This is a story about a mathematician who discovers that she can make any number equal any other number, if true would change most of maths.
It was really well explained, even overexplained in some places which did make it feel a tiny bit gimmicky, I understand that this genre is more idea driven than character driven which I do appreciate but I feel it could have worked slightly better, like there didn't seem to be motivation for Carl to leave Renee.
The reason in the story was because she wasn't experiencing a "normal" type of depression. She gave the Analogy that it was like a religious person had proven for certain that God didn't exist, that level of changing her fundamental view on the world. She had fundamentally changed as a person. But the last two paragraphs were really ambiguous so I didn't really understand Carl's motivation.
Hard science fiction shouldn't have to make any compromises in making the story character driven if the whole point of story is about an exploration of possibilities of ideas, it's not really aiming to be about people, But I think their choices should still make sense and Carl's didn't to me at all. Or I just didn't understand the ending.
Overall it was a really interesting story, I really liked the structure of referencing something from the history of maths, and then a little bit from each character's perspective,
It was kind of about a paradigm shift in thinking about the world, not necessarily a story about maths, it was a story about the philosophy of maths and the mindset of mathematicians. It kind of posed the question, of "should maths be in the same category as science?" Is it empirical knowledge or is it A priori, basically, can we prove it is true, or is it like science in that we can never really Prove, only falsify.
I thought the idea of maths not being known A priori was interesting but wish it had been pushed a bit further, Does maths offer a model for a way of understanding the world in the same way as science does or is it an inherent part of the world.
I'd love to see Chiang address this in a longer story.