Talk:Mathematics

BigCleanup deleted items

[[Image:Euclid.jpg|right|thumb|220px|[[Euclid]], a famous Greek mathematician known as the father of geometry, is shown here in detail from ''[[The School of Athens]]'' by [[Raphael]].]]
[[Image:Quipu.png|thumb|right|A [[quipu]], a counting device used by the [[Inca Empire|Inca]].]]
[[Image:GodfreyKneller-IsaacNewton-1689.jpg|right|thumb|Sir [[Isaac Newton]] (1643-1727), an inventor of [[infinitesimal calculus]].]]
[[Image:Pic79.png|right|thumb|In modern notation, simple expressions can describe complex concepts. This image is generated by a single [[equation]].]]
[[Image:Carl Friedrich Gauss.jpg|right|thumb|[[Carl Friedrich Gauss]], while known as the "prince of mathematicians", did not believe that mathematics was worthy of study in its own right{{fact}}.]]
[[Image:Abacus 6.png|right|thumb|Early mathematics was entirely concerned with the need to perform practical calculations, as reflected in this Chinese [[abacus]].]]
some images commented in the text
{{polytonic|μαθηματικὴ τέχνη}}

little comments

The word "pattern" doesn't appear anywhere in the article right now - while some would actually define mathematics as "the science of patterns". Also, historically mathematics was also driven by military engineering needs (ballistics, for example). It also mentions "amateurs" such as Fermat and Mersenne ... but in that time there were extremely few "professional" mathematicians, so the image conjured up by labeling Fermat an "amateur" is probably rather misleading.

Agree. I wonder whether improving the present text is easier/better than rewriting from scratch (some time ago I suggested it could be blanked). Any thoughts? --AlekStos 09:25, 26 March 2007 (CDT)

I'm not really happy with the article as written, either. Just removing (or truncating) the article does seem a little drastic, though. Is there any way to create an alternative article that might be used to replace it? Is this a good idea? Greg Woodhouse 07:31, 2 April 2007 (CDT)

Computation and Information Theory

I notice that such topics as computability and information theory are categorized under discrete mathematics. I'm not at all sure I agree with this classification. For example, it is not really clear what is meant by discrete mathematics: I have tended to think of it as having more to do with combinatorics than with formal logic to which I think the study of computation properly belongs. (Though there is certainly historicaal overlap here, the Busy Beaver function was introduced by Tibor Rado.) It may be worth some checking here, but I'm not even sure discrete mathematics is even a term generally used by mathematicians. I do certainly recall the term being used in the computer science curriculum, but there it seems to be more of a "catch all" for those aspects of mathematics that are important for computer science students. Greg Woodhouse 07:23, 2 April 2007 (CDT)

Pillar articles

In my mind these "Pillar articles" that Science itself is based on (such as Biology, Chemistry, Mathematics, etc.) should present a general overview to the reader (see User:Pat_Palmer for another Author that feels this way). As readers "drill down" into links on the Mathematics page such as Algebra, Geometry, or Computability (or whatever "Computability" is called at that point :) these articles should increase in their technical jargon and complexity. Just something to think about --Eric M Gearhart 07:55, 5 April 2007 (CDT)

Accessibility of mathematical notation across workgroups

As someone who has not taken postgraduate courses in maths but still regularly reads papers from a variety of disciplines using mathematical notation, I wish to add to continue this discussion by mentioning that it would be a great service for the reader (and potentially a pain for the writer) to have any mathematical symbols (be these logarithms, subscripts, superscripts, bra-kets, differential operators or anything else that may be ambiguous or non-intuitive) defined on first usage. To give an example from an example section, it is not obvious, based on the definition of the temporal derivative given as

${\frac {du(t)}{dt}}=u(t)$

that the dot over the x in the subsequent

${\dot {x}}=\sigma (y-x)\$

actually indicates the same operation, only performed on x instead of u. But if both the d and the \dot could be wiki-linked to the relevant section in a Mathematical notation article, the reader could get the information in a way not too effortful for the individual writer.

I have played around a bit with the <nomath> and <nowiki> commands but didn't see how such wikilinks from within <math> environments can be made (I suppose it's easy, though). Any hints on this, and comments on feasibility of consistent implementation across <math>-formatted articles, would certainly be appreciated.

And once we are at it, is there a way to search the wiki or the web for mathematical formulas, i.e. that points me to the second equation mentioned above if I enter something like

${\dot {*}}=?(?-*)\$

as the search term? This would greatly facilitate cross-disciplinary work on articles about certain mathematical concepts and structures, since many of them are employed in multiple contexts (with the original one often not being the most popular) that would not easily come together otherwise but could do so in an encyclopedic project like this. To give just two examples, the heat equation is nowadays used for many things that do not have anything to do with temperature, e.g. the smoothing of geometric shapes in computer graphics, and spherical harmonics have found applications in many spherical (or topologically similar) objects, ranging from molecules to brains. --Daniel Mietchen 10:32, 24 October 2008 (UTC

Excellent questions without excellent answers.

Regarding your search question, over several decades, the search engines of today cover more data than older bibliographic information retrieval and text searching tools, but have considerably less power. Your example, it seems, asks for regular expressions in search arguments. I don't know of any large search engine that has them, and, just yesterday, needed to search for my name with and without middle initial.

Taking that a step further, I could still have managed it with extended Boolean operations, which, until recently, were in most MEDLINE search tools. For example, while a regular expression would have been more elegant, I could have created two sets, not instantly displayed, one with my middle initial and one without, and then asked for the union of the sets and displayed that. The older search engines allowed AND/OR/NOT with parenthesizing for priority.

As far as I know, the CZ/MediaWiki search engine doesn't allow searching for strings. So, if I only want "alpha omega", I get every article with alpha and omega anywhere in the text. String search is a subset of something that again used to be reasonably common: proximity searches, which would allow me to say "retrieve these only if adjacent, in the same sentence, in the same paragraph, etc." I realize all these take more computational power as well as user skill, and perhaps the economics are not there.

Now, to go back to your mathematical notation example, the immediate problem is that mathematical symbols may not easily be searched because it's not obvious how to create the special character; I'm only beginning to use the HTML math notation. An ideal would be to be able to mouse over any individual symbol and get a definition. As far as I know, however, that requires a graphic over which the author maps a coordinate system, and defines responses when the mouse travels over some pair of coordinates. I'd make far more use of the feature, which is also convenient for organizational charts and a wide range of drawings, if there were a visual editor where one could circle an object, or click on it, and allow a locus of points to be named. It's usually too much effort to compute all the coordinates manually.

Coming from a computing background, I've always been comfortable in restricting myself to things that can be done in text, such as FOR 1 TO N SUM (F(X)), or any of a number of variants. Traditional mathematical notation simply does not lend itself to any general purpose computer interface I've ever seen. A radical solution might be the less dense programming-style notation. Howard C. Berkowitz 14:12, 24 October 2008 (UTC)

On hovering: For text, there is {{H:title}}, whereas the MediaWiki extension ImageMap that can be used to generate things like {{Biology open house}} can be used through handy graphical interfaces much like the one you imagined. --Daniel Mietchen 15:21, 24 October 2008 (UTC)

hcb> "... mathematical symbols may not easily be searched because it's not obvious how to create the special character; ...".
The UCS (http://en.wikipedia.org/wiki/Universal_Character_Set) should address this at the level of characters. Searching for an expression is a much bigger problem. Regards, ... Peter Lyall Easthope 16:10, 28 October 2008 (UTC)

I came across Google Code Search yesterday, and it does a decent job at finding code snippets. Perhaps one day that will be possible for mathematical symbols, too? --Daniel Mietchen 15:05, 4 November 2008 (UTC)

What did Gauss say?

The article quotes Gauss as saying that mathematics is the "Queen of the Sciences". Most likely he said this in German. I wonder, did he say "Königin der Wissenschaften" or "Königin der Naturwissenschaften"? This question is highly pertinent in the discussion whether or not Mathematics is a Science. I doubt it that Gauss would deny that mathematics is a "Wissenschaft", but he could have denied (as modern mathematicians do) that it is a "Naturwissenschaft" (a science). --Paul Wormer 19:45, 21 April 2009 (UTC)

He apparently said "Die Mathematik ist die Königin der Wissenschaften, und die Zahlentheorie ist die Königin der Mathematik." - no exact source given there, though. --Daniel Mietchen 08:48, 22 April 2009 (UTC)

Merits and demerits of mathematics

On one hand, we could give a ref to the (already mentioned, even twice) text of Wigner's "Unreasonable effectiveness...". For instance, here.

On the other hand, we could also mention Schwartz's "The Pernicious Influence of Mathematics on Science" and the like, see here.

Does this fit in?

Ran across something I liked, in a computer science prof's advice to students: http://www.paulgraham.com/college.html

" Like a lot of people, I was mathematically abused as a child. I learned to think of math as a collection of formulas that were neither beautiful nor had any relation to my life (despite attempts to translate them into "word problems"), but had to be memorized in order to do well on tests.

" One of the most valuable things you could do in college would be to learn what math is really about. This may not be easy, because a lot of good mathematicians are bad teachers. And while there are many popular books on math, few seem good. The best I can think of are W. W. Sawyer's. And of course Euclid. [4]