Dear Yoád,
Thanks for your reply. I was not referring to a single calculation or early example of the use of mathematics. I was referring to an actual treatise on mathematics that articulately discusses mathematical problems. This is evidence of mathematics as a scientific endeavour, as contrasted with demonstrations that the ancients used mathematics. This treatise is held at the Pushkin Museum in Moscow. It dates to ancient Egypt around 1850 BCE. There is a larger but slightly younger treatise at The British Museum known as the Rhind Papyrus. It dates to around 1650 BCE also from Ancient Egypt.
The clay tablet you mention is not a treatise. It is a calculation demonstrating that the people who made it could use mathematics. There is also recent evidence that Babylonians were able to use something like calculus on a cuneiform tablet dated to somewhere between 350 and 50 BCE. Once again, these are calculations.
A treatise is a systematic written discussion or argument on a specific subject. The treatise examines the facts and principles involved in the subject under discussion, demonstrating the path from principles to conclusions in a systematic way. In this sense, the two Egyptian papyri are examples of a treatise.
As I wrote in my first comment in this thread, there is evidence of early documents used to teach and study language. These documents differ from a systematic treatise examining facts and principles in much the same way that a contemporary research paper on linguistics differs from a vocabulary primer or a grammar textbook. A cuneiform tablet used to teach language to children is something like a textbook rather than a treatise.
Your question is interesting — to discuss it in a reasonable way takes more time and work than I can invest. The first problem requires stating the question clearly, to clarify what it is you want to know. Your question involves a great many ambiguous terms, and the question you seem to be asking has several answers that may vary by region and culture. To some degree, this is an historical question, and to some degree it is an anthropological question. I’m going to beg off and suggest that you do some desk research in the library. Your science librarian will be able to guide you to useful sources on some issues, and the librarians for human history and the social sciences will help you with other aspects of the question.
Hope this helps.
Yours,
Ken
Ken Friedman, PhD, DSc (hc), FDRS | Editor-in-Chief | 设计 She Ji. The Journal of Design, Economics, and Innovation | Published by Tongji University in Cooperation with Elsevier | URL: http://www.journals.elsevier.com/she-ji-the-journal-of-design-economics-and-innovation/
Chair Professor of Design Innovation Studies | College of Design and Innovation | Tongji University | Shanghai, China ||| University Distinguished Professor | Centre for Design Innovation | Swinburne University of Technology | Melbourne, Australia
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Yoád David Luxembourg wrote:
—snip--
I assume Ken refers to the Babylonians who compute the first known approximate value of π at 3.125 on, possibly, a mud tablet or a stone 2000 BCE.
However, predating that treatise on mathematics is a Sumerian treatise on nouns (on mud tablet), with which the Sumerians people, who began to adopt Akkadian for every day speech, taught their children (and possibly in an organized manner) how to continue and use Sumerian for legal and religions contexts.
In general. There is a big hypothetical question in my mind: It is more likely for primitive cultures to develop an organized teaching of their language before they could do so for stars and numbers or after the could so for stars and numbers.
—snip—
On 24-2-2016 20:14, Ken Friedman wrote:
—snip—
If you mean that linguistics as we understand the science of linguistics today is the “oldest science in the world,” this is not correct. It is true that the study of language and the way that languages work date back to ancient times. Nevertheless, the organised study of mathematics and geometry dates back further. The first known mathematical treatise dates to around 2,000 BCE. Astronomy may be far older, though we know this by inference from archeological calendars rather than written books. The oldest known such calendar dates to nearly 10,000 years ago.
While there may have been some organised study of language for translation, the earliest organised science of language is probably that of classical Athens with Aristotle. The Organon, especially Peri Hermeneias (De Interpretatione) would likely be the first books on language as an organised field of inquiry, but even these are closer to philology and philosophy than to modern linguistics.
—snip—
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