I noticed something curious in sci.math (I don't post much, but I'm addicted to James Harris, who in nine years has proved dozens of revolutionary principles of mathematics, and runs a crusade against the Mathematics Establishment's use of millions in fraudulently-obtained dollars to suppress him) and saw an example of a curious phenomenon. A question about sudoku brought a comment that sudoku Just Isn't Mathematics, and is hardly a fit topic for their discussion.
I grant sudoku isn't deep mathematics: it's mostly repeated application of reducto ad absurdum (``if we put a 5 here, then there's two 5's in this column; therefore it can't go there''). But that is mathematics, unless you're particularly intuitionist, and the rules implicitly exclude the middle anyway. Yes, you can solve a puzzle algorithmically, but you can say the same in principle (if you could have enough storage space) about chess or (if you allow a certain amount of guessing) Minesweeper, and nobody denies they're often fascinating mathematics. (Minesweeper lends itself to some of the most complicated problems in mathematics, including logic circuit design -- in principle, you could design a Minesweeper board that was also a digital computer.) They open deeper fields, granted, but puzzles should come in all categories, from mildly diverting to impossibly complex.
At the risk of getting sociological, it seems to me the ``problem'' with sudoku is no initiation is needed. If you recognize the numerals you can work out the puzzle competently, and there's not much help learning more. Granted any community likes little barriers between itself and the outsiders, and that extends to resisting people casually joining. Carrying that to rejecting what's popular in the outside community seems to me unhealthy, and at least as silly as science fiction fans who insist that Star Wars isn't a true science fiction film like Serenity is.
I know this extends across fandoms. There are Star Trek forums where you can count on nothing kind being said about The Next Generation, which you recall was the only Trek series to suffer a weird negative loss of audience. More people watched each year than did the one before, and many of them didn't even care about the hasty rewriting of the Klingons to stop being Federation members somewhere midway through the series. I don't know what L Frank Baum fandom is like but I'm sure somewhere in it are people who refer to the MGM The Wizard Of Oz only as ``the Abomination.'' I hadn't thought of it particularly happening in mathematics.
Trivia: Polish-born Samuel Eilenberg was the first non-French member of mathematician ``Nicolas Bourbaki''. Source: Life Science Library: Mathematics, David Bergamini.
Currently Reading: Sweets: A History of Temptation, Tim Richardson.