The Devotion of Suspect X - Chapter 6

..and it's flashback time. It's Teito university again, and a much younger Ishigami is sitting by himself in a lecture room. Another student behind him strikes up a conversation; this turns out to be a young, disagreeable Yugawa. Turns out they're both notorious and know of each other by reputation. There's some interesting banter about Paul Erdös and the Four-color theorem, mostly, I suspect, as a way for the author to establish a bit of local color. As they study different subjects - mathematics and physics - they don't interact much directly, but they hear of each other throughout their undergraduate days.

An aside:

Paul Erdős was a real character even by the standards of mathematicians; check out the Wikipedia entry on him, or see the movie. He spent most of his life traveling with no fixed address, and was such an amazingly prolific coauthor of papers that mathematicians (and even other researchers) sometimes keep track of their Erdős Number - how many steps removed they are from Erdős in coauthorship, with Erdős himself having number 0, his coathors having 1, their coathors in turn 2 and so on (I believe I have Erdos number 7 myself; that's pretty far away).

The Four-Color theorem is the claim that a two-dimensional map always can be colored with four - and no more than four -different colors, so that two areas sharing an edge (not corner) always have different colors. This was proved in the 1970's, and is famous because it is the first partially computer-generated mathematical proof. A computer program was basically used to check that a large number of special cases had a certain property; doing so by hand would have been infeasible. In the book our young Ishigami is vehemently opposed to this approach.

By the way: if you think about it, it's easy to figure out that two colors would be enough for any one-dimensional map, and that there's no limit to the number of colors you need for three-dimensional ones.

...anyway:

Returning from the flashback we have the middle-aged Ishigami and Yugawa in Ishigami's apartment, meeting each other again for the first time since they were students. Sharing takeout sushi and a bottle of spirits brought by Yugawa, they reminiscence and catch up their lives. As it turns out, Ishigami wanted to stay on for a doctorate. He was unable to do so as he needed to care for his ailing parents, leaving him with neither time nor money to continue studying. He worked as a teacher at a technical college for a few years but was so swamped with teaching duties that he was unable to do any studying or research. Also, the students were mediocre and the faculty more interested in politics and infighting than in research. He eventually gave it up and went into teaching high school instead.

Yugawa has brought a paper purportedly disproving the continuum hypothesis. Doesn't matter what it is (it's an unproven theorem about what kind of infinity the real numbers belong to) but it's a way for the author to show Yugawa and the reader that Ishigami still has it - he spends most of the night oblivious to time, finally finding the fault in the paper early next morning. Duly impressed, Yugawa follows Ishigami on the way to work. Ishigami confesses that he does frequent the bento shop where Yasuko works, and they part way as Ishigami heads that way to pick up his lunch.