# Talk:History of mathematics

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I'm developing some material from zero divided by zero for inclusion here. But its taking some time to work up so I'm putting it here temporarily while it is worked on. Feel free to contribute Barnaby dawson 10:13, 22 Sep 2004 (UTC)

Could somebody please clean up the first lines of 'complex numbers'? They sound rather trivial or non-encyclopedic. Radiant! 22:09, 12 Feb 2005 (UTC)

## Spherical trigonometry

I disagree with the following sentence "spherical trigonometry was largely developed by the Persian mathematician Nasir al-Din Tusi (Nasireddin) in the 13th century." Other mathematicians wrote about spherical trigonometry before him, including Ptolemy in the 100s AD in his book the Almagest long before the 1200s. NikolaiLobachevsky 21:08:49 12/26/2006 (UTC)

## start date of indian mathematics per boyer's page 208

hi,

it says in the wiki text that history of indian mathematics starts around 2600-1900BC, however the cited source (p 208 boyer edition 1) states:

"Chronology in ancient cultures of the Far East is scarcely reliable when orthodox Hindu tradition boasts of important astronomical work more than 2,000,000 years ago and when calculation leads to billions of days from the beginning of the life of Brahman to about A.D. 400. References to arithmetic and geometric series in Vedic literature that purport to go back to 2000 B.C. may be more reliable, but there are no contemporary documents from India to confirm this".

thus i'm wondering if even the dates 2600BC-1900BC are inappropriate? given that the edit i had to revert tried to extend this from 3000 BC, and the cited text says 2000 BC, i'm having a hard time understanding why it's 2600 BC to 1900 BC.

any clarification would be great. — Preceding unsigned comment added by 174.3.213.121 (talk) 00:18, 29 March 2015 (UTC)

## Influence

Boyer does not present any evidence for "All of these results are present in Babylonian mathematics, indicating Mesopotamian influence" and "showing strong Hellenistic influence". He may be correct that these results were there earlier, but "influence" is speculation. Evidence in the form of direct or indirect contact between the Indians, Babylonians and Greeks is lacking. Including material like this is giving undue weight to a badly written source.

JS (talk) 21:47, 6 April 2015 (UTC)

Boyer is a reliable source (not "badly written") and I take him at his word. You have nothing to base your claim that this is "speculation". His wording is not speculative. Athenean (talk) 22:49, 6 April 2015 (UTC)
very much agree with athenean. if further reverts occur i'll page in an editor. -- 174.3.213.121, 20:53, 12 April 2015‎

## Article Neutrality, Eurocentricity and Context

Don't you think we should reduce the eurocentric skew from these articles ?

Statements like

• The study of mathematics as a subject in its own right begins in the 6th century BC with the Pythagoreans, who coined the term "mathematics"
• Greek mathematics greatly refined the methods (especially through the introduction of deductive reasoning and mathematical rigor in mathematical proof

are unclear and false.

Firstly, Mathematics does not become a 'subject in its own right' by someone coining the term for it in a english(greek/latin) related language. Every language had a term for the field Mathematics.

Secondly, Mathematical rigor and deductive reasoning were evident in textual material ranging from the Egyptian and Babylonians in the West to the Indian and Chinese texts in the East.

I believe adding context to such statements will reduce friction and add accuracy to such topics. — Preceding unsigned comment added by Vanya (talkcontribs) 04:19, 13 September 2015 (UTC)

unclear and false. Firstly, Mathematics does not become a 'subject in its own right' by someone coining the term for it - you've failed to understand the sentence you've quoted. The qualifier ", who coined the term "mathematics" merely states that William M. Connolley (talk) 06:36, 16 September 2015 (UTC)
You do notice that the sentence starts with a statement about where the study of mathematics in its own right began and ends with a statement about how the word mathematics originates from a Greek word meaning "subject of instruction". I see the qualifier bit now but if this is not the meaning attempted the two statements may be better of in different sentences.

No comments on the Eurocentric leaning of at least the intro ?

I did a revision which added details of other cultures and reduced the content on the greek in that specific para above. It was reverted because "too much detail for an intro". The word count difference between revisions was ~3. The reverter did not consult the talk page before reverting. Of course it seems like too much detail if everyone starts talking about what every 'other' culture was up to in the intro. But who decides how much space which culture gets ? Vanya (talk) 16:25, 17 September 2015 (UTC)

That "The study of mathematics as a subject in its own right begins in the 6th century BC with the Pythagoreans" is sourced to Carl Boyer, History of Mathematics, page 48. It is not "eurocentrism" as you falsely claim, and by changing the wording you are altering the meaning of a sourced statement, which constitutes source falsification. As for the rest of your edit, we cannot cram every mathematical advance of every civilization in the lede. That you are intent on doing so constitutes POV-pushing. Athenean (talk) 20:22, 25 September 2015 (UTC)

Boyer's statement can be challenged. According to one source, Old Babylonian scribal schools (between 1900 and 1600 BC) also studied mathematics as a subject.[1] Quote: "Mathematics as a subject was born in the scribal traditions and the scribal schools." (p. 7) "The mathematical activity of the Babylonian scribes seems to have arisen from the everyday necessities of running a central government. Then, in the context of the scribal schools, people became interested in the subject for its own sake, pushing the problems and techniques beyond what was strictly practical." (p. 10) "A social change at the end of the Old Babylonian period seems to have brought this fertile time for mathematics to an end. [...] Scribal arts became family traditions, and scribes no longer specialized in mathematics. As a result, we see tablets in which mathematics is mixed with several other subjects. Mathematics loses its separate identity, and most of the enthusiasm and creativity disappear." (p. 12). Wiqi(55) 02:19, 26 September 2015 (UTC)
Very interesting but it appears this didn't last very long, thus there is no continuity in the study of mathematics as subject on its own before the Pythagoreans. Athenean (talk) 03:02, 26 September 2015 (UTC)
Not to mention that the source "A gentle introduction for teachers and other" isn't quite of the same caliber as Boyer. Athenean (talk) 03:06, 26 September 2015 (UTC)
Boyer's statement (as rendered here anyway) doesn't imply continuity. Hence it's more accurate to say that "The study of mathematics as a subject in its own right began in the Old Babylonian period". The source making this point[2] is definitely reliable and more recent (2004) compared to Boyer (~1976). Wiqi(55) 04:58, 26 September 2015 (UTC)
Nonsense. By your reasoning, it would also be accurate to say that the study of mathematics as a subject in its own right ended in the Old Babylonian period. Mathematics as a subject in its own right has been studied continuously since the Pythagoreans, and this is explicitly backed by Boyer. Furthermore there is no break in the mathematical tradition since the Pythagoreans started studying mathematics for its own sake and the present day. Are you suggesting there is? If so, that would be original research. By the way, Boyer's book was revised in 1991, and a few years' difference means nothing regarding a source's reliablity, so much for that card. Athenean (talk) 05:10, 26 September 2015 (UTC)
Could you quote Boyer's full statement from the 1991 edition? We only lack evidence that mathematics continued as a subject for the Babylonians after the Old Babylonian period (mostly because their older tablets are better preserved). Nevertheless, it is still notable to point out that mathematics as a subject began in that period and within a scribal tradition. Both these facts are notable and supported by reliable sources. If you think the continuity claim is important you can mention that too (although more clearly). But it's obvious that this concept precedes the Pythagoreans by more than a 1000 years. Wiqi(55) 06:37, 26 September 2015 (UTC)

...it is evident the Pythagoreans played an important role - possibly the crucial role - in the history of mathematics. In Egypt and Mesopotamia the elements of arithmetic and geometry were primarily exercises in the application of numerical procedures to specific problems, whether concerned with beer or pyramids or the inheritance of land. There had been little in the way of intellectual structure and perhaps nothing resembling philosophical discussion of principles. Thales is generally regarded as having made a beginning in this direction, although tradition supports the view of Eudemus and Proclus that the new emphasis in mathematics was due primarily to the Pythagoreans. With them mathematics was more closely related to a love of wisdom than to the exigencies of practical life, and it has had that tendency ever since.

As you can see, Boyer is quite explicit. As for the Babylonian claim, your own source explicitly states that they lost interest in the study of mathematics on its own, so it's not a question of a lack of evidence. It would be misleading to our readers to say that the study of mathematics on its own began with the Babylonians, unless we mentioned that this was a brief blip that died out several hundred years later (and even then "nothing resembling philosophical discussion of principles"). That, however, would be far too much detail for the lede. Athenean (talk) 07:20, 26 September 2015 (UTC)
The part you quoted doesn't mention anything about "mathematics as a subject". I guess it's reasonable to assume that Boyer never made any claims about mathematics as a subject, contrary to what's in the article. Furthermore, sources that explicitly mention "mathematics as a subject" point out that this development happened in the Old Babylonian Period. In short, the article misrepresents Boyer and ignores more relevant sources. Wiqi(55) 18:34, 26 September 2015 (UTC)
I had a feeling the BS was about to start. "I guess it's reasonable to assume that Boyer never made any claims about mathematics as a subject"? What does that even mean? Then as what? A hobby? This is sophistry, and pretty banal at that. What the lede currently states faithfully summarizes the spirit of what Boyer wrote. I have very little patience for this kind of nonsense, and even less time for it. Athenean (talk) 19:16, 26 September 2015 (UTC)
To spell it out for you, Boyer never made this claim: "The study of mathematics as a subject in its own right begins in the 6th century BC with the Pythagoreans". That statement is just poor quality original research. Reliable sources (e.g., [3]) state that the study of mathematics as a subject began in the Old Babylonian Period. Calling this "sophistry" is just being disingenuous. Wiqi(55) 20:33, 26 September 2015 (UTC)
If you cannot or don't want to comprehend what Boyer wrote, that's not my problem. He did not use those exact words, but the current wording of the lede captures the spirit of what he wrote perfectly. And if he had used those exact words, you would doubtless play the copyvio card. Like I said earlier, I have no time for sophistry and word games. So long. Athenean (talk) 21:35, 26 September 2015 (UTC)
Well, everyone can see that the above quote by Boyer says nothing about mathematics as a subject. Also, recent scholarship tend to reject the Pythagoreans' "important role" theory: "The majority opinion, however, now seems to be that the Pythagoreans did not play a unique role in the development of the mathematical sciences".[4] Wiqi(55) 11:52, 2 October 2015 (UTC)

(outdent) How do you know that one source is the majority opinion? William M. Connolley (talk) 15:28, 2 October 2015 (UTC)

"Majority opinion" means his own opinion. He is playing word games and refusing to comprehend what the source (Boyer) wrote. Clear case of WP:IDONTLIKEIT. Athenean (talk) 20:53, 2 October 2015 (UTC)

@Athenean: Sorry for the delay in a reply.

• In continuation of @Wiqi55:'s points. Your only refutation to his citations is that it looses continuity. The current statement on the wiki article has no reference to continuity. I don't know why you would bring that up as a refutation to his statement.
• I have cited two statements from the introduction as examples of eurocentricity in it. How is attributing one of the statements in the introduction to its author a refutation of the eurocentricity of the introduction or even that statement ?

You need to be clearer about what you want to articulate. Correct me if I'm wrong but it seems like what you actually want is to get a higher cumulative 'citation worthiness' for alternate viewpoints to edit or remove such a statement. Is that correct ?

• you make the point about 'POV-pushing', do you get that limiting what is allowed to be written is also 'POV-pushing' ? Controlling what is to be allowed in an article has to be a form of 'POV-pushing' on non-science topics. The best we can do is keep the article neutral. I was attempting this by increasing the cultural diversity of history of mathematics being discussed. Mathematics is not just or even pre-dominantly a european-centered topic.

Can we discuss this like civilized people who don't assume the person on the other side of every connection is a low IQ spammer here to waste your time ? We can discuss the Boyer point but all the rest of the edit did was increase the diversity and still kept the conciseness of the introduction. I don't see the problem with that ?

Vanya (talk) 20:56, 9 November 2015 (UTC)

I just came across this discussion so let me toss in my two cents worth. Boyer's discussion, quoted above, deals with the question of when mathematics changed from a practical discipline to a concern with abstract proof. Boyer advances the commonly held view that proof was a product of Greek philosophical thought and can be read as saying that without proof there is no mathematics.
More recent studies have questioned the importance of abstract proof and whether it is exclusively a Greek phenomenon. The Historian of Greek science, G. E. R. Lloyd, has in many places traced the Greek concern with proof to the agonistic (i.e., argumentative) nature of Greek society; at times he suggests that claims of proof were used as social claims for the superiority of one school of thought (e.g., the philosophers against the sophists). Interestingly, his co-authored comparison of Greek and Chinese science (Lloyd and Sivin, The Way and the Word, 2002) while pointing out the Greek emphasis on proof, points out the different Chinese approach to demonstrations: "Rather than formally proving that these methods will always work with the pertinent problem type, the compilers make the point with examples" (p. 230).
As I understand recent thinking in the history of mathematics, there is a tendency to move away from the notion that demonstrative proof, in the manner of Euclid, is the sole method of doing mathematics.
In conclusion, I suggest that the passage in the lede be changed to read: "The study of mathematics as a demonstrative discipline begins in the 6th century BC with the Pythagoreans,…"
--SteveMcCluskey (talk) 17:43, 10 November 2015 (UTC)
I disagree. Studying a subject in its own right and logical proofs are two different things. Biologist study biology for its own sake, without there being proofs in biology. Furthermore, Boyer nowhere links the studied mathematics as a subject for its own sake and the use of proofs. He mentions "philosophical principles", "intellectual structures" and "love of wisdom", but that is not the same thing as the concept of a proof. People like Thales and Pythagoras lived centuries before the formal Euclidean proof evolved. I also worry that almost all of our readers have absolutely no idea what "demonstrative discipline" means. Athenean (talk) 03:07, 11 November 2015 (UTC)
"I also worry that almost all of our readers have absolutely no idea what "demonstrative discipline" means" I think you are truly scraping the bottom of the barrel using that claim as an argument. If a reader doesn't understand the expression 'demonstrative discipline' they certainly won't understand a lot of other terms used in the article. This is an article about the history of mathematics, an academic subject, and not a first reading book for second graders. Thony C. (talk) 06:49, 11 November 2015 (UTC)
Not all of our readers are academics. In fact the vast majority are not. Wikipedia is meant to be accessible to the general public, it's not meant to be an elite academic publication venue. In any case, that is a secondary point. My main point is that the development of the mathematical proof and the study of mathematics as a subject in its own right are two entirely separate developments, separated by a couple of centuries. Athenean (talk) 07:54, 11 November 2015 (UTC)

The "majority opinion" is an assessment made by the source I quoted, not my own. Here is the quote again: "The majority opinion, however, now seems to be that the Pythagoreans did not play a unique role in the development of the mathematical sciences".[5] This quote is seemingly at odds with the weight given to the Pythagoreans in the lede of this article. It may also suggest that using more recent scholarship than Boyer should be preferred. Wiqi(55) 05:02, 8 December 2015 (UTC)