1353:). An article should begin with the most important fact about its subject. Even if the generating function allows convenient calculation of the numerical values, the numerical values are not what makes the Bernoulli or Fibonacci numbers important. In the case of the Fibonacci numbers, the important thing is the recurrence relation; in the case of the Bernoulli numbers, it is the Bernoulli polynomials and the sums of sequences of consecutive integer powers.
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century as an attempt to generalize the idea of the metric space, and the 'open set' was a generalization of the 'open ball' of a metric space; metric spaces in turn were a generalization of
Euclidean spaces, invented in an attempt to get better insight into problems of real and complex analysis. Topological spaces continue this investigation.
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Of course. In the case of sheaves, though, the story is quite complex; just because Leray was inventing the spectral sequence at the same time. There is a great deal to be said for the 'genetic' method. On the other hand clear statements are important too. It's only reasonable to say that there is a
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are examples. Here are some discussions I would like to see in such cases: Who invented the idea of a sheaf, and why? What were they studying, and how did the idea of the sheaf help them solve their problems? Were sheaves a generalization of some more specialized construction, or an attempt to
1331:
This is a good example of the problem that I think many of our mathematics articles have: an overreliance on definition. In some sense, once you have the generating function, you know everything there is to know about the
Bernoulli numbers. But really you know nothing of value. It is easy to
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Both motivation and clear definitions are necessary. Genetic surveys and motivation with ambiguous, vague, and imprecise definitions is interesting but confusing and ultimately useless; clear, crisp, formal and terse definitions with no idea why anyone would care is logically flawless but does
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Many mathematical objects are studied because they have intrinsic interest. For example, people now study topological spaces simply because topological spaces are known to be interesting. But it wasn't always so. The idea of the topological space was invented in the late 19th and early 20th
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I disagree. The same arguments could be made for a number of disciplines besides mathematics (that they deserve their own mediawiki sites because their terminology introduces "noise" into search results). I'm not sure what you mean by classification; the mathematics articles are fairly well
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formalize something people had been doing before? In what situations do sheaves arise? What other concepts are sheaves related to? In the context of what sorts of problems do people think about sheaves? The current article tells me everything about sheaves except why I should care.
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Some general comments about wiki work are: (a) telling others how to write may just not work; and (b) it's hypertext. On (b), objecting to definitions by themselves, and ignoring the backlinks, sometimes doesn't work. A page may be there because someone want to refer to a
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nothing to promote problem-solving or connections with anything else. The sheaf article is a bad article to pick on, because that's one of the most tortuous definitions around. I seem to remember it taking almost an entire class period to just define it.
1326:.) The older version of the article starts of by saying they were named after Jakob Bernoulli by Abraham de Moivre (which is not particularly important) and then follows with a definition of the numbers via an exponential generating function.
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In my opinion, one serious problem with many of the mathematics articles is that they do not contain any explanation of why their topic is interesting or relevant. In the most extreme cases, they are nothing more than lists of definitions.
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I think the revised version of the article is substantially better, because it explains right away why the
Bernoulli numbers are of interest and why they were studied. (They are coefficients of the closed form of
1358:
I am discussing this in detail not to criticize anyone's work on this article, but to try to make clear a specific way in which I think many other
Knowledge mathematics articles could be substantially improved.
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example because there is no such article and I don't think it is useful to discuss these matters in the abstract. Perhaps if there were such an article, I would agree with you, or then again perhaps not.
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This might just be because I am fond of history, but I think putting the history of the subject near the top of the article as opposed to near the bottom goes a long way towards solving this problem. --
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classified in categories and lists. In my opinion, part of what makes
Knowledge great is that all of the encyclopedic information is in one place instead of scattered across separate wikis. -
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imagine an identical article defining the
Glubbernog numbers as being defined by some other, slightly different generating function, say one where the denominator was
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It would be similarly peculiar to have an article about the
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I think mathematics deserve their own mediawiki site. In that way the search would not be disturb by noise and classification would be proper. Anonymous.
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I think many of the existing mathematics articles could be improved with the addition of some context of this type.
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I am not telling anyone how to write; I am not telling anyone how to do anything.
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I agree that that is sometimes a useful thing to do. I would like to contrast
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I have created a discussion page for the implementation of a wiki,
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I have no constructive response to your hypothetical
1306:an older version of the bernoulli numbers article
24:Knowledge talk:WikiProject Mathematics/Archive 0
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