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> "He incorrectly suggests that the axiom of choice is used for Cantor's diagonal argument"

This alone is a pretty substantial, even foundational, error.

The author of the review, Rudy Rucker, is a sort of cult/underground author of math-heavy science fiction. I don't think he's opposed to framing things in a literary way, so long as it's not misleading or falsely dramatized. Like, e.g., Godel ending his days in some sort of forced confinement, as DFW seems to have suggested?

The DFW style is not just "literary", it's dense, full of self-referential hints, critical footnotes, invented acronyms, retellings of the same events from multiple perspectives. I like Rudy Rucker a lot but his work is nothing like it.

The core problem with this book is that it is a great book for people who love both math and Infinite Jest. But, that might be an audience of nobody. Or almost nobody, because it does include me.

And me. I loved the book.

> The whole book is striking a middle ground between expressing every step of mathematical rigor, and describing in a more literary way how to feel about these concepts

I really hate this. If you don't care to understand something, why would you want to absorb the feelings that somebody else thinks you should have from understanding it? It reminds me of all the cringey posturing that undergrads engage in because their English professor mentioned a couple of philosophers during lectures and it totally changed their wardrobe.

Why would you hate a book exploring mathematics and reflecting on your relationship with it? What a weird thing to hate. Wouldn't you rather celebrate intellectual curiosity?

Like... I hate journalism that profits off of xenophobic fear mongering. A book from a genuinely curious and interesting author who did some moonlighting in more formal subjects, though? That seems harmless and kind of cute at worst. Maybe a little misguided, maybe not.

It's a weird energy to bring to a relatively innoccuous corner of the world.

It's like reading a review of a novel that tells you how to feel about it, and adopting that emotional response without reading the novel itself.

I already do understand set theory and the construction of the real numbers. There are plenty of great books on that, or really nowadays you can simply ask ChatGPT. I am interested in learning about how Cantor, Weierstrass, the ancient Greeks, and others felt, as they grappled with the challenge of making rigorous mathematics handle the infinite. That's what this book is good at.

That's fair, it makes sense for people who already understand the math and are reading for the other aspects. I don't think that was his target audience, though.

As a mathematician, I think it is very hard to write popular expositions of mathematics. It is acceptable and even necessary to skip the technical details and replace rigorous definitions with intuitive explanations, but it should be done with great care to avoid statements that are plainly wrong and only introduce more confusion. I think the majority of texts on complicated mathematics that target the general audience suffer from this issue.

The review mentions some very unfortunate errors that are not "passing over a point in less detail": suggesting that Cantor's diagonal argument depends on the AC and that CH is equivalent to c = 2^ℵ₀.

I wasn't familiar with the book and had just read the review; I wouldn't blame the author, but the publisher should have contacted someone for proofreading.

I read it and it made me pretty upset... Wallace clearly got way out over his skis and simply shouldn't have been writing about the topic. There were way too many moments interspersed throughout the book where it was obvious that he didn't understand what he was talking about or trying to prove. I think one of the key lessons to be learned from the study of mathematics is intellectual honestly and humility. It felt like Wallace hadn't learnt that lesson and had something to... ahem... prove?