While training to be a psychohistorian, our hero Eron Scogil tries to use the Founder's math to study the ancient history of the planet "Rith" [Earth]. (It is both humorous and depressing to see a believable presentation of how little our world would be remembered and understood by our descendants if they inhabit other planets 70,000 years from now.) In doing so, he discovers a modification to the "classical" mathematical techniques used by others which reveals both the role that secrecy plays in maintaining the status quo and the danger posed to the "Pscholars" by the possible existence of other groups who know these secrets. His reward for bringing this knowledge to the attention of his teachers and mentors is a type of capital punishment: the electronic computer that has been part of his brain since his youth is removed and destroyed, leaving him "just an animal" like his ancient human ancestors. (No offense intended to any humans who might be reading this novel, I assume.) And, that's where this story starts. The book is weighty and difficult to get through, but I highly recommend it.

Of course, there are quite a few other books with similar themes. Aside from the already mentioned Foundation, there is The Chimera Prophesies (by a professor of math education), The Dark Side of the Sun (where the math is more a part of a joke than a serious statement of any kind), and In the Country of the Blind. Of these, the last is actually the most similar since it puts a lot of focus on the math itself (and because it is used in Eifelheim to look to the past rather than the future, as it is here).

Since the author taught mathematics at McGill University in Montreal for many years, there is reason to have high hopes for the mathematical content in this book. In fact, mathematics is discussed with great frequency. However, in most cases it is just vague comments about how important math is, how talented the main characters are as mathematicians, and so on without any details.

A more mathematical part of the book occurs when the protagonist arrives at university to study psychohistory. The reader is presented with some hints of what he is studying (e.g. category theory which I think would be unlikely to be useful for predicting human behavior) and quotes from some of his textbooks (I love the one from his physics text).

In addition, some of the other chapters begin with quotations from the writings of the Founder himself, which often contain interesting mathematical ideas:

When we later learn a bit about his modifications to the "classical" math, it is framed in terms of dynamical systems: