Wikipedia:Peer review/History of mathematical notation/archive1

History of mathematical notation

This appeared as a request in the mathematics portal. It was created primarily by P.L.A.R. and the main source was Carl Boyer's A History of Mathematics. It obviously needs more information, but the beginning is there. Any comments at all are appreciated.P.L.A.R. 00:59, 25 September 2006 (UTC)

• Very interesting article. This reads more like "Types of mathematical notation" rather than "History of . . ." I don't understand how the different notations interacted with each other. What caused old notations become insufficient and require the the delveopment of more advanced models? How did they spread to different areas and who is responsible for one type becoming standard instead of another? Why do clocks still use roman numerals? :) Seriously it is a good start but the sections do not flow together and I am unsure of the reasoning for the current order. Obviously there is much missing. The entire New World for one. Also I wonder if historically there was any connection between "math" and "astronomy" notations? One nitpick you say For example, the four vertical lines used to represent four were replaced by a single horizontal line. This was first introduced in the Rhind papyrus Do we really know this is where it is first introduced, or is it rather the earliest example we are aware of?--Birgitte§β ʈ Talk 17:48, 25 September 2006 (UTC)
• No quick fix here. This will just require more research. Mathematical history has a lot of very good sources. - Taxman ^Talk 20:16, 25 September 2006 (UTC)

• Yes it's an interesting article, although it seems a little short. Here's a few notes:
  • There is no coverage of the still-used Roman numerals.
  • How did π come to symbolize the ratio of a circle's circumference to it's diameter?
  • There are some sections that are devoid of references. What reference, for example, would I consult to confirm the claim that arabic numerals actually started in India?
  • Pre-calculus could also cover × and ÷.
  • How did we get the square root symbol?
  • Calculus can also cover the use of the ′ (prime) for derivatives, such as $f'(x)$.

Thanks. — RJH (talk) 22:30, 25 September 2006 (UTC)

• Thank you; all this advice is very helpful, especially the point on the article being more "Types of mathematical notation". Once the basic research is done, the entire article should be gone through and made to flow together, not only in terms of prose, but in how the information in each section goes into the others. There are two books I think would be very helpful, A History of Mathematics mentioned above and A History of Mathematical Notation, by Florian Cajori. Both of these are in nearby libraries, I hope to get them as soon as possible. The order is a bit arbitrary, it is based more on the information at hand than actual history. And the notation outside of Europe should certainly be mentioned too, thank you for bringing it up.P.L.A.R. 00:39, 26 September 2006 (UTC)

• The article seems to be a bit broad in scope. History of numeral systems is worth its own article. Some materal duplicates other articles. Personally I find the name Pre-calculus rather jaring as we don't use it this side of the water, algebraic symbols might be nicer. To × and ÷ I'd add the equals sign. Also important is the notation for functions f(x). Modern computer typesetting LaTeX, MathML etc, might be worth a mention.

• I've mentioned the request on Wikipedia talk:WikiProject Mathematics. --Salix alba (talk) 19:30, 30 September 2006 (UTC)

• A few remarks:
  • There should be a link to the article Mathematical notation.
  • The first sentence suggests it's all about symbols. But it is also about how these symbols are put together (syntax).
  • A reader who knows absolutely nothing about the topic might think from the second sentence that these symbols are all letters.
  • Worth mentioning: the introduction of letters to stand for arithmetic quantities, the start of algebraic notation. Vieta is credited with making the custom popular. In older mathematical discourses, everything was expressed in natural language, as in: If the number of things is augmented with the part that was taken away from ...
  • The origin of the square root symbol, a lower-case r  for radix.
  • The < and > symbols (if found in Cajori).
  • For the integral symbol ∫, refer to Long s. (See also the article Integral.)

 --Lambiam^Talk 21:12, 30 September 2006 (UTC)

• Thank you for the new comments. There should be a link from this article to Mathematical notation; I think the converse is true but it doesn't make sense to have only one. I agree that Pre-calculus is a poor title. Algebraic symbols would work, or maybe Renaissance (although as more material is added, that title may become a misnomer). I think the biggest problem is still lack of content, which will hopefully change soon. Also, I recently discovered something about Benjamin Peirce's idea for notation, that would fit in with whatever the section Pre-calculus will become or the section on Euler. The section on Euler is connected with a question I have: should he have his own section? He was very important in notation, but it doesn't fit well with the chronological order of the other sections.P.L.A.R. 02:58, 8 October 2006 (UTC)
• Please see automated peer review suggestions here. I also think this cries out for a figure at top right - maybe a bunch of the symbols used in notation? Thanks, Ruhrfisch 01:26, 16 October 2006 (UTC)
• This can certainly benefit from more inline citations. At the very least, each para should have one, at best, each fact.-- _{Piotr Konieczny aka Prokonsul Piotrus | talk}  02:43, 21 October 2006 (UTC)