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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 ALogTime, LogCFL, and threshold circuits: dreams of fast solutions November 2, 2017
 A subset interpretation (with context morphisms) of the sequent calculus for predicate logic September 24, 2017
 Logic without negation and falsehood December 11, 2016
 Logic without truth September 3, 2016
 Learning category theory: a necessary evil? April 3, 2016
 A canonical labeling technique by Brendan McKay and isomorphism testing of deterministic finite automata November 15, 2015
 On Zeros of a Polynomial in a Finite Grid: the AlonFuredi bound September 19, 2015
 Groupoids August 3, 2015
 Reversibility of binary relations, substochastic matrices, and partial functions March 22, 2015
 Algebraic characterizations of inverse semigroups and strongly regular rings December 6, 2014
 Gentzen’s consistency proof is more impressive than you expect December 5, 2013
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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.