Talk:Mathematics

Early Zero

The Olmecs in Mexico developed the Zero before the Indus Valley civilzation. There should be a mention of them and of course the Great Mayas. —Preceding unsigned comment added by 128.196.165.102 (talk • contribs) 22:24, June 13, 2008 (UTC)

Wrong impression

Dear all,

I am sick and tired (just to exaggerate) of people who think that mathematics is only about numbers. Any mathematician who reads this will understand what I am trying to say. Mathematics is such a diverse field and in my opinion this should be mentioned as early as possible in the article. Just to make my point clear, it is virtually impossible for anyone in the current day to learn all of mathematics.

Also, I think that the article conveys the impression that mathematics is about numbers from the start. For instance, the article claims that mathematicians seek patterns. In topology for instance, I have never even encountered a problem that requires one to find patterns. This statement is only true in the most obscure sense and therefore it should be made more precise.

I hope that you agree with me; if not, please give your opinion on the matter.

Topology Expert (talk) 06:48, 19 August 2008 (UTC)

I think the article makes it very clear that mathematics is not arithmetic with its emphasis on "patterns". I'm not sure why you think otherwise.

For example, take the bridges of konigsberg problem. Some arrangements of bridges and islands permit a tour, some do not. It is the essence of mathematical thinking to look for a pattern in this - to try to see what the arrangements which permit a tour have in common, which they do not share with the others. EdwardLockhart (talk) 08:23, 19 August 2008 (UTC)

There is more to topology than the bridges of Konigsberg problem; one of the other common misconceptions about mathematics is that topology deals with shapes. It does, but topology is much more abstract than that. Perhaps when one views the fundamental group of the circle; the intuitive idea behind this is that the number of turns in a given loop determines its uniqueness (uniqueness in this sense means homotopic to no other loop with a different number of turns). This suggests that the given fundamental group is isomorphic to the integers. If you are suggesting that this is why mathematics has a link with patterns then I agree. However, now that you have found this link between the fundamental group of the circle and the integers, you must actually prove your claim (i.e construct an isomorphism between these two mathematical objects). This is an example in which one can believe that mathematics is about patterns. However, the 'patterns part' of the problem accounts for only 20% of the thinking.

I can even construct other such examples where one does not even encounter a pattern. For instance (a typically easy problem), how would one prove that every locally compact separable metric space is sigma compact? There is more to this then just finding patterns. One would use the local compactness of the space (choose a compact set for each point in the space that also contains a neighbourhood of the point in question). Then one must reduce this collection to a countable number. One may note that if the space is countable this is trivial and then notice that countable spaces are Lindelof. Since the metric space is separable, it must be Lindelof (which one should prove), and the result follows.

I am not particularly a fan of the bridges of Konigsberg problem. It gives the wrong impression of topology and really, finding an arrangement that permits a tour is just plain luck; proving that there exists no arrangement for a particular network involves more thinking. Surely you do not claim that topology is centered on this problem?

Topology Expert (talk) 03:24, 20 August 2008 (UTC)

I didn't pick the Konigsberg problem because of any supposed link to topology, but as an example of mathematics as a search for (not necessarily numerical) patterns. It has a personal resonance for me because the first explicitly mathematical thinking I remember doing as a child was to try to work out which house-like join-the-dots shapes could be drawn without retracing a line - essentially the same problem. For what it's worth, I would consider it to lie in the domain of combinatorics.

I would consider many mathematical theorems to be statements of a certain kind of regularity or pattern. To take your example, one might wonder whether separable metric spaces are sigma compact, perhaps initially supposing that all of them are, before coming up with a counterexample or two. Then observe that one needs some sort of local compactness property, convince oneself that this is sufficient, and finally procede to state and prove a theorem. This is very much a search for a pattern.

You are certainly right; this is how I would also approach the problem. I can now see you logic in why mathematics is related to patterns and I have also found many examples to convince myself. However, ignorant people who think mathematicians deal with numbers should actually learn that mathematics is a lot more diverse. My original request was to somehow emphasise in the lede paragraph that mathematics is a diverse field and perhaps list some branches of mathematics. In my opinion, this should be emphasised throughout the article. I agree with you regarding the claim that mathematics is, in a way, related to patterns but the average reader may interpret this in the wrong way and conclude that mathematics is about numbers. My intention is to do something about this. Do you have any suggestions?

Topology Expert (talk) 11:24, 23 August 2008 (UTC)

Lastly, you seem to think that "patterns" means something necessarily numerical. I'm not sure why this is, but I don't think it's the common understanding of the term. The article I think rightly emphasises "patterns" to counteract the (otherwise likely) view that mathematics is all about computation, or symbol manipulation, or formal proof. EdwardLockhart (talk) 09:44, 20 August 2008 (UTC)

MMPR VS PRDT episode 1/8 "1st Fight"

dMMPR VS PRDT episode 1/8 "1st Fight" —Preceding unsigned comment added by 71.190.84.21 (talk) 20:09, 23 August 2008 (UTC)

Making mathematics articles more accessible to a general readership

Please visit Wikipedia:Village pump (proposals)#Easy as pi? to see a discussion about making mathematics articles more accessible to a general readership.

-- Wavelength (talk) 17:37, 1 September 2008 (UTC)

I'm afraid I have insufficient interest to wade through that very long discussion thread. Is there an actual proposal in there somewhere ? If there is, perhaps you could summarise your proposal in two or three sentences. In a nutshell, can you please make "making mathematics articles more accessible" more accessible. Gandalf61 (talk) 10:34, 14 September 2008 (UTC)

According to my interpretation of your request, and according to my view of the discussion, the best summary is found where I listed several options under Wikipedia:Village pump (proposals)#WHICH problem??? by a distance of about three screen-heights.

At this stage of the discussion, I do not have a preference from among the various options, which include the following.

• linking to articles in Wikibooks
• linking to articles in Wikiversity
• linking to other articles in Wikipedia
• linking to a very large prerequisite chart of articles (and/or to one of a number of smaller prerequisite charts of articles)
• having a feature similar to the one currently used with articles about cities (where a mouse over a globe icon, in the upper right corner of the page, displays the expression "show location on an interactive map"), but with an interactive prerequisite chart instead of an interactive geographical map

Any one or combination of those options is acceptable to me.

The proposal (initiated by another editor) is to make mathematics articles more accessible to a general readership, and the options are proposals on how to fulfill that proposal.

-- Wavelength (talk) 03:56, 16 September 2008 (UTC)

It is worth pointing out that the original poster's complaint was focused on equations — that there was notation, such as lim, that he could not decipher. Of course explaining notation such as variable names is essential, but the original poster wanted explanations even of standard notation, since he did not know it. I'm not sure how we can explain "lim" everywhere it arises without destroying the text. The Village pump discussion suggests annotated equations; they are too cluttered, I think.

I dislike the "prerequisite chart" idea; it will have to be so large as to be unnavigable and difficult to maintain. I like the "linking to other articles in Wikipedia" idea, because that is what we already do. When you read a math article and come across a term you don't know, it should be linked, and you should follow the link to learn about it. (Of course, you might not return for some months...) The prerequisite chart is already encoded into the structure of wikilinks among the articles, or should be.

Many of the math articles (including ones I've written) could be made more accessible by adding more "soft text" about the history, goals, and applications of the idea in question. I strongly support that. But we do need to remember that Wikipedia is not a textbook. It is not designed to lead a beginner from no-knowledge to full-knowledge. Mgnbar (talk) 12:19, 16 September 2008 (UTC)

According to the past discussions listed under Wikipedia:Village pump (proposals)#Subsection 5, editors of Wikipedia mathematics articles have disagreed for years on whether and how to make them more accessible to a general readership. Is this problem (this lack of consensus) destined to continue ad infinitum or does it have a solution?

-- Wavelength (talk) 16:19, 17 September 2008 (UTC)

Inaccessibility is a problem in math and physics articles, but are these subjects truly qualitatively different from other subjects, so that we must create a special system for accessibility? I don't think so. We just need to keep doing more of what is done throughout Wikipedia — making sure opening paragraphs are not just jargon, linking to prerequisites, giving plenty of history, motivation, and applications, etc.

Perhaps we are not doing these things as fast as we'd like — because there are not enough editors? One problem I've seen is that mathematically unsophisticated editors are sometimes intimidated (even abused) by the math-savvy around here, and leave. These laypeople, even if they can't write about math with encyclopedic precision, can help us write articles that are actually useful to laypeople. Mgnbar (talk) 21:02, 17 September 2008 (UTC)

My interest in the accessibility of Wikipedia articles (without limitation as to subject) predates my involvement in the current discussion at Wikipedia:Village pump (proposals), a discussion which began on 22 July, 2008. Because the focus of the discussion is on mathematics articles, the focus of my involvement in it is likewise. If certain suggestions are followed first on mathematics articles, they can be followed later on other articles.

When I mentioned prerequisite charts, I was referring to prerequisite charts of any kind(s), although I was thinking mostly of prerequisite flowcharts. Incidentally, a prerequisite chart can provide a convenient overview that would be difficult to picture mentally from merely examining links to prerequisite articles.

Here is a suggestion which I made on 9 August 2005.

• Temporary link: User talk:Wavelength#Subject (difficulty) level
• Permanent link: User talk:Wavelength (subsection 4.2) "Subject (difficulty) level"

Here is a suggestion which I made on 15 January 2008.

• Temporary link: User talk:Wavelength#Suggestion: readability test(s) for Wikipedia articles
• Permanent link: User talk:Wavelength (section 36) "Suggestion: readability test(s) for Wikipedia articles"

Here is a permanent link to the current discussion:

Wikipedia:Village pump (proposals) (first section) "Easy as pi?"

When I noticed the discussion two months ago, I postponed some major plans and I added my comments, hoping that I could make a positive difference toward a consensus. Maybe someone else can help toward consensus. My involvement in the discussion has almost finished. Here are three related links.

• Wikipedia:Make technical articles accessible
• Category:Wikipedia articles that are too technical
• Category:Mathematical disambiguation

-- Wavelength (talk) 00:48, 26 September 2008 (UTC)

It occurs to me that Wikipedia: Wikiproject Mathematics would be a better forum for this discussion. Maybe that's why others are not commenting here. On the other hand, if your goal is to institute changes throughout Wikipedia, then going back to the Village pump might be best. To respond to one point that you made: I know that you were suggesting prerequisite flowcharts. I don't think the idea is inherently bad; I just think that the flowchart for mathematics would be impossibly large. Mgnbar (talk) 12:43, 26 September 2008 (UTC)

Thank you both for your comments. I have added sub-subheadings, including some which indicate the presence of proposals. Some sub-subsections are still long, because I decided not to split any post into more than one sub-subsection. Generally, the very long posts were made my me, and I probably would have separated them into smaller posts at that time, if I had anticipated that I would be adding sub-subheadings. I named one subsection "Subsection 0" for consistency with the other numbered subsections. There is already a link to "Subsection 5" from this section of this page; otherwise, I would probably rename the numbered subsections by increasing each number by one.

-- Wavelength (talk) 01:06, 28 September 2008 (UTC)

Type of science

maths is a type of science —Preceding unsigned comment added by 84.69.67.194 (talk) 08:50, 14 September 2008 (UTC)

Indeed it is - it is a formal science, rather than a natural science. See the Mathematics as science section of the article for more details. Gandalf61 (talk) 10:26, 14 September 2008 (UTC)

Oh, that formal science article needs work. To call mathematics a "formal science" and then say that formal sciences are "built up of formal symbols and rules" is unacceptably POV. To a realist, the formal symbols only denote and describe the underlying mathematical reality, and the rules are valid in it; they're not what mathematics is "made of". --Trovatore (talk) 18:30, 14 September 2008 (UTC)

Hear, hear. While the practice of mathematics may not be bound by the physical reality in the sense of computation and measurement, it is naive to think that mathematical thinking is detached from reality in some meaningful wider sense. Certainly we can do away with the parallel postulate, skip euclidean geometry and replace it with general relativity, extoll the genius of the uncertainty principle, but thinking that one can push symbols in a way independent of our perceptions is a variety of fundamentalist belief (i.e. POV as above). In fact the corresponding section of mathematics should be rewritten or deleted. Katzmik (talk) 16:42, 17 September 2008 (UTC)

Link to wilbourhall.org

I run a website, Wilbourhall.org that distributes PDF files of many important ancient and medieval mathematical texts in Greek, Latin, Arabic and Sanskrit, along with translations for most of them. As I explain on the website, I of the things I try to do is to repair scans of these texts from Google books, the Digital Library of India and elsewhere by replacing missing pages with my own scans, digital photographs etc. For example, Google books has many versions of Heiberg's Greek edition of Euclid's Elements available for download, but the vast majority of them are missing anywhere from several to (in one case) several hundred pages. The "repaired" version of Euclid is available on wilbourhall.org and is hopefully complete. I named the site after Wilbour Hall at Brown University, former home to the History of Mathematics Department, where I had the pleasure of studying with Dr. David Pingree. In the year and few months the site has been operating, it has distributed tens of thousands of these texts worldwide. Please take a look at the site and let me know if you think it would be appropriate to have a link to it from this page. (I completely understand if you think it would be more suitable for other, more historically-oriented articles on mathematics). Thank you for your time. BillLoney (talk) 04:31, 22 September 2008 (UTC)

I've two thoughts on this. One, the site does seem to offer useful information, and is relatively free of advertising. However, I'm honestly not impressed by the message you've posted at the top of your page.

(Text of Wikipedia criticism from "Wilbourhall" site removed to facilitate discussion)

Why would you trash Wikipedia's "History of math" article on your site, then come here and ask to post a link? --Ckatz^chat_spy 04:57, 22 September 2008 (UTC)

You're right. Its gone. Apologies. Nevermind. —Preceding unsigned comment added by BillLoney (talk • contribs) 05:55, 22 September 2008 (UTC)

They were stupid remarks I wrote several days ago when I was very upset. I thought I had removed them, when in fact I had only commented them out. I have yet to learn the value of "restraint of tongue and pen", quite obviously. I did not mean to re-open an issue that was resolved. It was completely inadvertent. Apologies while I go crawl under a rock and hide. —Preceding unsigned comment added by BillLoney (talk • contribs) 06:05, 22 September 2008 (UTC)

I feel absolutely horrible. I honestly thought I had removed those stupid words. I have removed everything from the site except the links to the PDFs. I think it would be nice if these PDFs were available for distribution. I apologize again and again for my sheer stupidity. I am really, really, really not cut out for this. Again I am sorry for any offense. —Preceding unsigned comment added by BillLoney (talk • contribs) 06:14, 22 September 2008 (UTC)

Please. No one from Wikipedia ever contact me again under any circumstances. I really can not take any more of this. Apologies again to anyone and everyone. You win. —Preceding unsigned comment added by 68.195.75.223 (talk) 06:24, 22 September 2008 (UTC) Please remove the remarks you quoted above from my webpage. Distateful as you may find them I OWN THE COPYRIGHT. YOU COPIED IT AND POSTED IT WITHOUT MY PERMISSION. PLEASE REMOVE THEM AND ALL REFERENCE TO THEM. PLEASE COMPLY WITH WITH THE LAW REGARDING COPYRIGHT INFRINGEMENT. AS IT SAYS "Content that violates any copyright will be deleted." PLEASE DO SO IMMEDIATELY. —Preceding unsigned comment added by BillLoney (talk • contribs) 15:43, 22 September 2008 (UTC)

FYI, there was absolutely no question of copyright infringement, especially given that the quote of your tirade against Wikipedia was part of a discussion with you, regarding your efforts to list your site on Wikipedia. In addition, the text was not taken from "source code"; it was clearly visible to anyone who visited the site (at least with Firefox; can't speak for other browsers.). You claim to have commented it out, but obviously had not done so when I visited the site. --Ckatz^chat_spy 08:00, 23 September 2008 (UTC)

Bill, please restore your website first and then I will restore the links. We can't have the link to your website unless you restore it first. Khoikhoi 21:03, 23 September 2008 (UTC)

Agreed. Bill, your site appears to contain useful information, and no-one wants you to close it down. There is no "war" against you; it would be great if you would return here so that we can find a way to incorporate a valuable resource. --Ckatz^chat_spy 21:58, 23 September 2008 (UTC)

It is online again. He does seem might pissed of with wikipedia though. --Salix (talk): 08:14, 27 September 2008 (UTC)

Yes, he certainly does. Quite the imagination as well. --Ckatz^chat_spy 08:25, 27 September 2008 (UTC)