Yes, I agree with you. My comment looks dull with your explanation. Of course, I also don't advocate doing something without any hypothesis. Though, I think hands-on practice on a subject can help you learn things better. For example, I find it very useful for linear algebra (maybe this is not applicable to other subjects). I can analyze my flawed intuitions.

When I first heard about the Monty Hall problem, I didn't understand it and tried it myself. It was way easier for me to understand the flawed intuition by analyzing each line as opposed to, say, for example, the explanation of Judea Pearl (which is also good).

What I wanted to emphasize is that it is not bad guessing your way through a problem you don't understand. But yeah, of course, you should have some knowledge.

Mathematics is the exploration of the a priori. Historically some axioms have been deemed more real than others. I think Gauss rejected non-eulidean geometry for instance. But this point of view has changed. With abstract algebra, and I believe also computer science, modern mathematics is about exploring connections between structures such as they emerge from stipulated axioms and rules of inference. It is science in the sense that ideas and hypotheses can be tested experimentally. But a proof requires more than non-falsification. Then there is the complication of potentially irreducible computation problems, where essentially a kind of mining of the computational space is the only way forward. This is the new kind of science Stephen Wolfram speaks of.