Wikipedia:Peer review/Mathematics/archive1

Mathematics
Hello everyone. This article is very close to being nominated for an Article Improvement Drive and I thought it would be good to get a decent peer review done before this. Any and all comments or suggestions for the AID will be appreciated and very helpful. Cheers! -- darkliight [&pi;alk] 11:00, 16 May 2006 (UTC)

I have just had a cursory read through the article and have a few questions that iw ould like to see adressed in the article, please bare with me though as my mathematical knowledge is pretty slim and some of these questions/suggestions maybe daft.


 * This article tacitly assumes that mathematics is a language but in my cursory read through i saw no discussion of why it is considered a language. Is mathematics a language and in what sense can we call it a language? What are the critiscims against mathematics being considered a language?


 * there is no discussion about the centres of the brain responsible for the processing of mathematical thought or the fact that some people have an inability to make sense of numbers as in the condition of Discalcula.


 * is a mathematical language solely the domain of humans or is there any research that would suggest that animals have a basic concept of number or quantity?
 * On a purely aesthetic level i think that some of the formatting could be tweaked. I think in my opinion it would look a lot better if the lists were formatted in the style of the mathematics portal lists.

I will go over the article again at some point today and try and give some more specific suggestions from my own laymens perspective.

yakuzai


 * Thankyou yakuzai! I think these are all very valid and to be honest, despite having some background in mathematics, your first three points haven't come to my mind, so thankyou again and I'm looking forward to your continued suggestions. As a bit of a side note to everyone, such a root topic should be accessible by everyone, regardless of their mathematical background. If things aren't clear or you think there is something missing, anything at all, please speak up. Regards. -- darkliight [&pi;alk] 13:41, 17 May 2006 (UTC)

It looks like a good article that with a little work should be a FAC. I think it ought to be to, given the topic. I have a few comments regarding the article. Here they are:
 * The lead section should say more about the uses of mathematics, and in general I would like it to be a bit longer.
 * All the sections need citations.
 * The sentence "Mathematics since has been much extended,..." seems awkward and out of place. Either remove it or make it a full paragraph.
 * The sentence "Mathematics arises wherever there are difficult problems that involve quantity, structure, space, or change." seems wildly speculative. At the very least it needs a citation, but probably its best removed
 * It might be worth referencing work in the Philosophy of mathematics especially in the section regarding simplicity and generality.
 * The rigor section might benefit from a discussion of surprising mistakes in mathematical proofs. There is something regarding Hilbert and proofs about Hilbert spaces that I seem to recall, although I don't know the details.
 * Again, I know some philosophers have written about why axioms ought to be accepted, perhaps this should be included in the "notation" section.
 * The sentence "If one considers science to be strictly about the physical world, then mathematics, or at least pure mathematics, is not a science." needs a citation at least. I think there are some philosophers of math and science who would disagree.
 * The sentence "An alternative view is that certain scientific fields (such as theoretical physics) are mathematics with axioms that are intended to correspond to reality." doesn't seem to fit in the context, could it be made more clear?
 * "that is, long papers not supported by previously published theory" this doesn't seem right to me. Mathematics encourages innovation.  Wouldn't a more proper characterization be "long papers not following widely accepted norms" or something like that?

Okay, that's what I have. As a philosopher, I notice the lack of reference to philosophical work even when problems discussed by philosophers are being described. Generally, I think the article quotes a lot of physicists on these topics, who are often ignorant of substantial discussion that preceeded them. --best, kevin [kzollman][talk] 22:27, 19 May 2006 (UTC)