In the comments on my previous post about Gerhard Opfer’s proposed proof of the Collatz conjecture, several different people expressed the opinion that my tone was rather arrogant, and I think they have a point. So: I apologize for my tone. I have fallen prey to the all-too-easy pleasure of pointing out how other people are wrong.

I do not, however, apologize for the *content* of my post: I am still firmly of the opinion that Opfer’s proof contains an unfixable hole.

What surprised me about your post was the dismissive phrase

“just boils down to some number theory”. I’d have thought any imaginable proof of Collatz would satisfy this!Well, I actually don’t think that’s true. It’s easily imaginable that a valid proof might involve other branches of mathematics in non-trivial ways. For example, Fermat’s Last Theorem is in some sense “just a statement of number theory” but I don’t think anyone would argue that the proof of Wiles et al “just boils down to some number theory”!

Sure. My point was that the phrase “just boils down to X” implies a certain triviality to X, at least to my ears. While number theory is about as non-trivial a subject as it’s possible to imagine!

Wiles’ proof already constitues “some number theory”, with no need to boil down any further.

Anyway, thanks for your thoughts on the latest Collatz ‘proof’.

Ah, good point. I suppose I meant that Opfer’s proof in particular boils down to some

trivialnumber theory (and also that it doesn’t really depend on the complex analysis), not that number theory in general is trivial.Meh. Don’t let the tone trolls get to you. You have nothing to apologize for.

I’m sure, you didn’t mean anything offensive. :-)

In case you didn’t see this: http://www.spiegel.de/wissenschaft/mensch/0,1518,768289,00.html

Your posts made it to the major German News magazine website — congrats.

I didn’t think your tone was “arrogant.” That’s all in the mind of the reader.

Your readers want to know what an arrogant tone is? Try d-flat an octave above middle C! That is an unbearably arrogant tone.

I’ve seen arrogant. I’ve been arrogant. You weren’t arrogant. Only someone who was quite thin-skinned would think otherwise.