Talk:Mathematics/Archive 9

message: Higher maths, like arithmetic and geometry is founded explicitly on arithmetical principles, which themselves require numerals to demonstrate. The following quotation is definitive: " In the expression of algebraical principles we proceed analytically: at the outset we do not lay down new names and new ideas, but we begin from our knowledge of abstract Arithmetic; we prove certain laws of operation which are capable of verification in every particular case, and the general theory of these operations constitutes the science of Algebra. Hence it is usual to make a distinction between Arithmetical Algebra and Symbolical Algebra, and to make a distinction between them. In the former we define our symbols in a sense arithmetically intelligible, and thence deduce fundamental laws of operation; in the latter we assume the laws of Arithmetical Algebra to be true in all cases, whatever the nature of the symbols may be, and so find that they may obey these laws. Thus gradually we transcend the limits of ordinary Arithmetic, new results spring up, new language has to be employed, and interpretations given to symbols which were not contemplated in the original definitions. At the same time, from the way in which the general laws of Algebra are established, we are assured of the permanence and universality, even when applied to quantities not arithmetically intelligible." QED Geologician 16:24, 5 July 2006 (UTC)
replies: text: Since I completely miss the point, maybe you can explain to me why a long quote that does not even mention the word "numeral" says something definitive about the importance of numerals. Rick Norwood 23:30, 5 July 2006 (UTC)
replies: text:  Sure. The entire warehouse of mathematics collapses in a pile of dust, leaving perhaps a couple of orthogonal straight lines and a few boring expressions in set theory, if we remove all the proofs that depend ultimately on proofs that depend on abstract arithmetic that cannot be expressed without recourse to numerals. QED Geologician 05:59, 6 July 2006 (UTC)

text: No.  And certinly the paragraph you quote doesn't suggest that.  The laws of mathematics are independent of numeration systems, and the real numbers, for example, can be defined and their properties deduced without any reference to a numeration system.  I love the wonderful utility of the Indo-Arabic numerals as much as anybody, but numeration systems are important but not fundamental to mathematics.  I think you would be hard pressed to find any quote by a mathematician that said otherwise.  On the other hand, you find set theory boring, so we obviously have different taste as to what is interesting and what is not.  Back up your taste with a citation. Rick Norwood 13:48, 6 July 2006 (UTC)
thread_title: Even Higher Mathematics is founded on Numerals

message: In the section on notation and language, I think it would be pertinent to mention the role of geometry in historical math.  Yes, proofs were "written out in words", but often with accompanying geometric diagrams.  This is the style in which Newton first wrote his works.  However, I'm not entirely sure if this falls under the start of "modern notation" or not.  Even so, the role of geometric style proofs seems to have played a large enough part in the development of mathematical notation to be mentioned here.  --Archmagusrm 15:11, 12 July 2006 (UTC)
thread_title:  History of Notation 

message: I've had a go at adding some pictures. I make no claim that they are the best for the purpose, so feel free to replace them if you can do better, but I thought it was strange that something so eminently visual as mathematics was so lacking in illustrations. Soo 14:03, 16 July 2006 (UTC)
replies: text: Yes I like the new images and the captions which explain in nice simple language some aspects of mathmatics. You might also be interested in Wikipedia:WikiProject Mathematics/Graphics where there is a small degree of cordination in mathematical graphics. --Salix alba (talk) 17:38, 16 July 2006 (UTC)

text: The images rock!  The captions are really helpful too.  capitalist 02:27, 17 July 2006 (UTC)
replies: text: Well that was a better reaction than I expected :) Soo 06:00, 17 July 2006 (UTC)
thread_title:  Pictures 

message: Is there a way for providing something in the way of instructions regarding how it is that the above referred to visualisations were created?  The link to Wikipedia:WikiProject Mathematics/Graphics 
This question (as always) has been implicitly answered.  However, the codes, etc... and explicity instructions for generating large amounts of information have not yet been collated into one place. 
--Nukemason 10:58, 08 August 2006 (UTC)
thread_title: Instructions for creating beautiful mathematical visualisations 

message: These two sections really ought to be merged since they deal with essentially the same thing, albeit in a different format. I really like the graphical boxes but the lists of articles are not useful for someone unfamiliar with topics and are likely to be unpopular with FAC. I suggest a hybrid approach, which can mainly be achieved by just reorganising the two sections into one. I'm going away for a few days now, so I'll leave this suggestion here and see what the other editors around here make of it. If the idea proves popular then I'll act on it when I get back. Soo 08:12, 18 July 2006 (UTC)
replies: text: I've had a go. The layout may still need a bit of work, but I'll wait for the text to stabilise before fiddling with that. I defer the Applied mathematics section to someone more knowledgable than me - it needs to be transformed into prose, and ideally a box like that of other subsections would be added, but I don't have the expertise to do that. Anyone want to take it on? Soo 17:42, 21 July 2006 (UTC)
thread_title:  "Fields in mathematics" vs "Major themes in mathematics" 

message: The "Fields of mathematics" section is a bit messy. For example, the "Structure" sections contains illustrations for arithmetic and number theory, but these are both covered in the text under "Quantity". I also don't see how vector calculus belong under "Structure". Fredrik Johansson 20:24, 21 July 2006 (UTC)
replies: text: You're right, I didn't really review the contents of the boxes, although I do like the idea. Go ahead and add/remove/rearrange as you see fit. Leave the illustrations blank if you can't find anything suitable, there are plenty of talented people around here who can sort out such things. Soo 23:52, 21 July 2006 (UTC)
thread_title:  Messy sections