I read about the provable cryptography in Wikipedia. The article referred to tense controversies around 2007.

Do these controversies still exist?

What is the substitution for the provable-security? Is not it sufficient? I think AES does not follow provable cryptography style, am I right?

Which is the accepted/preferred view in the Cryptography community?

Why did it started in the first place, Is not proof something desirable?

What are the achievements of provable cryptography?

Where to start cryptography study/research given these controversies?

I read through some objections, I felt that it is a matter of two things: the starting assumption is not strong, and some errors that existed in some paper, am I right? I think the first is essential to even get started (given the awareness of such assumptions), and the second is individual cases (given that it is wrong) not enough to refute the whole branch of science.