[spekcular]

This is an incredibly strange slate of reviewers. Only the first seems to really understand the mathematical context. It's odd to appeal to the peer review process when the "peers" are not suited to complete the review.

I assure you that Calegari knows more about number theory than any of those referees, and the reasons why the paper is bad are well-explained on his blog (cf. the two links above) and by referee #1. Speaking of "peer review," look at how all the excellent mathematicians commenting on that blog agree with him!

[timkam]

I agree. Without being an expert in the field, the 2nd and 3rd reviews "smell funny"; they clearly lack depth, are very enthusiastic, and don't seem to make a good and comprehensive point as to _why_ this paper is supposed to be as great as they claim it is. In a strong community, any editor should consider these reviews disappointing, and any author should at least have mixed feelings about them.

[scihive]

Calegari gets to cherry-pick comments he approves or rejects on his blog, so calling it "peer review" is taking the concept out of context =).

[Daniel51]

True! I tried several times to comment on his blog - but Calegari didn't confirm my comments

It's hypocritical to criticize but to avoid criticism ...