Is this response ok? (I feel like a 5 year old asking for permission to go to the men's room,but better safe then sorry.........):

I may get clocked for putting my 2 cents in here.But since everyone else is chiming in on this without fear,here goes.

I don't like the expression one bit for several reasons. First of all,too many lazy professors or writers use it to get out of explaining a proof in some detail. My favorite example:I once saw an analysis text where the author said the proof of the Tychonoff theorum on the product of compact spaces is obvious. I was like,HUH? It took me almost a week of struggle to prove the result myself-I refused to look it up just to see for myself how "obvious" it really was.

(Actually,I'm developed a measure of lousy teaching/writing partly based on this phrase:Any professor who uses "It's obvious" more then 10 times in a 1 hour lecture or a 20 page chapter of a text either doesn't know what he or she is talking about or doesn't care.This measure,I find,is piecewise continuous on the set of all mathematics PHDs.)



Secondly,I've seen a lot of professors use it as a subtle "bullying" tool-especially prominent research professors who hate teaching-to get out of "wasting time" explaining something to thier puzzled students.I once saw a fairly well known algebraic geometer-whose name will be omitted to protect the innocent,namely ME-state a theorum in a graduate algebra class without proof and state it's proof was obvious "...to anyone with a half a brain. Any questions?"Total silence-even though I know I personally was puzzled by the claim and so were a lot of the students.But who'd dare ask a question after that?

I feel a much less self-aggrandizing and contemptuous phrase to use is,"It's straightforward to prove...." or "It's pretty easy to show....",followed by the first step the proof to show how one gets started.

Anyhow,that's how I feel about it.

I think it'd really be better if you would make *mathematical* questions and answers on the site, instead of concentrating on controversial topics. Furthermore calling people "lazy" or a "bully" is the kind of insulting language that annoys people.

@AndrewL: okay, let's fact check: in which analysis text is the proof of Tychonoff's theorem asserted to be obvious?

You should also spellcheck, e.g. "thier".

Royden's Real Analysis (at least the third edition, which is the one I have handy) devotes a whole section (§9-3) to the proof of the Tychonoff theorem. It is prefaced by

In this section we prove the Theorem of Tychonoff -- that a product of compact spaces is compact. It is probably the most important theorem in general topology.

Nowhere that I can see does it even hint at the fact that it's trivial or obvious.

Andrew, about Deane Yang, I think that could be a really valuable relationship. People have different modes of pairwise communication. Many cannot be bothered with email, for instance, so just recently I wound up joining Facebook by invitation, not really sure what it's good for. Actually seems to keep people at arm's length.

So you might see if you can call Deane during his office hours, classes must be starting soon. You live close enough (the M.A.A. has you in Ozone Park) to meet in person as well. I found various of his comments to you, he really would like to help and is clearly smart enough to read between the lines even when it is fairly public writing as on MO. Anyway, email, telephones, every now and then in person.

Also, I looked at your profile here, almost all your answers are about books. Don't you enjoy solving goofy little math problems? It's like crossword puzzles or sudoku. Research or classroom graduate mathematics is generally far harder (and far more time-consuming, appropriate when the importance is known) than MO problems, which often have relatively quick answers, and come in a variety of difficulties, same as sudoku.