"Just follow this simple road map".
I think about it differently. If you want to become a pure mathematician, you have to publish research in pure mathematics. There are many different routes one can take to accomplish this, and the route that you can stick with and enjoy is the best one.
What different routes are there to publish research besides academia? I would love to work on publications but it is not practical for me to return to an institution right now.
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I could not agree more. I am on my second try to master mathematics (30 years after the first), and I can see, understand and appreciate mathematics mainly from the constructive standpoint.
Nothing wrong with classical mathematics, as also used in this roadmap. Having axioms and drawing logical conclusions or searching proof does just not click for me.
Give me 0: N and suc: N -> N and I see how to construct stuff. Induction makes sense right away as a case distinction on those two constructors.