I haven't downvoted your answer! Indeed, I haven't found it rude at all. On the contrary, I enjoyed it a lot, though It was real close to the bone.

quid/ Thanks for your advice. I'll try the site you mentioned

/paul I do certainly agree that mathematicians work with ideas when they are at their own desk. But, iamgine what would happen in a few years if they (as a community) do not organize their knowledge: no two mathematicians could speak with each other since that "union of all the different ways" of defining an object/idea/concept would be too big that makes it hard (if not impossible) even for the people working in the same area to communicate with each other. Thus, by and large, it seems there should be a "mechanism" to choose agreed upon definitions. – Amir Asghari

Sergei : Let me do not answer your question and just say it was in a math department. I certainly agree that was very strange. (Qiaochu,Steven) However, I think the main argument was if there are different ways of convincing and your paper would be rejected if you are using one or the other while it is supposed that there is only one (i.e. proof) ,there should be something wrong and forced upon you!