tea.mathoverflow.net - Discussion Feed (Response to "The value of "It's obvious" in the Mathematical Literature")

Will Jagy comments on "Response to "The value of "It's obvious" in the Mathematical Literature"" (8605)

2010-08-24T13:15:38-07:00

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.

Andy Putman comments on "Response to "The value of "It's obvious" in the Mathematical Literature"" (8602)

2010-08-24T07:28:59-07:00

@Andrew L : Are you sure that you aren't thinking of the special case of the Tychonoff theorem dealing with finite products of compact spaces? I don't think I'd use the word "obvious" for it, but I would use the word "unsurprising", and I might assign it as a homework problem (probably with a hint).

José Figueroa comments on "Response to "The value of "It's obvious" in the Mathematical Literature"" (8600)

2010-08-24T03:16:09-07:00

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.

AndrewL comments on "Response to "The value of "It's obvious" in the Mathematical Literature"" (8598)

2010-08-24T00:34:02-07:00

@Will Sadly,no, I never did get to talk with Deane,but I still intend to when I can. And thanks for the commentary,I'll draft it further.AND I haven't forgotten,we need to talk,too-but things have been crazy.

@Steve Yes,I DO make that mistake constantly. I think I'm missing an enzyme or something.........

@Pete Fair question.I'll get back to you on that,but I THINK it's Royden's Real Analysis. Either that or he included it as an exercise for the reader-which to me,is tantamount to the same thing. It's one of many reasons the book annoys me.

@Noah.Scott Noted and thanks.

Scott Morrison comments on "Response to "The value of "It's obvious" in the Mathematical Literature"" (8595)

2010-08-23T23:24:13-07:00

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

Will Jagy comments on "Response to "The value of "It's obvious" in the Mathematical Literature"" (8594)

2010-08-23T22:08:57-07:00

Andrew, did you ever get to talk with Deane Yang?

Pete L. Clark comments on "Response to "The value of "It's obvious" in the Mathematical Literature"" (8593)

2010-08-23T21:41:51-07:00

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

Will Jagy comments on "Response to "The value of "It's obvious" in the Mathematical Literature"" (8591)

2010-08-23T21:00:56-07:00

Hello, Andrew. I looked at the question. The single response that mentioned classroom behavior rather than writing was posted a couple of days after the others and got just one vote. My guess it is that it would be better to excise the material on bullying. The question was about writing and most respondents took it that way. Meanwhile, you might avoid discussing bullying there, precisely because it makes you angry.

The demands on the reader of a research article are different from the reader of a textbook and yet different fom the demands on a student.

I would drop the word "lazy" as well. We all judge each other constantly in life. Living, or communicating, in some sort of close proximity, requires that we not pronounce all such internal judgements.

I think your ideas could be transformed into something less provocative with a little effort. Many of the responses or comments amounted to "I don't like it." If you merely wish to add "I really really don't like it" you might consider a more nuanced approach.

Also, as I generally do, consider typing your response at home and even printing it out, in Latex if there are formulas. Once it has reached an acceptable standard of proofreading you can just copy and paste into an answer window in MO. The total time is similar but the result is better.

Noah Snyder comments on "Response to "The value of "It's obvious" in the Mathematical Literature"" (8590)

2010-08-23T20:56:16-07:00

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.

Steve Huntsman comments on "Response to "The value of "It's obvious" in the Mathematical Literature"" (8589)

2010-08-23T20:39:04-07:00

Just FYI, it's "theorEm": this is a persistent misspelling that you would do well to correct.

AndrewL comments on "Response to "The value of "It's obvious" in the Mathematical Literature"" (8588)

2010-08-23T20:24:55-07:00

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.