Do the thing that the learning was supposed to enable you to do. Introspection and reflection look at the work you put in, the resources spent, not the thing they were spent for. You can only observe where it got you to by doing the thing itself.
In mathematics, do the exercises. Do variations on the exercises. Prove the theorems you learned, without reference to the books.
If learning a language, use it: have conversations in it, read it, write in it.
In statistics, analyse published papers as if you were a referee vetting them for publication.
In programming, write software. Software that does stuff you want done rather than toy exercises.
And so on. Notice how well you are doing all this. That is the test of what you have learned.
Do the thing that the learning was supposed to enable you to do. Introspection and reflection look at the work you put in, the resources spent, not the thing they were spent for. You can only observe where it got you to by doing the thing itself.
In mathematics, do the exercises. Do variations on the exercises. Prove the theorems you learned, without reference to the books.
If learning a language, use it: have conversations in it, read it, write in it.
In statistics, analyse published papers as if you were a referee vetting them for publication.
In programming, write software. Software that does stuff you want done rather than toy exercises.
And so on. Notice how well you are doing all this. That is the test of what you have learned.