Galois theory is so useful that, besides its fundamental importance in algebra, it birthed the whole subject of Galois connections, which crop up all over the place, including in theoretical CS: https://en.wikipedia.org/wiki/Galois_connection .

Galois connections are super useful for static program analysis.

In particular, for abstract interpretation. A great intro book is [1].

[1] Program Analysis – An Appetizer. https://arxiv.org/pdf/2012.10086

Similarly, Galois theory was a penny dropping moment in my understanding of mathematics and has remained surprisingly useful late into by career, as software has become increasingly "mathy".

Would you mind sharing how it turned out useful?

Curious too. It feels like the maths parts of programming are the hobby (proof checkers, Haskell) and the cranking out Go/JS etc is the paid bit. I studied maths but never used more than high school level at work.

Me too! But I can't really remember why. The proof was impressive.

As another math major who doesn't do math anymore, I feel this comment so deeply in my soul

It's a bit shocking to me: I still remember all the concepts quite clearly from when I studied Galois theory ~20 years ago, to the point where I can run through a lot of the proofs conceptually in my head, but the vocabulary is GONE. Like, completely a blank, I don't remember almost any of the abstract algebra terms that all of this is expressed in.

It reminds me of the truth of the advice that my category theory professor gave us, that the definitions are both the least important and the most important things, simultaneously. They're the least important in that they're just words that wrap up very simple concepts, and merely knowing the definitions doesn't actually mean you can work with the concepts. But they're the most important thing in that most of higher level math really boils down to picking out the exact right set of definitions to use, at which point proofs tend to pop out as trivial and obvious statements using those definitions. And at a more practical level, you won't be able to read any math if the definitions are not ingrained, so you might as well get a head start and just rote memorize them if you want to succeed.

But it's interesting that the language is far less sticky in memory than the underlying intuition. My guess is that because the intuition is so much harder to develop, it wires itself in much more deeply than the words themselves, which can be pretty easily learned in a few hours of flashcard work.