What determines you have learned a (theoretical) subject? My question primarily pertains to advanced/research level mathematics.
I would like to know how you can determine whether you have learned a subject? Of course, you'll never master an entire subject, but at what point you can claim that "I know" functional analysis, algebraic geometry, etc? What determines the boundary of "knowing" and "not knowing" these subject?

This forum might not be the best place to ask this question, but I thought it would be even more inappropriate for MathSX and MathOF (for different reasons).

Update: As mentioned in the comments, "knowing" may have some negative connotations which I did not intend to convey. What I meant is simply that how much you should know about a subject so that you get the confidence to do research?
I asked myself this question a lot during my undergrad - "Did I learn anything here?"

This is how I determined if I have learned a subject:  Can I teach it?

Now, I don't mean can I get certified to teach it, or can I go teach the course in the next semester. If I could sit my parents down and explain to them subject X and have them grasp it then I believe I have learnt it. If you can't inform someone about a subject well enough that they understand it then you cannot possibly understand it. 

You could also write a (fake) course outline. Pretend that you would be teaching this subject as a course. Create an outline such as

1). Major point

   A). Sub point

      I). Explain sub point with case x

      II). Explain sub point with case y

B). Sub point


Etc.

This is what I do when I tried to determine if I learned enough about a subject and if I felt as though, for example, on main point 5 sub point B I can't explain it very well or I am even too confused by it to really grasp it - back to the textbook, or google.