Run, don't walk, and get "An Introduction to Mathematical Reasoning"by Peter Eccles. That will open your eyes to mathematics, as done by mathematicians.
After that, anything by Serge Lang. He is a first-rate mathematician and a fine educator. A master of mathematical exposition, a rare talent.
I started with two books: "Principles of Mathematical Analysis" by Walter Rudin, and "Abstract Algebra" by Israel Herstein. Keyword is "started". Nearly every paragraph of either book sent me to a goose-chase of research and reading up on supporting materials. Safe to say that by the time I was nearly done with either, I have acquired about 50 other math books and had about zero social life ;-)
Good news is that good math books are cheap, compared to anything computing. You can find classics for $1-$5 in most yard sales and 2nd hand bookstores. The trick is to buy thin math books; the giant, multi-color text books they use in schools are highly confusing, at least to me. It's 200 pages of math stretched to 1200, with a similar jump in price.
Mathematics is both style and substance. Once you get the hang of the basic language, the succinct delivery style, the proofs and generalizations, how notation is introduced and then elided when it becomes too apparent .. all these will add up to help you navigate more "advanced" texts. You will come to recognize what is a well-posed mathematical problem, and what is not, even if you don't understand the domain itself.
Finally, if you have the option to study this formally at an institution, do it. The 2nd best option is to find a friend that shares this interest and discuss things. I didn't study it formally, but I was a barista at a coffee shop with plenty of mathphile customers. I had a lot of 1:1 instruction for highly qualified people on my 10 minute breaks :-)
After that, anything by Serge Lang. He is a first-rate mathematician and a fine educator. A master of mathematical exposition, a rare talent.
I started with two books: "Principles of Mathematical Analysis" by Walter Rudin, and "Abstract Algebra" by Israel Herstein. Keyword is "started". Nearly every paragraph of either book sent me to a goose-chase of research and reading up on supporting materials. Safe to say that by the time I was nearly done with either, I have acquired about 50 other math books and had about zero social life ;-)
Good news is that good math books are cheap, compared to anything computing. You can find classics for $1-$5 in most yard sales and 2nd hand bookstores. The trick is to buy thin math books; the giant, multi-color text books they use in schools are highly confusing, at least to me. It's 200 pages of math stretched to 1200, with a similar jump in price.
Mathematics is both style and substance. Once you get the hang of the basic language, the succinct delivery style, the proofs and generalizations, how notation is introduced and then elided when it becomes too apparent .. all these will add up to help you navigate more "advanced" texts. You will come to recognize what is a well-posed mathematical problem, and what is not, even if you don't understand the domain itself.
Finally, if you have the option to study this formally at an institution, do it. The 2nd best option is to find a friend that shares this interest and discuss things. I didn't study it formally, but I was a barista at a coffee shop with plenty of mathphile customers. I had a lot of 1:1 instruction for highly qualified people on my 10 minute breaks :-)