Last week, I had reached the last section of the 420 book (Linear Algebra, Hefferon) we are studying together with Tom. Also I have just now reached page 93 (Section 11, Roots, Irrational Numbers) in Zakon's 'Analysis Basics' (Our approach is very patient, complete, sequential and meticulous), along with a great deal of less meticulous reading in other books, papers and 'opinions'.
I can now say, one of the original questions that this blog carries as it's title, namely the square root of two, has been almost demystified!
The next adventures have already been planned quite some time ago: https://sites.google.com/site/77neuronsprojectperelman/jad/theplan.
As with every checkpoint, a huge huge thanks goes to my wife and love Lena.