How much of the "accepted" knowledge in mathematics and physics fields do we know to be true?

Everything that you could check. I.e. set up real experiment that will prove or disprove them.

How much of them are reasonably doubtful?

Everything that you could not check. I.e. everything that could not be proven or disproven by real experiment.

That is why every real scientist do everything to think out how to experimentally prove his theory.

Especially as it pertains to what may be taught in universities nowadays.

IDK how they teach youth in universities now, but I was teached mostly to think, not just learn by rote some formulas or laws. I was teached of how all that things works and tied together, how to find relations and connections and it was much better than learning by rote, because if you get an ability to think that way, you could anytime derive any law or formula form the very basic knowledge. Also you could find new laws and formulas if you found a new relation or connection.

Looking at complete disability to make their own conclusions from some related facts in most young people I think that situation in education changed heavily and not to the best.

Do you think one field is worth studying more than the other?

It depends on your own interest and curiosity, not on some fashion, profit, whatever. In any case it is better to choose field you really interested in, even there could be much more popular or profitable fields. Science is about curiosity and attempt to uncover the secrets of Universe or God's plan if you wish, not about doing some boring uninteresting job for money. If you are not interested, Universe/God will not share its secrets with you. :)

How much of the "accepted" knowledge in mathematics and physics fields do we know to be true?

Everything that you could check. I.e. set up real experiment that will prove or disprove them.

How much of them are reasonably doubtful?

Everything that you could not check. I.e. everything that could not be proven or disproven by real experiment.

That is why every real scientist do everything to think out how to experimentally he could prove his theory.

Especially as it pertains to what may be taught in universities nowadays.

IDK how they teach youth in universities now, but I was teached mostly to think, not just learn by rote some formulas or laws. I was teached of how all that things works and tied together, how to find relations and connections and it was much better than learning by rote, because if you get an ability to think that way, you could anytime derive any law or formula form the very basic knowledge. Also you could find new laws and formulas if you found a new relation or connection.

Looking at complete disability to make their own conclusions from some related facts in most young people I think that situation in education changed heavily and not to the best.

Do you think one field is worth studying more than the other?

It depends on your own interest and curiosity, not on some fashion, profit, whatever. In any case it is better to choose field you really interested in, even there could be much more popular or profitable fields. Science is about curiosity and attempt to uncover the secrets of Universe or God's plan if you wish, not about doing some boring uninteresting job for money. If you are not interested, Universe/God will not share its secrets with you. :)