The Annotated Turing by Charles Petzold really is great. It comes up a lot on this website but it was a great follow up, a good bridge from the fun almost hack-y math to a more "serious" approach. This led me to:
Computability and Logic by George S Boolos. A standard textbook in universities across North America (and maybe further?).
In the end I didn't become a mathematician. I hardly use advanced math compared to many other engineers and scientists but the ideas have stuck with me for years, and I think my life is richer for knowing them
However, the pure-mathematics coursework ended up being the most useful: two or more mathematical analysis courses, non-Euclidean geometry, statistics, algorithmic analysis, and mathematical topology.
The two take-these-if-you-want-a-future courses I’d recommend are discrete mathematics (which I use every day) and abstract algebra (which I also use every day).
There are a lot of good college textbooks for both; mine is long gone, though you may find one that you absolutely love.