Talk:Mathematics

weasely, contradictory and unsuported "It has no generally accepted definition"

1) It makes no sense to define the topic in sentence 1 and then say it has no definition in sentence 2.

2) The references don't seem to say that it has no accepted definition. One reference is about what teachers think mathematics is (interesting but not relevant), and the other says no consensus has been reached about whether mathematics is a natural science, a branch of the humanities, or an art form. (Something can obviously have a definition while being hard to categorize)

I understand the first paragraph has been extensively discussed but this second sentence is terrible. I have no opinion on the first sentence. Bhny (talk) 02:13, 26 June 2013 (UTC)

Could I ask as a favor that you glance over my remarks at talk:mathematics/Archive 13#Definition as description vs definition as demarcation? It's not extremely short, but not extremely long either, and it would explain the terminology I'd like to discuss the question with.

(Assuming you've read it.) What is really meant here is that there is no generally accepted demarcation between that which is mathematics, and that which is not. That is, some people would like to say that mathematics is whatever comes out of rigorous proof, but others find that unnecessarily limiting (and possibly including stuff that they don't want to include, such as proofs in philosophy). That's why the article should start with a non-exclusive list of things that are generally accepted as mathematics, but make it clear that these may not exhaust the topic, and confess failure in giving a complete definition.

I think those are the principles we should strive for. That said, I'm not in love with the current first sentence, which does seem to be in the form of a demarcation. --Trovatore (talk) 02:47, 26 June 2013 (UTC)

I'd like to stay out of arguing about the 1st sentence- a descriptive definition is fine by me. But this 2nd sentence is a disaster and should just be deleted. Are you are suggesting it should be changed to- There is no accepted demarcation of what is and what is not mathematics. ? Bhny (talk) 02:57, 26 June 2013 (UTC)

No, I'm just as happy staying away from any active denial that such a thing exists, just as long as we ourselves don't write something that appears to be one. --Trovatore (talk) 03:08, 26 June 2013 (UTC)

OK we seem to agree that it should be deleted Bhny (talk) 03:42, 26 June 2013 (UTC)

Well, if the first sentence is explicitly open-ended, which it isn't right now. Also we don't want it to be a one-sentence paragraph, and it wouldn't be too unnatural to note positively that there's a range of opinion on the exact definition (as opposed to negatively saying there's no exact definition). --Trovatore (talk) 05:35, 26 June 2013 (UTC)

• There is an enormous amount of disagreement as to what mathematics is, in at least two respects:

1. What is the extension of the concept "mathematics"? I.e., exactly what subject matter is included under that term?
2. What is the nature of mathematics? I.e., granted "1+1=2" is included under the heading "mathematics", what does it mean to say that it is "mathematics"? What is it about some things which makes that "mathematics", as distinct from other things which are not "mathematics"?

Of course, the two issues are intertwined, and not independent, but they are not by any means the same. Even among mathematicians and philosophers who substantially agree on the answer to the first point, there has been much debate and disagreement about the second.

I believe it is right that the lead should contain, very early on, a statement indicating that there is no agreement on what mathematics is. I don't at all agree that the "second sentence is terrible", though it is not perfect, and could no doubt be improved. Simply removing it, and putting nothing in its place, would not be at all helpful. Indeed, doing so while leaving the first sentence in place would give the extremely misleading impression that the first sentence is an adequate definition. Leaving the sentence even in its present imperfect form is a much better option than removing it.

• I have considerable reservations about the first sentence, particularly in its present form, which is due to a recent undiscussed change, which replaced "abstract" with "scientific". To me, it is clear that mathematics is abstract, and by no means clear that it is scientific: that depends critically both on what one sees as the nature of mathematics and on what one sees as the nature of science. For now, on the bold, revert, discuss principle, I shall revert that change, though that will still leave me somewhat unhappy with the rest of the sentence.

• One last point. In answer to the "It makes no sense to define the topic in sentence 1 and then say it has no definition in sentence 2", Who said that the first sentence was a definition? It makes perfect sense to make an attempt to describe in general terms what the subject of discourse is, and then mention the difficulty, or even impossibility, of giving a precise definition which is universally accepted. JamesBWatson (talk) 09:23, 26 June 2013 (UTC)

An editor has tried a couple of times to insert, without reference, the statement that mathematics is always true. This is a question much debated, and cannot be settled here. Is mathematics true, or is mathematics merely valid. For a discussion of this subject, see the book Plato's ghost by Jeremy Gray. Rick Norwood (talk) 14:04, 27 June 2013 (UTC)

Indeed. "Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing. It is essential not to discuss whether the first proposition is really true, and not to mention what the anything is, of which it is supposed to be true ... Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true" - Bertrand Russell. Gandalf61 (talk) 15:03, 27 June 2013 (UTC)

For better or worse the first sentence is a definition- "Mathematics is <definition>". I stand by my comment that the second sentence contradicts the first. Can we come up with a sentence or two that actually says something about the scope and demarcation? Bhny (talk) 15:30, 27 June 2013 (UTC)

Well, that looks rather like a categorical statement that only one interpretation of the word "definition" is acceptable. Trovatore has done a pretty good job of outlining some of the variation in what that word may mean, in the archive page linked to, and I see no benefit in insisting that the word can be taken in only one way. However, accepting for the present that we interpret the word in a way which encompasses the first sentence of the article, how and why does the second sentence contradict it? It seems to me perfectly possible to give a definition and then go on to state that it is not the definition, and that no one definition is universally accepted. By all means, the article stands to be improved by replacing the blank statement "It has no generally accepted definition" by a more comprehensive statement, that goes some way towards indicating how and why it has no generally accepted definition, but it is a clear and unambiguous fact that mathematics does have no generally accepted definition, and it would not be at all helpful to pretend that it does. However, I see no contradiction at all in recording the fact that there is no generally accepted definition, while at the same time trying to give at least a general indication of what sort of thing is meant by "mathematics", whether or not we choose to call that "general indication" a "definition". JamesBWatson (talk) 16:07, 27 June 2013 (UTC)

We are defining a topic for an article. It doesn't have to satisfy every one on earth and we can we can specifically state the limits of our article topic. (It has no generally accepted definition implies we don't have a topic) Bhny (talk) 20:46, 27 June 2013 (UTC)

The point of my mini-essay that I linked above (here, for convenience) is that there is a confusion between the sort of definition you're correctly talking about, and the sort of definition mathematicians are used to when defining mathematical objects. We need a definition in the former sense, because that's how WP articles start. We should make it clear, by stating it in an explicitly open-ended form, that it is not a definition in the latter sense.

That's why I propend for the "shopping-cart" style definition, something along the lines as Mathematics is the field of study that concerns itself with such topics as ..., without ever attempting to definitively characterize what these topics have in common. --Trovatore (talk) 21:19, 27 June 2013 (UTC)

"It has no generally accepted definition implies we don't have a topic" is close to (though not identical to) what Geach called "the Socratic fallacy". The fact that we can't give a definition of a topic which everyone will accept does not by any means imply that the topic doesn't exist, and, frankly, I am bewildered as to why anyone might think it does. We can give a "definition" in the sense of a general description of what sort of thing we are referring to, but no matter how we word such a description there will be someone who doesn't think it's right. I have known quite heated arguments among mathematics teachers in secondary schools about whether a particular topic is included in mathematics or not. British university mathematics faculties teach topics which they regard as "applied mathematics", but which continental European universities do not regard as mathematics at all. That means that any definition we give will either include content which some people do not accept as mathematics, exclude content which some do accept as mathematics, or both. However, it does not mean that we can't provide a description giving a general idea of what sort of things mathematics deals with. That means, as far as I can see, that we can give a "definition" in the sense in which Bhny is using the word, but that the definition will not be universally accepted. Where is the contradiction there? JamesBWatson (talk) 07:19, 28 June 2013 (UTC)

• There is no generally accepted definition of "tree". Most people accept the concept of a banana tree, but some insist that it is not truly a tree, because it lacks sufficient lignified tissue. Many people regard elder (Sambucus nigra) as a tree, to others it is unambiguously a shrub. Does this mean that the word "tree" has no meaning? Of course not. JamesBWatson (talk) 07:23, 28 June 2013 (UTC)

  Yes, but it is true that (without having looked), I doubt that the second sentence of the tree article explicitly asserts that there is no accepted definition. I think the situation can be adequately dealt with without the second sentence, by giving a definition that is sufficiently (and sufficiently obviously) open-ended. We had one, for a while, until someone added the bit about "anything quantitative", which again appears to be an attempt at a demarcation. Maybe that bit should just be removed.

  Even if it is removed, of course, we don't want to leave a one-sentence opening paragraph, and something about the wide variety of attempts to give a more comprehensive and unified definition might be in order. But it's probably better if it's stated positively rather than negatively. --Trovatore (talk) 07:32, 28 June 2013 (UTC)

I would be careful about specualting what an article does and does not say "without having looked". The first sentence of the Wikipedia article Tree gives a definition of "tree", and the second sentence goes on to indicate that usage varies. It does not use the words "no generally accepted definition", but that is the fact that it conveys. (It does better than the article Mathematics, because it briefly indicates the sort of variations that there are, rather than just stating that there are variations, but there is no more a "contradiction" in the one article than in the other, and it is no more true to say that the topic doesn't exist because there is no universal agreement as to its extension in the one case than in the other.) JamesBWatson (talk) 07:35, 28 June 2013 (UTC)

Completely agree with you on the last point, but I don't think that's Bhny's main complaint. --Trovatore (talk) 07:43, 28 June 2013 (UTC)

Somebody added the assertation that everything that involved quantities was mathematics. I removed it as too broad.Rick Norwood (talk) 15:34, 28 June 2013 (UTC)

Our reader reads the first sentence- "ah this is how our topic is defined", then reads the second sentence. I don't how to be clearer- this is a contradiction. Maybe there are two senses of "definition" being used but it doesn't say that. I believe the second sentence should just be deleted, but if it stays it has to be re-worded to actually say something. It could say- "In academia the scope of mathematics varies and disagreement is common especially concerning...." Then it has to say what the main disagreements are otherwise it is uninformative weaselness. Bhny (talk) 17:27, 28 June 2013 (UTC)

I don't think anybody is that far apart here. Isn't it acceptable to everyone to make the first sentence open-ended, and rephrase the second one in positive terms to talk about disagreements as to the scope of mathematics? --Trovatore (talk) 20:18, 28 June 2013 (UTC)

ok, I'll let someone else draft this new 2nd sentence. It would be good to source it of course. Bhny (talk) 21:21, 28 June 2013 (UTC)

I suggest: "Many attempts have been made to define mathematics, but none has been universally accepted." Rick Norwood (talk) 00:32, 29 June 2013 (UTC)

I would prefer something stated in such a way that we don't have to find a source denying that any is universally accepted. How about something along the lines of

There is a range of views among mathematicians and philosophers of mathematics as to the exact scope of the discipline. Some of these are summarized at definitions of mathematics.

It's not ideal; I usually prefer to avoid referring to other articles by mention rather than use. But I can't think of a way to do that that doesn't either seem contrived, or else undesirably resurrect the conflict between the definitions of the word "definition" that we're trying to escape here. --Trovatore (talk) 00:42, 29 June 2013 (UTC)

You know, the more I think about it, the more disturbed I am by the article-reference issue. My proposed third sentence would make no sense at all in a printed version, where you don't see that there's a wikilink. So I don't think this exact language will work. But you see the general direction I'd like to go; maybe someone can come up with a fix. --Trovatore (talk) 00:49, 29 June 2013 (UTC)

Is the 2nd sentence more true of math, than of physics, psychology, or literature? It seems unnecessary to me. Biology is the study of life, but defining life is problematic. But, biologists are the primary virologists, not geologists. The 2nd sentence is about this Talk page, not about math. itself. JJL (talk) 01:16, 29 June 2013 (UTC)

Well, we need to have a second sentence. We definitely don't want the article to start with a one-sentence paragraph. To me a remark about there being a range of views on the subject's scope seems like a fairly natural continuation, but I might be persuaded that there's some better direction to go. --Trovatore (talk) 02:09, 29 June 2013 (UTC)

Yes, I think mathematicians have argued more about the definition of mathematics than people in other disciplines have about the definition of their discipline, maybe because within mathematics precise definitions are so important. The big question is: is mathematics a method (deduction from axioms using formal rules of logic) or a set of subjects: numbers and shapes (plus some other stuff). The article art has a similar problem, and solves it by mentioning several views without explicitly saying that there is no single definition of art. We might follow that example, giving two or three major definitions without preferencing any one definition.Rick Norwood (talk) 12:09, 29 June 2013 (UTC)

Most mathematicians don't bother to try to precisely characterize what mathematics is. I think the best choice is to open with a description-definition rather than a demarcation-definition, and make it obviously open-ended so that no one thinks it's a demarcation-definition. It should be possible to give a head-check to the "method" view within such a format, though I don't have an exact proposed wording at this time. --Trovatore (talk) 20:47, 29 June 2013 (UTC)

I once asked Philip J. Davis to define numerical analysis for me and instead he gave me an explanation of why he was refusing to do so on principle. To my mind defining math. is best left to the philosophers, though what I'm hearing is a distinction between (neo)-Platonism (number, shape) and formalism (method) that I view more as a discussion of how math. is done than what math. actually is. Regardless, the current 2nd sentence is fine by me. I too am a little bit queasy about directing change to calculus but frankly that is what we are principally talking about by change here, I assume--not stuff like topological deformations and such. JJL (talk) 17:06, 21 July 2013 (UTC)

I did a first pass at a new second sentence based on the suggestion above. It is at the very least better than what was there Bhny (talk) 21:34, 29 June 2013 (UTC)

Not bad from my POV, with some minor concerns:

1. First sentence didn't end in a period and didn't have an "and" before "change". I've fixed that.
2. First sentence needs to be explicitly open-ended. Fixed that too.
3. I don't like the WP:EGG of piping "change" to "calculus". This needs further thought.
4. Though it's not my personal view, Rick Norwood does have a point — something needs to be said about the "method" view. Something is said, in the following paragraph. Rick, can you accept this as it is, given that it's obviously not trying to characterize mathematics, but just point the reader to the subject of the article?

--Trovatore (talk) 21:47, 29 June 2013 (UTC)

I like it a lot. I hope it will be stable. Rick Norwood (talk) 23:11, 29 June 2013 (UTC)

Edit request on 31 August 2013 from Franco Boggi, concerning the first origin of the term mathematics

For the origin of the term mathematics is necessary to go Egyptian word maat, in which composition appears the symbol of the cubit, linear measuring instrument: a first approach to the mathematical concept. Geometric symbol of this order is a rectangle, from which appears the plumed head of the Egyptian goddess Maat, the personification of the concepts of order, truth and justice, daughter of Ra, the only One, Creator of all things, not even the father can live without daughter: his demiurgic power being limited and ordered by mathematical laws. At the beginning of the Rhind papyrus is this statement: "The accurate calculation is the gateway to the knowledge of all things and the dark mysteries." The term maat reappears in Coptic, in Babylonian and in greek. In greek the root ma, math, met enter in the composition of words that contain the ideas of reason, discipline, science, education, right measurement, and in Latin the term materia indicates what can be measured.

Source: Boris de Rachewiltz - Magic Religius Egipt. Chapter: Mathematical Universe, cult of Maat, abstract goodness of truth and giustice.

Franco.boggi (talk) 09:07, 31 August 2013 (UTC)

In the above message, "Magic Religius Egipt" was replaced by "Egitto Magico Religioso" by 2.33.197.47 after I had replied to the comment below, thus making nonsense of my quoting it. I am restoring the original text, to make the context of my reply clear. JamesBWatson (talk) 20:01, 31 August 2013 (UTC)

 Not done Is there any reliable source that establishes a connection between this Egyptian word and "mathematics"? Does de Rachewiltz present the firm evidence for the connection, or just give it as a speculation? I am unable to find any mention of "Magic Religius Egipt" anywhere at all. JamesBWatson (talk) 11:58, 31 August 2013 (UTC)

I'm not an espert of egiptology, this is fruit of an holiday lecture (I'm just a engineer, in Europe there is time in summer for divagations) but seemed to me very interesting. This book is only edited in italian. Just now, I have discovered that the author is a mistic involved in a process for neo fascism, but I think, neverthless, that the connection between the goodness Maat and the origin of mathematics is to take in account. I'm non an expert titolate to affirm it, but I invite the comunity to go deeper. Thank You — Preceding unsigned comment added by 2.33.197.47 (talk • contribs) 12:47, 31 August 2013 (UTC)

Please sign your talk page messages with four tildes (~~~~). Thanks.

That doesn't look like a wp:reliable source to me. - DVdm (talk) 13:29, 31 August 2013 (UTC)

Semi-protected edit request on 20 January 2014

197.77.0.57 (talk) 19:43, 20 January 2014 (UTC)

Not done: as you have not requested a change.
If you want to suggest a change, please request this in the form "Please replace XXX with YYY" or "Please add ZZZ between PPP and QQQ".
Please also cite reliable sources to back up your request, without which no information should be added to any article. - Arjayay (talk) 19:47, 20 January 2014 (UTC)

Issue with the "Mathematics as profession"

The "Mathematics as profession" section does not talk about the profession of mathematics. It only talks about accolades awarded in the field of mathematics. However, it would be hard to argue that the purpose of professional mathematics (or any profession) is to pursue such rewards.

Suggest renaming the section to "Mathematical Accolades" or "Mathematical Rewards". — Preceding unsigned comment added by Tac-Tics (talk • contribs) 04:01, 14 March 2014 (UTC)

Mathmatical origin

Well, I think that it was the Babalonians that probably invented math when their nation just started. --Jutty10 (talk) 22:47, 18 March 2014 (UTC)