An Artificially Created Universe: The Electronic Computer Project at IAS (2012)

This article is an excerpt from the book Turing's Cathedral, which, coincidentally, I'm currently reading. Sometimes I wish it went into a little more technical detail (and I think it's a little too charitable toward von Nuemann and the IAS) but it's still a worthwhile read and I think covers that era much more completely and with more depth than other works. Anyway if you like that article, the book is equally fascinating throughout.

There are many such books! It's hard to suggest something in particular because almost everything about computers comes from some area of theory. I'll try giving you a few specific suggestions while also touring some broad areas.

One really active area of research is type theory. Another easy one is differential geometry and linear algebra, which are fundamental to machine learning. Try searching for resources about manifolds and dimensionality reduction. While we're at it, any kind of vectorized computation can also be modeled through linear algebra. There's probably material somewhere that formalizes a lot of Intel CPU architecture algebraically.

Actually, we can basically just take linear algebra and talk about its applications to nearly any area of computing, since it's one of the most ubiquitous areas of mathematical theory. What are you interested in? Graphics? Algorithm design? Data analysis? Parallelism? Statistics?

Combinatorics is also a big one. Knuth's The Art of Computer Programming has a wealth of material on combinatorics and its applications to computing (and in particular, algorithms thereof). You also might like learning about the way complex numbers and quaternions are used to computing spatial rotations.

I'm not personally a fan of category theory, but if abstractions are your thing you might enjoy Bartosz Milewski's Category Theory for Programmers. Along similar lines (and circling back to type theory), there's CMU's Software Foundations series of books[1].

If you are interested in cryptography, you might really enjoy reading Chris Peikert's A Decade of Lattice Cryptography[2]. The author is a prominent researcher in post-quantum cryptography, and walks through the last decade or so of research in cryptography based on a type of structure in abstract algebra called a lattice. This is very technical material, since it's more like a survey than a book.

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1. https://softwarefoundations.cis.upenn.edu/

2. https://web.eecs.umich.edu/~cpeikert/pubs/lattice-survey.pdf