation solvers. Sage is free and can do some wild stuff like finding Sylow subgroups.