If an INTJ is playing around with math problems on a regular basis then he is sacrificing his will to embrace new ideas, and to follow them in how they relate to his other ideas in search of a more detailed "big picture". Secondly, the ESFP shadow of the INTJ is the meticulous detail-maven.

The idea that Kurt Godel was an INTJ is absurd. Simply absurd. I've studied the man well beyond Wikipedia. An INTP, yes. An INTJ, NO.

Note: INTJs don't become schizoid. EVER, unless they have an accident, and it is very, very rare that an INTJ lets their guard down enough to go into a situation dangerous enough to injure their brain. And even if they do, they keep a very, very close eye on the unconscious throughout the entire ordeal (and that's what it is) and when they get out of it the people who had gotten them into the mess had better brace themselves for a whithering verbal assault, at least. We take the emergence of forces that end up nearly costing us dearly very seriously, and this is when we are at our most ruthless. "You dare to presume to threaten me?! Die...."

An INTJ wouldn't let themselves get paranoid. They'd have gone to any necessary depths to so shock the world into thinking they were untouchable long before hand. (in the mind of the INTJ at least, and that's all that matters)

Socionics and MBTI ARE THE SAME. The suggestion that they aren't is a misinterpretation of the meaning of Ti. Ti acts as a filter overtop of Te. Thoughts in the INTJ's mind emphasize the importance of the subject over the object, for the purpose of preserving the INTJ's pursuit of the aims assembled by extroverted intuition: continuous pursuit over what "should" be over what is, where "should" refers to the values of the INTJ wrapped in a logical coating of "moral principles". As INTJs mature, the moral principle set is extended to include those thought patterns that implicitly promote the physical health of the community and, by extension, of the INTJ. INTJ maturation is advanced through the conscious exhaultation of Te alongside Ti.

Any system that attempts to describe the INTJ otherwise is simply flawed.