Here I see many say, language has an important impact on our thoughts.
But according to this question,
Foucault in the preface to The Order of Things wrote how he 'laughed out loud' when he discovered a Chinese Encyclopedia whose categorization of knowledge was different from his European presuppositions.
And I agreed so.
For example, kindly take a look at The Nine Chapters on the Mathematical Art, which dates back to BC179, but according to the link, Wiki says,
The full title of The Nine Chapters on the Mathematical Art appears on two bronze standard measures which are dated to 179 CE, but there is speculation that the same book existed beforehand under different titles
Consider, for example, Integral, according to Wiki, the origin of the purpose of the integral in Greece is
This method was further developed and employed by Archimedes in the 3rd century BC and used to calculate areas for parabolas and an approximation to the area of a circle.
It was used to calculate areas, ( as for now, please forget about Newton and Leibniz for further sophisticated proof. ).
Now going back to Chinese The Nine Chapters on the Mathematical Art, the contents of the books are
Contents of The Nine Chapters are as follows:
方田 Fangtian - Rectangular fields. Areas of fields of various shapes; manipulation of vulgar fractions. Liu Hui's commentary includes a method for calculation of π and the approximate value of 3.14159.5
粟米 Sumi - Millet and rice. Exchange of commodities at different rates; pricing.
衰分 Cuifen - Proportional distribution. Distribution of commodities and money at proportional rates.
少廣 Shaoguang - The lesser breadth. Division by mixed numbers; extraction of square and cube roots; dimensions, area and volume of circle and sphere.
商功 Shanggong - Consultations on works. Volumes of solids of various shapes.
均輸 Junshu - Equitable taxation. More advanced problems on proportion.
盈不足 Yingbuzu - Excess and deficit. Linear problems solved using the principle known later in the West as the rule of false position.
方程 Fangcheng - The rectangular array. Systems of linear equations, solved by a principle similar to Gaussian elimination.
勾股 Gougu - Base and altitude. Problems involving the principle known in the West as the Pythagorean theorem.
Now, according to the Wiki in my language, the 方田 ( Fangtian ), to me an Asian, explicitly understandable if you know Chinese, seems to mean to measure the size of rice field, which in my language's one says same thing. The 方田 ( Fangtian ) was used to measure the area of rice field in order for lords in feudal era to calculate the size precisely so that he or she can deduct the amount of tax.
Now more, same according to The Nine Chapters on the Mathematical Art
The method of chapter 7 was not found in Europe until the 13th century, and the method of chapter 8 uses Gaussian elimination before Carl Friedrich Gauss (1777–1855).2
So, although mostly math was developed in Western countries, I think, historically speaking, how could the Westerners not find the method 7 and 8 prior to Chinese??
And I would like to go further. I am sorry I was unable to find English source but Japanese explanation of origin of Chinese characters.
指事 - 点や線などの印で表した字（一、二、上、下･･･）
In English, "1", "2", "up", "down" expressed by linear lines-symbols respectively.
If the language has any impact on our human thoughts, since the method how to count the outside object would be different and consequently, as I said, math, particularly sophisticated in Western country, could not have been developed in China 2000-3000 years ago using their own language, I think.
There seems to me the math, and in analogy language, had no particular impact on human being's thoughts particularly especially considering integral, --- the origin of which seems to me the measurement of areas. ( By cutting curved area into rectangles and sum the size of the total sphere of each rectangles. ) Chinese could not have even tried to measure the size of the area using their own language which already existed.
And in addition, as I commented here, how come, the trading of future happened before semi-future trading was enlisted in Chicago in mid 19th century whilst there had already existed in Japan in mid or late 17th century? Did or does this have anything to do with math-in analogy-language?
If you say language had very important role on our thoughts, how come Chinese tried to measure the size of the area ( = later integral ) by their language which had already differed from the Western one at that time?