Talk:History of science

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House of Wisdom[edit]

In similar fashion to the medieval universities from the twelfth c., a a British scholar, Jim al-Khalili, has identified the Baghdad House of Wisdom as a cause for the success of Islamic scientists from the ninth c. for 5 centuries, until the sack of Baghdad. Might this merit a mention in the article? --Ancheta Wis (talk) 13:47, 23 May 2011 (UTC)


I have improve a litte the section of Indian metallurgy. But the history of the stainless steel it is very very complex. Indeed, before the eighteenth century, the discoveries were accidental and sometimes not reproducible as in Delhi Iron pillar. For example, the Ferrum Noricum that contending to Indian Iron the best quality in Roman Empire was stainless steel because it had into a percentage of Titanium derived from unconscious processes. I remember the drunk man in Toledo that created the inimitable first Sword of Toledo that are better than those of Damascus, tempering the sword into the urine rather than in water by mistake. — Preceding unsigned comment added by (talk) 12:47, 5 August 2011 (UTC)

See this link: (about stainless steel). — Preceding unsigned comment added by (talk) 13:04, 5 August 2011 (UTC) And also

Origins of Maize[edit]

A recent edit removed the discussion of the domestication of maize with the justification that "removed reference to maize that is not supported by the reference, which addresses age of last common ancestor but not of domestication." In fact both references, the NY Times article and the PNAS article, explicitly discuss the time and place of the domestication of maize:

"If maize is the product of a single domestication event as our results indicate, then its origin can be pinpointed to a specific geographic locality.... it is possible to estimate the date of this event with the microsatellite data ... [to] 9,188 B.P. (95% confidence limits of 5,689–13,093 B.P.)."

I have reverted that edit (along with another major edit to the Lede discussed above). --SteveMcCluskey (talk) 16:30, 11 August 2011 (UTC)

This article continues to be anti-European[edit]

Years ago I came on here and got involved in this discussion, bringing up the fact that this article had a very pro-Muslim, Indian, and Chinese bias on the topic. Now I have come back and I see the problem has been improved but there is still a lot of work to be done.

As someone else already mentioned, science in itself is mostly a European achievement, and Wikipedia seems to be the only "Encyclopedia" that gets this wrong. I have read all sorts of books on the history of science, and they all somehow miss these achievements that your article claims that China came up with before the West did. One very good book on the topic is "Human Accomplishment" by Charles Murray. He draws his information from sources from all over the world, and still comes to the conclusion, backed up by plenty of data which he provides, that the West has dominated not just in science but in other areas as well. Any book that tries to claim otherwise (and there are few in number), usually has a pro-Asian bias to begin with. I have yet to read a book strictly on the history of science that DOES NOT devote most of it's attention to Europe and there is a reason for that.

Also , as someone else mentioned, we need to distinguish between what is real science and what is NOT real science. I would like to list some specific quotes from the article that are downright irresponsibly lacking in facts:

"By the 12th century, they could reasonably accurately make predictions of eclipses, but the knowledge of this was lost during the Ming dynasty, so that the Jesuit Matteo Ricci gained much favour in 1601 by his predictions.[41] "

This is strictly a hypothesis based on an excuse. If the evidence isn't there, then it didn't happen.

"From antiquity, the Chinese used an equatorial system for describing the skies and a star map from 940 was drawn using a cylindrical (Mercator) projection."

Nope, the first Mercator map was invented by Mercator, a European, just as the history books say.

"The use of an armillary sphere is recorded from the 4th century BC and a sphere permanently mounted in equatorial axis from 52 BC. "

There is no evidence of anybody knowing that the Earth was round other than the Greeks and then later Europeans after the Renaissance.

"To operate the crowning armillary sphere, his clocktower featured an escapement mechanism and the world's oldest known use of an endless power-transmitting chain drive." What type of power?

"The Jesuit China missions of the 16th and 17th centuries 'learned to appreciate the scientific achievements of this ancient culture and made them known in Europe. Through their correspondence European scientists first learned about the Chinese science and culture.'[46] "

This is an example of your biasness. You say nothing of all the things that the Chinese in turn learned from Europeans at the same time. And what exactly did China have that could really be called "science" as opposed to practical technology? Is there a historical source that actually lists all these scientific discoveries that Europe supposedly learned from China?

"Western academic thought on the history of Chinese technology and science was galvanized by the work of Joseph Needham and the Needham Research Institute. Among the technological accomplishments of China were, according to the British scholar Needham, early seismological detectors (Zhang Heng in the 2nd century), the water-powered celestial globe (Zhang Heng), matches, the independent invention of the decimal system, dry docks, sliding calipers, the double-action piston pump, cast iron, the blast furnace, the iron plough, the multi-tube seed drill, the wheelbarrow, the suspension bridge, the winnowing machine, the rotary fan, the parachute, natural gas as fuel, the raised-relief map, the propeller, the crossbow, and a solid fuel rocket, the multistage rocket, the horse collar, along with contributions in logic, astronomy, medicine, and other fields."

I've noticed that Needham's name comes up over and over on this topic as if he is the only one who says these things. Even Charles Murray in "Human Accomplishment" researched Needham's work, but STILL came to the conclusion that 95% of science has come out of Europe. As for the inventions you list, some of these are legitimate, others are not, some have obscure origins, and finally others were actually much cruder and primitive than what we are to believe they actually were.

"However, cultural factors prevented these Chinese achievements from developing into what we might call 'modern science'. According to Needham, it may have been the religious and philosophical framework of Chinese intellectuals which made them unable to accept the ideas of laws of nature"

Perhaps because there never was real science in China to begin with.

"This led to an early scientific method being developed in the Muslim world, where significant progress in methodology was made, beginning with the experiments of Ibn al-Haytham (Alhazen) on optics from circa 1000, in his Book of Optics."

But it wasn't enough to constitute a scientific method, which is why , for centuries, up until the politically correct period, Muslims have never been given credit for it.

"In mathematics, the Persian mathematician Muhammad ibn Musa al-Khwarizmi gave his name to the concept of the algorithm, while the term algebra is derived from al-jabr, the beginning of the title of one of his publications. What is now known as Arabic numerals originally came from India, but Muslim mathematicians did make several refinements to the number system, such as the introduction of decimal point notation. Sabian mathematician Al-Battani (850-929) contributed to astronomy and mathematics, while Persian scholar Al-Razi contributed to chemistry and medicine. "

No mention of all the influences from Greek math?

"Heliocentric theories may have also been discussed by several other Muslim astronomers such as Ja'far ibn Muhammad Abu Ma'shar al-Balkhi,[60] Abu-Rayhan Biruni, Abu Said al-Sijzi,[61] Qutb al-Din al-Shirazi, and Najm al-Dīn al-Qazwīnī al-Kātibī.[62]" You say "may have", which is the key phrase here. What is this based on? This is where falsehoods get turned into facts, completely fabricating history.

"Muslim chemists and alchemists played an important role in the foundation of modern chemistry."

Even though just about every book on the history of Chemistry spends very little time talking about Islamic achievements.

"As well as this, Europeans began to venture further and further east (most notably, perhaps, Marco Polo) as a result of the Pax Mongolica. This led to the increased influence of Indian and even Chinese science on the European tradition."

While it is true that Europe became reaquainted with Greek science through arabic texts, as well as Persian, Indian, and Greek math, it is factually irresponsible to say that Europe learned SCIENCE from China and India at this time. What science are we talking about and how come it hasn't been mentioned in the average history book? Read the book "MARCO POLO" by Michael Yamashita. In it, Marco Polo describes India as quite backwards, and while he was impressed with China, the book says nothing about him learning any so-called "science" from there.

"The first half of the 14th century saw much important scientific work being done, largely within the framework of scholastic commentaries on Aristotle's scientific writings.[88]"

This proves my point. It is funny that certain biased history books want to claim that Europe during the Renaissance learned science from the Middle East, India, and China, yet in books on the actual history of science inparticular, it is only Greek names that get mentioned when listing specific scientists that Europe learned from. Why is this? — Preceding unsigned comment added by (talk) 02:37, 16 November 2011 (UTC)

I don't quite think the situation is so dramatic, i.e. that the article is "anti-European". If you look at the very large modern science section, it goes into great detail about advances that mostly took place in Europe. That said, there is a lot of crap and puffery in the article (the stuff about the Pax Mongolica for one), and the India, China, and Islamic sections are written from a fan's point of view. If you feel the article needs work, the way to do it is to be WP:BOLD (and get an account) and edit the article accordingly. Complaining on the talkpage is unlikely to achieve anything. As a rule of thumb, any unsourced claim is fair game for removal. By the way, do not indent your paragraphs, otherwise wikipedia treats them as quotes and it makes your talkpage posts very difficult to read. Athenean (talk) 03:21, 16 November 2011 (UTC)
If there is work to be done, the only way is to get an account and get the work done. That's how things are done. :-) Gun Powder Ma (talk) 12:27, 16 November 2011 (UTC)

Sentence (in lead) about the "natural world", "scientific methods", and emphasizing "experiments"[edit]

In this edit, I had done a couple of things. First, I changed "natural world" to "world". Second, I changed "scientific methods" to "scientific method" (forgot to mention the second part in the edit summary - sorry!). Machine Elf 1735 (talk · contribs) changed it back, writing (including quoting my edit summary at the start) '“The "natural world" is generally taken to not include human beings” in this context, it refers to natural philosophy in contradistinction to supernatural explanation.' In my second edit, I summarized my edit as follows: 'OK, if you want "natural" in there, let's specify "humans" (plus be a bit more accurate regarding the scientific method, etc - observational sciences like astronomy still use the scientific method)'. Machine Elf 1735 (talk · contribs) then changed it back (again), writing 'why on Earth wouldn't the natural world include humans? / there's no single “scientific method” / undermines meaning of “emphasizes… experiment"'.

I don't want to get into an edit war, so I'm taking it here to see what others think. Three points:

  • The Nature article, to which "natural world" links, says in its lead section (emphases added):

Within the various uses of the word today, "nature" often refers to geology and wildlife. Nature may refer to the general realm of various types of living plants and animals, and in some cases to the processes associated with inanimate objects – the way that particular types of things exist and change of their own accord, such as the weather and geology of the Earth, and the matter and energy of which all these things are composed. It is often taken to mean the "natural environment" or wilderness–wild animals, rocks, forest, beaches, and in general those things that have not been substantially altered by human intervention, or which persist despite human intervention. For example, manufactured objects and human interaction generally are not considered part of nature, unless qualified as, for example, "human nature" or "the whole of nature". This more traditional concept of natural things which can still be found today implies a distinction between the natural and the artificial, with the artificial being understood as that which has been brought into being by a human consciousness or a human mind. Depending on the particular context, the term "natural" might also be distinguished from the unnatural, the supernatural, or synthetic.

I also note the antonyms of artificial (including "natural"), manmade (including, again, "natural"), and natural. I furthermore note the distinction between the "natural sciences" and the "social sciences". I do not disagree that, properly speaking, everything that humans do is de facto natural, since we are natural creatures; unfortunately, a significant number of people do not regard this as true.
  • I would be interested in hearing about the alleged different "scientific methods" that Machine Elf 1735 claims exists, including citations for each of them and why they cannot be summed up as "the scientific method with different means of application suitable for different sciences", as is my contention. In support of my side of the argument, I cite (as the most readily available reference to me) the section entitled "The Scientific Method" from chapter 2 of:

Leedy, Paul; Ormond, Jeanne (2005). Practical Research: Planning and Design (8 ed.). Merrill Prentice Hall (copyright Pearson Education, Inc). 

Note that the text in question is not meant for one variety of scientific research, but includes material for both the natural sciences and the social sciences.
  • In regard to experiments, I note the Experiment article's Observational science section. I also cite the book referenced above for my contention that, while experiments are the ideal, sometimes observations must substitute for experiments, and this does not make the sciences in question any less sciences.

So, I suggest that the sentence in question (in the lead) does need changing. I would be happy - if other commitments don't cause a problem - to help with coming up with a compromise phraseology. Allens (talk) 20:05, 14 December 2011 (UTC)

Some comments, in case they help:
  • I am not convinced by either side of the argument which focuses on whether humans are part of nature or not. This is a complicated point, but in the end even Aristotle talks of human nature. Of course Aristotle thinks there is both nature and natures. And so on.
  • I think the point about the word choice for "world" or something like it is truly difficult. We had the same discussion on the Science article and I suggest looking at the discussion there, which had several good-natured participants.
  • The last bit about method or methods is for me less interesting than the question of whether science's core is really getting a good description here. What do all things called scientific have in common? Again I would suggest looking at the science article where this has also come up frequently.--Andrew Lancaster (talk) 20:44, 14 December 2011 (UTC)
Thank you. As I indicated above, I actually do think that humans and their activities are "natural"; I simply have reason to believe that some readers of the page may not, and may thus misinterpret the phrase "natural world" (linking to Nature) without clarification. (I will take a look at the Talk:Science page at the discussions there, however, including on definitions of what is science.) I strongly suspect that the question of science's description/definition will depend - particularly on this page! - on whether one counts as "science" that work done prior to the scientific method. (As both a scientist and as a teacher of research methods, I don't, but I realize that others may disagree.) Allens (talk) 22:10, 14 December 2011 (UTC)
I agree that humans are part of nature in some way. But according to some traditional schemes, the minds of humans, or some part it, and things they cause to come into being, are not natural, but artificial. You might want to also look at Nature (philosophy). Anyway, I am not sure that this point is the most important one for this passage. It would be pretty easy to find a wording that avoids taking a position?--Andrew Lancaster (talk) 09:40, 15 December 2011 (UTC)
I would think so; would Machine Elf 1735 (talk · contribs) care to suggest a clarification? I'll leave a message on that editor's talk page requesting a look at this. Allens (talk) 13:05, 15 December 2011 (UTC)

────────────────────────────────────────────────────────────────────────────────────────────────────A chapter in a recent historical study of science has this to say about scientific methods:

"Scientific method, like science, was thus never one thing. It was many potentially useful things." The author goes on to discuss the ways in which the concept was a "valuable source of rhetorical weaponry" for individuals and groups who used various definitions to distinguish science (what they were doing) from non-science (what others were doing).

Daniel F Thurs, "Scientific Methods," pp. 307-335 in Peter Harrison, Ronald L. Numbers, and Michael H. Shank, ed., Wrestling with Nature: From Omens to Science, Chicago, University of Chicago Press, 2011. (quotation at p. 310). --SteveMcCluskey (talk) 02:33, 16 December 2011 (UTC)

Another historian of science, G. E. R. Lloyd, has this to say about scientific methods:
"...quite what the scientific method or methods consist in is itself intensely problematic. We cannot assume that there is a consensus on this issue in principle. Moreover in practice the methods adopted by today's scientists are in many cases very different from the neat schema of the hypothetico-deductive experimental method, as that is taught in schools. That schema plays an important pedagogic role, in introducing the pupil to certain model pracitces, but it is an idealization. It is one that certainly does not capture the complex processes by which a researcher decides his or her next moves in following up their hunches, getting round the difficulties, devising new protocols to crack the problems."
G. E. R. Lloyd, Ancient Worlds, Modern Reflections: Philosophical Perspectives on Greek and Chinese Science and Culture, Oxford: Oxford University Press, 2006, p. 15. --SteveMcCluskey (talk) 03:09, 16 December 2011 (UTC)
Interesting. Regarding the first, I argue that one needs to distinguish particular applications of the scientific method in different fields from different scientific methods. Regarding whether scientists actually put into practice the method taught in schools, I suspect that the answer will differ depending on whether one looks at what people specifically state or what can be deduced from what they do. This has come up with my students' attempts to extract hypotheses from articles - they typically can't find (because it isn't there) a direct statement of the hypothesis/hypotheses concerned, whereas with a bit of logic one can frequently figure out what hypothesis is being actually tested by the research described.
However, more important is that this seems to be an area where sources disagree, and this should be reflected in the sentence in question, as should that sciences can do research using observation as well as experiments. Allens (talk) 23:39, 17 December 2011 (UTC)
Give it a rest.—Machine Elf 1735 08:03, 18 December 2011 (UTC)
I'm not sure Allens seriously believes there's only true scientific method… No doubt every practice the ‘same’ method, in spirit. Apparently the user would agree, but prefers a fantasy in which their contention was “"the scientific method with different means of application suitable for different sciences"” and that I'm an entrenched polemic adversary who “claims” that “alleged” scientific methods “cannot be summed up” that way. Obviously, if the user were to undertake an exhaustive analysis of my two edit summaries, they would find my only comment on the subject was: 'there's no single "scientific method"'. As far as I'm concerned, they're welcome to change scientific methods to the scientific method, absent the unrelated remarks that needlessly detract from the article. Frankly, apart from the abuse of language, I agree different means are applicable for different sciences. Does the ‘the same means’ leading to ‘the same ends’ come in handy for the more lack-luster of the soft sciences? Surely the least squishy of the has-been anointed, don't traffic in matters of opinion?
Perhaps the user would be interested in explaining why they “note” so many “citations” for no apparent reason. I can't find a preview of ed. 8, but I'll take the user's word for it that chapter 2 contained a section called Scientific Method. Is there a reason to “note” that apart from the title? I have no problem stipulating it presumptively verifies the many sciences are transubstantiated under one ousia, or that different means the same, whatever… No sense wasting time on the bogus:
“Note that the text in question is not meant for one variety of scientific research, but includes material for both the natural sciences and the social sciences.”
It's meant for students, in general. It includes no such material for the sciences. Compare:
The Yellow Pages is not meant for one variety of scientific research, but includes material for both the natural sciences and the social sciences.
Practical Research: Planning and Design is a broad-spectrum, cross-disciplinary book suitable for all courses in basic research methodology. Many basic concepts and strategies in research transcend the boundaries of specific academic areas and such concepts and strategies are at the heart of this book. To some degree, certainly, research methods do vary from one subject to another: A biologist might gather data by looking through a microscope, a historian by examining written documents from an earlier time period, and a psychologist by administering tests or systematically observing people's behavior. Otherwise, the approach to research is the same. Regardless of the disciple, the researcher identifies a question in need of an answer, collects data potentially relevant to that answer, analyzes and interprets the data, and draws conclusions that the data seem to warrant.
Students in the social sciences, the natural sciences, education, medicine, business administration, landscape architecture, and other academic disciplines have used this text as a guide to the successful completion of their research projects. […] Essentially, this is a do-it-yourself, understand-it-yourself manual.
2 Tools of Research
… The tools that researchers use to achieve their research goals may vary considerably depending on the discipline. The microbiologist needs a microscope and culture media; the attorney, a library of legal decisions and statute law. We do not discuss such discipline-specific tools in this chapter. Rather, our concern here is with the general tools of research that the majority of researchers, regardless of discipline and situation, typically need to collect data and derive meaningful conclusions.
Yawn.Machine Elf 1735 08:03, 18 December 2011 (UTC)
I suggest two points about the lede.
  • Scientific methods should be treated in plural because
  • Historians of science cited above (and philosophers of science not cited) treat it as such (after all, this is an article about history of science)
  • The Leedy and Ormond book cited above is a textbook, not an example of scholarly research.
  • I agree that the phrase "by experiment.", added in these edits, can be readily deleted from the lede -- astronomy, whose history I study, is an observational, not an experimental science.
--SteveMcCluskey (talk) 16:38, 19 December 2011 (UTC)

Ordering of discplines[edit]

Is there a particular reason why physics is ordered as the first natural science (in the modern science section)? How were the others ordered afterwards? It doesn't seem to follow any objective order except for that which some would argue as the "purity" of the discipline. Not really a crucial subject in terms of substance, but I'd like to know if there was logic behind it. NNN15 (talk) 00:37, 21 January 2012 (UTC)

Sorry for the length of this reply but your question led me to look at the tplable of contents of George Sarton's Guide to the History of Science (1952). He placed the more abstract sciences at the top of his list and the biological and social sciences near the bottom, with little emphasis on the social sciences. His organizational structure influenced the thinking of many historians of science and, to some extent, is followed in this article.
History of Special Sciences
  • Logic
  • Western Logic
  • Eastern Logic
  • Mathematics — Bibliography
  • History of Mathematics
  • General Mathematics and Special Subjects Not Covered in the Following Sections
  • Arithmetic, Algebra, Theory of Numbers
  • Geometry
  • Mathematical Analysis
  • Statistics
  • Astronomy
  • Physics
  • Mechanics, Including Celestial Mechanics
  • Heat — Thermodynamics
  • Optics
  • Electricity and Magnetism
  • Chemistry
  • Technology, "Inventions"
  • Navigation
  • Metrology
  • Chronometry and Horology
  • Photography
  • General Biology and Natural History
  • Botany and Agriculture
  • Zoology
  • Geodesy and Geography
  • Geology, Mineralogy, Palaeontology
  • Meteorology
  • Anatomy and Physiology
  • Anthropology, Ethnology, Folklore
  • Psychology
  • Philosophy
  • Medicine
  • Dentistry
  • Epidemiology
  • Gynaecology and Obstetrics
  • Pharmacy and Toxicology
  • Veterinary Medicine
  • Education
  • Sociology
  • Prehistoric Archaeology
--SteveMcCluskey (talk) 04:08, 21 January 2012 (UTC)
see also the ordering (especially section 6) by Robert Kilwardby (13th c) de ortu Scientiarum (from the garden of science) -- Ancheta Wis   (talk | contribs) 09:09, 23 April 2012 (UTC)

On my wish list[edit]

(I'm not qualified for WP:BOLDing myself on this).

On my wish list: The history of history of science. AFAIIM2K (as far as I imagine myself to know) the history of science as a history-science have improved lately to be more reflective about the relation of science towards religions, politics and economy, rather than an idealistic heroic cavalcade of lonely genii conquering. Rursus dixit. (mbork3!) 09:52, 27 March 2012 (UTC)

Library of Alexandrea destroyed by Arabs[edit]

"The Library of Alexandria had been destroyed by 642, shortly after the Arab conquest of Egypt" - this is disputed in it's own article, and regarded as being false history. Faro0485 (talk) 05:49, 8 May 2012 (UTC)

The library has undergone much destruction and reconstructions from Caesar onwards. The fundamentalist Christians also did their damage, surely the Arabs closed the library definitively. — Preceding unsigned comment added by (talk) 22:17, 2 August 2012 (UTC)

About of the Fall of Constantinople there is only a little raw....[edit]

The importance of crisis of Byzantine empire in XV century and the fall of Constantinople in 1453 were crucial for the development of science in western europe.

With the intellectuals, arrived lot of ancient books. For example Marciana library of Venice is founded from Bessarione. With refugees began the study of greek language to approach to ancient books with the original language. The importance of byzantine refugees for humanism example in Padua and Bologna universities or in Florence accademies is undubitable.

The emphasis in the 60s and 70s of XX century on the arabic wire often is founded on the ideologies of post-colonial Europe and in the political correctness. This emphasis has hidden the byzantine wire that is not less important...

-- (talk) 21:56, 2 August 2012 (UTC)

mathematics: natural science?[edit]

Sorry to barge in from the cold but there does not seem to be an entry for "mathematics" under the various sciences listed in the "natural science" section. Was this discussed in the past? Tkuvho (talk) 17:39, 25 February 2013 (UTC)

The explanation is simple: Mathematics is not listed as a science because it does not qualify as a science. The scientific method requires that hypothesis and predictions be tested to confirm correctness. This is not possible with mathematics as it is a form of logic (e.g. there is no means to independently test and verify that 1+1=2). Mathematics is instead one of the primary "languages" used by science. --Allen3 talk 19:01, 25 February 2013 (UTC)
Mathematics has always been considered marginal in definitions of the history of science. Here are two recent ones:
  • Science comprises, first, the orderly and systematic comprehension, description and/or explanation of natural phenomena and, secondly, the [mathematical and logical] tools necessary for the undertaking. Marshal Clagett, Greek Science in Antiquity, (1955)
  • Science is a systematic explanation of perceived or imaginary phenomena, or else is based on such an explanation. Mathematics finds a place in science only as one of the symbolical languages in which scientific explanations may be expressed. David Pingree, "Hellenophilia versus the History of Science," (1992)
--SteveMcCluskey (talk) 19:37, 25 February 2013 (UTC)
The closest one could call it science is formal science which also includes things like computer science and decision theory, as opposed to natural science which is what most people would mean when they talk about the history of science. I guess the theory of the scientific method would actually count as formal science but that's not enough to include all the rest of it in. Dmcq (talk) 13:07, 26 February 2013 (UTC)
Yes, mathematics is generally considered a borderline case of science. It has many characteristics of a science, and mathematicians are sociologically closer to scientists than to people working in other fields of research. The scientific method is a valid argument to exclude mathematics from the sciences, but not a very good one. Mathematics is not about 1+1=2 but about much more advanced stuff. There are scientific experiments in mathematics, such as checking a statement about all numbers for many numbers to see if a counterexample comes up. They just don't have the same prominence as in other fields because mathematics is the only field in which something better can be attained: strict proof. One can also argue that mathematics is not concerned with nature, though ultimately numbers and the rest of mathematics are part of observable nature in a wider sense. In addition, mathematics has historically engendered disciplines of science and engineering such as physics or very recently computer science. Hans Adler 13:16, 26 February 2013 (UTC)
Mathematics however has historical ties to (non natural sciences fields) as philosophy, economics or arts as well. And while physics might have the strongest ties to mathematics, in particular since 20th century various areas within the humanities and social sciences increasingly rely on mathematical methods. In fact there is even humorous exploitation of that trend by Tom Lehrer (singing about the mathematization of the social sciences, see sociology at 7:20 min)--Kmhkmh (talk) 01:55, 27 February 2013 (UTC)
Ooh, I wonder if a friend of mine will stay one if I send her that link to Tom Lehrer ;-) Dmcq (talk) 09:43, 27 February 2013 (UTC)

──────────────────────────────────────────────────────────────────────────────────────────────────── This thread discuss if mathematics is a science. The article defines science as "a body of empirical, theoretical, and practical knowledge about the natural world". It is clear that mathematics does not belong to the natural world. But most mathematics is theoretical knowledge about the natural world. Moreover, until 18th century, and even 19th century, physicists and mathematicians were usually the same people, and it is therefore difficult to dissociate physics from mathematics. For example, are Kepler laws mathematics or celestial mechanics? (By the way, Kepler laws, that are the starting point of celestial mechanics are not even cited in the article.) When Newton did shown that Kepler laws may be deduced from gravitational law is that mathematics or mechanics? Who can pretend that the mathematics he has developed for this purpose is not "theoretical knowledge about natural world"? More recently, when a mathematician, like the field medal Cedric Villani explains some physical phenomenons, which were not understood by the physicists, is that formal science of natural science?

On the other hand, while the introduction assert that "science is knowledge about the natural world", there are sections about political science, sociology, psychology, linguistic, economics, ... Is that "natural world"?

Knowing if mathematics is science is controversial, even among mathematicians. I do not know if there are reliable sources asserting that mathematics is not science. There are many such sources asserting that it is science, at least the work of Auguste Comte, who not only considered it as science, but rated it at the first science.

My conclusion is that, excluding mathematics from the history of science, as it is presently, is not only a historical error, but, as a large proportion of scientist consider mathematics as science, this breaks the neutral point of view policy of Wikipedia.

D.Lazard (talk) 16:51, 27 February 2013 (UTC)

(This comment is directed to no one in particular.) This article (correctly) includes the history of mathematics, in several places: there're sections on the sidebars for it, it's mentioned in the various sections on historical science in different regions and eras, etc. However, it's missing from the sections on modern science. This is obviously an oversight that should be corrected; the natural thing to do would be to create a section called "Mathematics" under "Modern science"; the person who creates this section can decide whether to put it under "Natural sciences" or in its own heading, and then we can have a wonderful argument about which of those two choices is right. But I don't see the point of having the argument before the section exists. --JBL (talk) 16:59, 27 February 2013 (UTC)

I think we need to depend on histories of science and say what they say and only put in the maths connections that occur with at least some regularity. I would only include that amount which would be considered applied mathematics, which would include most of what Kepler and Newton did as well as ancient astronomy. However I believe there is already a lot in the article about maths which should not be there. Dmcq (talk) 17:30, 27 February 2013 (UTC)

The Mathematics#Mathematics as science section has some useful discussion and references on mathematics as a science. It looks like there are reliable sources on both for and against math as a science. There are also the book MATHEMATICS:The Science of Patterns by Keith Devlin; (reviews are at [1] and [2]) and the similarly named book Mathematics as a Science of Patterns by Michael Resnik. --Mark viking (talk) 18:05, 27 February 2013 (UTC)

There are already a number of discussions of mathematics at various points in the article, including Babylonian discussions of Pythagorean triples, Egyptian geometry, the Pythagorean tradition, the Euclidean idea of rigorous proof, Indian mathematics (including the concept of zero), Chinese math (including an approximation for π). In sum, there seems to be enough precedent for including some math in this article (despite Clagett and Pingree).
Discussions on whether maths is a science or not are not really relevant. What is relevant is reliable sources on the history of science. We should not apply logic saying some books say maths is a science this is a history of science therefore we should stick in maths history. What do books on the history of science say, that is what should be summarized here. Dmcq (talk) 20:51, 27 February 2013 (UTC)
As noted above, George Sarton included history of mathematics in the history of science, but then he also included the history of logic. Since there's already a page dedicated to the History of mathematics, probably we should only have a small discussion of the history of math here, with a link to the main article. --SteveMcCluskey (talk) 22:11, 27 February 2013 (UTC)
That was just a big bibliography, it wasn't a history. I mean histories. Dmcq (talk) 22:28, 27 February 2013 (UTC)
The issue of "natural science" versus "formal science" that dominated the discussion above is a bit of a red herring. I would suggest replacing "natural sciences" by "exact sciences" and including an entry on mathematics that shouldn't be any longer than that on physics. "exact sciences" is a more precise formal opposite of "social sciences" for the purposes of classification. In this way we avoid an endless debate on the precise nature of the mathematical sciences, and fix a blatant omission in the list under "exact sciences". Would anyone like to propose a brief paragraph? Tkuvho (talk) 14:47, 28 February 2013 (UTC)