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I haven't quite reached the "mathematical maturity" but what you describe seems like something I have be after too.

I think you need to have a look at Kolmogorov's Mathematics: Its Content, Methods and Meaning [0]

You can also get it in print [1]

[0]: https://archive.org/details/MathematicsItsContentsMethodsAnd...

[1]: https://www.amazon.com/Mathematics-Content-Methods-Meaning-V...




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