|The way this science fiction novel conflates technology and religion is more interesting than anything it does with mathematics. The "gods" in the book are advanced artificial intelligences and "angels" are their cyborg assistants, but they still play a role in the belief system of humans very much like that of supernatural deities in traditional religions.
The plot concerns two scientists, a senior researcher and her young protege, who use what the book refers to as "heretical mathematics" to access "The Outside". What that means is never really explained, but it seemingly distorts the laws of physics, collapsing space and time. It also has the effect of killing many people who are there when it happens and driving the rest insane. The elder scientist has known about this from childhood and does not mind that many people are dying in the disasters that she causes. (She blames many of the deaths on the attempts of the gods and angels to stop her heresy, but still acknowledges that some of the deaths are her own fault and doesn't seem to care.) The younger scientist, Yasira, only learns about the dangers after a new reactor based on her ideas results in a localized collapse of space and many deaths. Yasira is the protagonist of the book and her uncertainty about whether she supports her mentor or the angel attempting to capture her is the main source of tension.
But, this is a website about mathematics in fiction. So, let's talk about the math in the book for a moment. Yasira is described as a prodigy and a mathematical genius. On several occasions we hear that she is doing computations and analyzing data:
|(quoted from The Outside)|
This was what Yasira excelled at. Finding patterns in numbers, working out what they meant. She was faster at it than almost anyone else on the ship. It might no longer fill her with glee, but she could still get lost in it, pleasantly absorbed for hours until someone reminded her it was time to eat.
The adjective "fractal" is used in a few sentences. The few discussions of mathematics that include any detail do not make much sense to me. For example:
|(quoted from The Outside)|
"It's a standard set of Erashub equations, but she's taken out all of the representations of space, size and distance and replaced them with this awful looking symbol. When I try to solve for it, I get infinity or nothing. Like...the portal creates a singularity but with distance instead of mass. Infinite distance in zero time. Not folding the distance using quantum mechanics, which would be sensible, but just pretending it isn't there. Because apparently," Yasira shuffled through the pile of papers and opened Dr Talirr's diary to a marked page, "space is a lie".
I suppose this paragraph does bring to mind some real mathematical physics. We have learned from relativity (not quantum mechanics) that space is not the flat, three-dimensional manifold we previously imagined it to be. And there are troublesome "infinities" that show up in some equations of quantum field theory (cf. "renormalization"). Perhaps such vague analogies are all that this paragraph was intended to evoke. However, since I am fluent in the language of mathematics I feel that I should actually understand what it is actually saying, and I do not.
Moreover, although the idea that there are dangerous mathematical ideas which the gods and angels hunt down as heresy is interesting (and reminds me of the Laundry books by Charles Stross), the author does not do much with it. (Perhaps it will be better utilized in a sequel, if one is published.)
On a separate note, the book clearly states that Yasira is autistic. (In fact, the cover says the book should be filed under "Autistic in Space" and the author also is identified as autistic.) That is notable because both in fiction and in "common knowledge" there is a link between autism and mathematical ability (though I have never been able to determine whether there is any evidence to back up this belief). So, I have tagged this book with "Autism" as a motif. However, I really do not see anything in the character that would lead me to describe her as autistic! I can tell that she is a lesbian by observing her behavior but I would not know that she was autistic if I wasn't told that she was. It is true that she is sometimes shown to be uncomfortable as the center of attention at a huge party and not being 100% sure of what she should say to her partner, but I would think that both of those are things that could happen to "neurotypical" people. (This all leaves me wondering whether the definition of the word "autistic" has changed during my life time and I no longer really know what it means.)