Asking a question to invite an open-ended discussion which is unlikely to convince any of the parties taking sides in it is by definition a non-constructive question which invites closing (and possibly deletion) votes.

As for my subjective point of view, yes. It is my subjective point of view that Thomas made a condescending comments here, but it is the responsibility of whoever poses the provocative question to avoid hurting the feelings of other people, not the other way around. Thomas failed in that task, which signals me (and probably other people too) that it is not a well-phrased question.

My point is that if you want to ask provocative questions, of any sort, then you need to be:

1. Extra careful in their formulation, as not to offend those that you want to answer. It's easy to misunderstand Godel's incompleteness theorems, but there is a huge difference between asking "What am I missing here?" and "Is Godel wrong because ...?". Where the former shows some humility and respect to the generations of mathematicians that examined the proofs from top and bottom, the latter implies that the person asking the question is better than those people because they are all wrong.

2. Very open to the fact that it is far more likely scenario that you are wrong/misunderstanding the concept, than to that your "thought provoking question" is going to wake everyone up from the Cantorian/Godelian/otherwise nightmare that has been haunting mathematics for the past who knows how many years.

Thomas' comment on the meta makes him sound as if all those hundreds (if not thousands) of extremely capable people that studied set theory in the past 91 years are wrong, and blind and it's quite insulting. I was ambivalent regarding closing/reopening the question in the topic, but I can assure you that with the current attitude I find it quite worthless and will vote to re-close it if it were to reopen (unless I'll see an improvement from Thomas' side).

Why your answer downvoted? Probably because it's not really an answer but more of "Ah! I agree!!! Look at the question I asked which proves that incompleteness is a disease in the foundations of mathematics!" sort of a comment. I didn't downvote, but I can understand those who did.

Some year and a half ago I ran into an economics Ph.D. student who did his undergrad in math & economics. When he heard I was a set theory student he began asking me "foundational questions", but he wasn't at all interested in an answer. He was interested in showing his superiority over a set theorist. The discussion quickly deteriorated into me trying to explain something and him replying "So what's <something>?" without paying any attention or showing the slightest interest in my actual answer.

People who want to ask provocative questions must listen to others, otherwise they are no better than the cranks we keep banishing from the site. If you want to complain about how you don't understand a particular topic, that's fine, but unless you are going to be receptive to the likely possibility that you are wrong, and listen to what others have to say, there is little to no point in posting on this site, or on any other community which respects itself.

There are some intriguing points of your comment that -- if I understand them correctly in their intended spirit! -- I can find agreement with. You probably anticipated that the brief passing mention of bicategories would catch my eye, and you'd be correct in that. Specifically, there is the wonderful and powerful method of string diagrams (whose precise expression was given by Joyal and Street) that provides rapid-fire methods for calculating in bicategories, that those with experience would accept as fully convincing, encapsulating in a flash what would require many lines of calculation in a more traditional style of proof (including proofs by appeal to commutative diagrams). If this is the type of example you had in mind when you wrote

finding a pattern or configuration inside some larger structure, and exhibiting such as an alternate to a proof in some formal system in a symbolic language

then I can find agreement in spirit, but -- I'd still call such calculations "proofs". Such proofs are also recognized by the cognoscenti as fully formalizable in the fuddy-duddy first-order theory of bicategories. And I think this last sentence is an important point, and is one illustration of the essential deep purpose of reductionism in mathematics. (Just last night I was reading Saunders Mac Lane's eloquent reply to Freeman Dyson in the New York Review of Books, <a href="http://www.nybooks.com/articles/archives/1995/oct/05/a-matter-of-temperament/?pagination=false">here</a>, on the purposes of such reductionism in mathematics. I might recommend this to your attention as well.)

To circumvent further misunderstandings, it might help to specify clearly and carefully what you mean when you say "proof". I don't mean that you should do this here! But if you have further discussion with The User, this could have the welcome effect of making your provocations seem less off balance. (I also suspect The User is more sophisticated, or at least less prone to 'misguidance', than you seem to be giving that user credit for. A more careful and mathematically nuanced discussion on your part, if you have the time and interest, might elicit the same from him/her.)

Finally, to indulge in some provocation of my own: I find something deeply ironic in Gerhard "Proofs: Crutches For The Unimaginative" Paseman. Might it be you who is considering proofs in a limited and unimaginative way? But, I might immediately withdraw from that by remembering that I normally have a very high opinion of you as well, and also by seeking solace in your

I can imagine a situation where the present form of doing mathematics would be replaced by an activity of structure building

since this is actually how modern conceptions of proof appear: as constructions! Here I would draw your attention to the fantastic comment by Andrej Bauer (http://mathoverflow.net/questions/127889/is-rigour-just-a-ritual-that-most-mathematicians-wish-to-get-rid-of-if-they-could/130125#130125), and ask you, if you haven't done so already, to read it five or ten times and take the message deeply into your heart. And just for kicks, try substituting "Numbers: Crutches For The Unimaginative" and see how that would sound. :-)

Peace.