Having an understanding of mathematical foundations and proofs can be very beneficial to software developers; but I agree there are much better books than the ones suggested here. "Elements" is an historically important book (arguably the most important in math), but like you said is fairly outdated. Real Analysis is critical for higher level maths and theoretical computer science and does have some value even in software development. But with books like Spivak's Calculus you spend more time memorizing definitions and theorems than abstract thinking or problem solving.

Some better math books that I would recommend off the top-of-my-head:

* "How to Solve it" by George Polya - A great book on breaking down complex problems.

* "Mathematical Logic" by Stephen Kleene - A much more contemporary math book on building axiomatic theories from scratch.

* "Godel, Escher, Bach" by Douglas Hofstadter - Also about mathematical foundations but for a much broader audience.