I recently said something about the impossibility to prove the consistency of PA, and that Gentzen proved just this in 1936. Because I got critizised quite a bit, and realized that even famous mathematicians get critizized if they dare to mention this, I decided to read the original papers of Gentzen. I was deeply impressed how well explained they are, and how much more perspective they add. But I also realized that they are written in German, and that it will probably be impossible to express the thoughts with the same clarity in English, at least for me. Still
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Recent Comments
 Fields and total orders are the prime objects of nice categories  Gentzen translated on Defining a natural number as a finite string of digits is circular
 Fields and total orders are the prime objects of nice categories  Gentzen translated on Algebraic characterizations of inverse semigroups and strongly regular rings
 gentzen on ALogTime, LogCFL, and threshold circuits: dreams of fast solutions
 gentzen on Theory and practice of signeddigit representations
 gentzen on Defining a natural number as a finite string of digits is circular
 gentzen on Defining a natural number as a finite string of digits is circular
 gentzen on Theory and practice of signeddigit representations
 rjlipton on Theory and practice of signeddigit representations
 Defining a natural number as a finite string of digits is circular  Gentzen translated on Theory and practice of signeddigit representations
 Theory and practice of signeddigit representations  Gentzen translated on ALogTime, LogCFL, and threshold circuits: dreams of fast solutions
 Ajit R. Jadhav on A list of books for understanding the nonrelativistic QM — Ajit R. Jadhav’s Weblog
 gentzen on I’m not a physicist
 gentzen on ALogTime, LogCFL, and threshold circuits: dreams of fast solutions
 gentzen on ALogTime, LogCFL, and threshold circuits: dreams of fast solutions
 gentzen on ALogTime, LogCFL, and threshold circuits: dreams of fast solutions
not aware of any controversy on this. why do “even famous mathematicians get criticized if they dare mention” it?
I added links to the criticisms of Voevodsky’s position now.
Linking to the criticism of my statement turned out to be difficult, because the downvotes and comments were removed after I updated my answer. If I remember correctly, the criticism was targeted against my conclusion: “Well, even mathematical proofs depend on general context, implicit assumption and explicit premises.” Especially the part with the “implicit assumptions” was ill received.