Anathem, by Neal Stephenson.
The book is set in an alternate timeline, where a tradition has taken root (over thousands of years) for academics to isolate themselves from society for long periods of time. There are those who are in for a year, and aren't allowed to mingle/communicate with those who are in for 5 years, or 10, or 100. There are some actual proofs in the text that are crucial to the plot. The book contains a serious discussion (which I wouldn't have thought possible, much less interesting) of whether mathematics is discovered or invented, and what would the nature of an experiment that could distinguish these possibilities be like.
I liked the book when I read it. It has really "stuck to my ribs", however, and I now love the book.
