Just about everything I was taught in school is something I can’t prove:
• I can’t derive all the mathematical formulas I learned.
• I can’t conduct all the necessary experiments and observations to prove what I was taught as science.
• I can’t prove the received principles of psychology, sociology, economics, or political science.
• I can’t go immerse myself in a foreign culture and language to prove that what I’ve learned of German, French, Latin, Sanskrit, or any other language is authentic.
• I can’t undertake my own study of history from primary sources and examination of artifacts.
• I could (theoretically) go read all that philosophy, and I have read some of it myself (trusting in the unproved faithfulness of translators’ renditions), but I’m not qualified to analyze and distill it all to prove that the summations I was taught are valid.
• I can study literature, grammar, and composition and evaluate them for myself, but my understanding of them and my analytic tools were passed down to me by my teachers.
And I do, for the most part, accept that what I was taught is true; not without skepticism, to be sure, but in the main I do think much or most of it is provable, even if not by me.
Education would be a poor thing if every student had to start from scratch and redo all their predecessors’ work. We would never progress very far. We have to accept some things as givens, having confidence in their authenticity and demonstrability (and learning something about the methods of deriving and validating information so that we know how it can be done), in order to build on them.