As it happens, I was there when Greg Chaitin began the quest that led him to this book. In 1962 he was in the Science Honors Program, a Columbia University summer school computer program for bright high school kids. I had been in it three years earlier, programming an IBM 650 in machine language and eventually a seemingly magical advance called Fortran, and I returned as an unpaid lab assistant when Greg was there. One of the issues discussed in the program is the halting problem: How do we know if a program can complete in finite time? Thinking about that leads to the kind of provability problems Godel discussed, and Greg came up with an advance on Godel that I do not pretend to understand.
(Confession: Greg was a nerd, even by the standards of a program for gifted high school kids. I must admit I mocked him for being one. We all know about the guy who really wants to beat up "fags" or at least laugh at them. Same thing. I was a latent nerd in full denial, and I took it out on others.)
Thanx to andrewducker