http://goo.gl/forms/KuXqj0wgZu
Edit: for those who are interested in the results, here's a one-click link https://docs.google.com/forms/d/1_RkOUYEoC4m9mYQZKexp2uSuj63...
I'm pretty comfortable with probability and optimization, which is my day-to-day. I will probably never be better at topology than I was when finishing my undergrad degree. And in my one brush with differential geometry, I struggled to reach the rigor.
And even then it's more complicated, because human intuition is notoriously bad in probability.
It's very exciting, I feel like I'm finally able to play by the rules of math, and I'm looking forward to the places this newfound knowledge can take me.
It would be interesting to know if there are corresponding hierarchies in subjects such as science, computer programming, or even music.
I think that you could probably apply the labels to just about any profession, or even hobby (I'm thinking of rock climbing as one close to my heart), and it might even be interesting, but it probably wouldn't have quite the same resonance: I don't think that there are many other fields where being rigorous is seen as an end in itself, and people already tend to think of post-rigorous proficiency in, say, music as a desireable state to reach.
Unlike math, it's just really, really difficult to ascertain that the theory is correct and it's never correct at all levels. I have always called geology 'the science of exceptions' because many of our laws are actually tendencies, and given 4.6 billion years, any bug or loophole in the theory will be exploited--and this is when you really learn stuff.
In practice, I actually think the three steps there are kind of fractally embedded throughout in the stages of one's career, one's individual research project, or the overarching evolution of the science.
It's pretty fun.