Our narrator returns to the distant future, expecting to find the peaceful Eloi and beastly Morlocks that he saw the first time he went. However, he finds that there are no longer any Eloi, and the Morlocks are instead an intellectual race. Nobogipfel, Morlock who ends up going with our hero back to the past, helps him understand the fact that the narrator's own time-travels caused these changes, and teaches him about the Many-Worlds Interpretation of quantum physics.

Like the original novel, there is some discussion of higher-dimensional geometry. But, that is not the primary reason that I am considering Baxter's sequel to be a work of "mathematical fiction". Early in the book, Nebogipfel also tells the narrator about Gödel's Incompleteness Theorems:

Personally, I found it a bit hard to believe that a Morlock would know so much about Kurt Gödel after so many years had passed. Then, coincidentally, they just happen to meet Kurt Gödel.

In the 1930's universe where they find themselves, England and Germany are war. But, it is not World War II as we know it. Instead, it is a war involving time-machines. Two copies of the narrator from Wells' book (a young one and an older one) and Nebogipfel are brought there by the British government and they find that Gödel is also there, working on the theory of time travel.

In fact, as the author surely knows, Gödel did do some work on theoretical aspects of time (though not exactly "time travel".) As a gift to his good friend Albert Einstein, he found a solution to the equations of general relativity which included closed time-like curves. This means that general relativity allows for causal loops (such as a people being their own grandparents).

And, there are other little "Easter Eggs" that can be noticed by readers who know a lot about Gödel: such as his concern about the loopholes left in the constitution of the United States of America and his explanation of why he is in London rather than Princeton.

Gödel himself only appears as a character for a few short chapters. However, the idea of Gödel's Incompleteness Theorems returns at the end of the book as part of a "gosh-wow" explanation of the multiverse: