What the hell is math
How did mathematics and its ideas go from ancient to medieval to modern times
What kind of transition has been made
Why do we need to understand the dynamics of math
An interesting aspect of academic development is that the “front line” is connected to “the simplest”, and that mathematicians, after many years of thinking, have studied the most difficult aspects of their thinking in a way similar to that of primary school students. The thinking methods of modern mathematics (only thinking methods) are very close to the mathematics that pupils learn。
In its mathematics and life series, expedition focuses very much on the links between different mathematical fields, different mathematical knowledge, and links between the logic of knowledge and successive historical developments, giving readers a sense of proximity to mathematics。
The new book, mathematics and life 5, is a continuation of the old style and focuses on the historical development of mathematical thinking methods, leading readers to a deeper understanding of mathematics。
Mathematics and life 5: history, modernity and methods of math
I'm the author
Translator
01
Mathematical change
Mathematics have been changing, and i want to talk to you about this, and it's going to really help you understand math and what it is。
And maybe one wonders, "is math really changing?" and here, "change," actually, is math changing in the face. Although the essence of mathematics has not changed, its “morphology” has changed a lot from ancient to modern. Understanding these changes will lead to a better understanding of mathematics in substance。
Of all the studies, mathematics is probably the oldest. The subject of mathematics was born thousands of years ago when human civilization began. In that sense, mathematics is a long-term source。
In order to look at the mathematical history of thousands of years, it would be easier to divide it into several times. The book is divided not by definition, but by mathematics. And i think this sort of division allows you to better understand the changes in the mathematical look。
I have divided the history of mathematics into ancient, medieval, modern and modern times, and in the later part i will explain how mathematics changes in these four times。
Ancient mathematics is the mathematics that was born in ancient civilization. An ancient civilization refers to ancient egypt, cuba, birun, ancient india and china. These civilizations were born with agriculture at their centre. Mathematics in this period are now more in primary school math classes. At the turn of time between ancient and medieval times, the ancient greeks opened up a whole new mathematics, which then entered medieval. In the long medieval period, it was cartesian of the 17th century that drew the next boundary for mathematical history. You're probably all familiar with the idea of the coordinates, and this is the beginning of modern mathematics. Modern mathematics went from the 17th century to the 19th century, and since the 20th century, mathematics has entered modern mathematics。
Modern mathematics is the newest part of the history of mathematics, and the front line of mathematical development. That is why some readers may find the thinking of modern mathematics difficult, not understandable in a day or two. But in fact, in a sense, modern mathematics is better understood than ancient, medieval and modern mathematics, because it has a much closer side to common sense。
Modern mathematics, which began in the twentieth century, is, in a sense, very close to the mathematics that pupils learn (only in the case of thinking methods). In other words, the “front line” is connected to “the simplest”, which is also an interesting point for academic development. It is interesting that mathematicians, after many years of thinking, study the most difficult things and think in a way similar to that of primary school students。
Many of the ideas in modern mathematics, such as collections, have gradually been incorporated into school math textbooks. Some parents may not have studied them at all when they went to school, and parents do not know how to deal with them when they ask them about them. The book may also be helpful to such parents。
Ancient mathematics does not really have the "theorem-prove" system that's common in mathematics, which can be very empirical. Texts from ancient mathematics are not available. There are “general rules” in these books called “theorems”, but they are not produced in the form of “certification”. The writings of ancient mathematics take the form of the inclusion of many questions and the recording of the answers to them。
02 ancient mathematics - ancient egypt, china
I just need to think about the math of primary school. This is the type of content recorded in the mathematical books of ancient egypt in the 3400 b. C. The chapters of these mathematical books document similar problems and describe their solution. Mathematic books at this time do not record “general rules” but, by allowing readers to solve the problem on an ongoing basis, ultimately obtain a general solution of their own。
In addition, there is an older chinese math book called nine chapters of arithmetic. The math book is composed of nine chapters and is therefore named. The exact age of the book is unknown. According to the researchers, its contents had been around the time of china's war, and after the reunification of qin, the qin emperor had not been spared math books such as " nine chapters " . After qin, the handai people collected the remnants of the scattered areas, re-organised, updated and compiled the nine chapters of arithmetic. China has many mathematical works, of which the nine chapters are older and are written in the same way as we mentioned earlier: it does not use the “theorem-certification” system, but records many similar topics and then records their detailed demarches. It is worth mentioning that chapter nine is the most advanced in terms of mathematical writings in other places。
Chapter viii of the chapter ix arithmetic is entitled “equals”. This is the origin of the term “equipment” that is now commonly used in mathematics. As can also be seen, the equation is an antiquities with a long history. “tangular” means “comparison”, while “process” means size, that is, “quantitative”. That is to say, "equals" means "comparisons". The equation now actually has the meaning of “comparison of the volume on the left and the right and on the right”. That is the equation we are talking about today. The nine chapters of arithmetic document very systematically the solution of these equations. But even good mathematical writings like "the nine chapters" do not use the "theorem-prove" system, so i said that ancient mathematics was empirical。
At that time, the nine chapters were written for mathematics learning by officials (government employees). The same is true of ancient egyptian math books that we mentioned earlier. This type of book is equivalent to a reference book for the current national civil service examination rather than a popular reading. That is to say, without the mathematical knowledge of the books, it would not have been possible for government staff at the time to successfully complete their work. For example, calculating the size of the field requires knowledge of the quadrilateral, triangle and circular area. And, in ancient mathematics, there was a fairly high level of mathematical content, even from today's perspective. For example, in the mathematics of birón, cuba, there is a solution to the current secondary equation。
How did mathematics develop these things
I think it was the social development of the time that made this level of demands on mathematics. For example, maintaining the functioning of the state requires an effective administrative system, which naturally requires a tax system. In addition, the construction of roads, the construction of hydroelectric projects to manage rivers and the construction of large buildings such as pyramids require a considerable level of mathematical knowledge on the part of managers。
It is clear from this that mathematics is not a simple mind game in mind, but that its development is stimulated by the demands of social development, especially in ancient civilization。
In an ancient civilized country dominated by agriculture, there is also a knowledge that has developed along with mathematics, namely astronomy. The development of ancient astronomy is not due to the pleasures of the ancients to look at the stars, but to meet agricultural needs。
For agriculture, understanding of the climate, that is, of the season, is of paramount importance. We now know that there are 365 days a year, but the ancient people did not know that at first, which is actually the result of a long view of the stars. If this is not understood, then one cannot know when to sow. Understanding time changes and managing seasonal shifts are essential for agricultural countries. Even in modern times, while people living in urban areas are no longer paying much attention to seasonal changes and are moving away from such things as seeding, ignorance of seasonal changes can be described as a failure to survive for those still engaged in agriculture. As a result, the ancient nations, predominantly agricultural, will naturally develop their astronomy。
There is a need for computing in the development of astronomy, which in turn stimulates the development of mathematics. It can be said that this is the basis for mathematical development. That's what ancient mathematics looks like。
03
Old greek math and tylers
The evolution of ancient mathematics to the next stage is taking place in ancient greek civilization. Between the sixth century bc and the fifth century bc, ancient greek civilization took on the stage of history. Unlike ancient civilizations such as egypt, cuba and bilun, ancient greek agriculture is not prosperous, producing mostly olives, grapes, etc。
In ancient greece, trade dominated, with olives, grapes and other products sold by boat to areas near the mediterranean sea. And that's why ancient greece needs a mathematical knowledge that is different from those of earlier civilizations that were predominantly agricultural。
You may have heard of teless, the head of the seven gens of ancient greece, in the classroom. Tylers is often called the archaeologist of ancient greek philosophy, and he is also the archaeologist of ancient greek mathematics. Moreover, taylor is said to be a businessman with a very good mind and a very successful business。
The ancient greeks of that time often went to ancient egypt and cuba to do business in birun, thanks to which the ancient greeks also studied ancient mathematics. Then the ancient greeks moved mathematics into a completely new phase with a completely new way of thinking. What is this new way of thinking? And that's what ancient mathematics lacks。
Tylers himself did not write anything. At that time, it did not seem that writing was a remarkable thing. And most of those who wrote were regarded by men as second-rate, not first-class. For example, jesus himself did not write a book, nor did he. Buddha is a record of his proselytism. Socrates (former 470 – former 399) has not written a book of his own, and most of his protégé plato (former 427 – former 347) is recorded as a “dialogue.” the same is true of the confucius of china, which was written by his disciples for recording confucius'statements. In that time, great thinkers didn't write much themselves。
Tylers is one of those who don't write books. What he thinks, and how he thinks, is recorded. And, of course, the records also include his thinking about mathematics. One of taylor's mathematical achievements is said to be the introduction of a triangulation theory, i. E. Two triangles equal to each of the angles and their sides. In other words, if the two angles of the triangle and the edges of the triangle are determined, then the triangle is established. Tylers first presented this triangulation full of theorem and proved it。
In fact, taylor had a great deal to do with the business he was engaged in, or with his father as a businessman travelling to and from the mediterranean. If two points on the coastline were to be used to determine the location of vessels sailing offshore, then that theory could be used. For example, it is possible to measure the angle of the two points on the terrestrial coastline to the position of the vessel, to know the two angles and the distance between them, to determine a triangle and to determine the location of the ship. In addition, taylors is said to have proved “the two bottom angles of the paraplegic triangle equal”。
Taylor brought the word “prove” to mathematics. Thereafter, “certification”, i. E. “describe and prove the general law”, became indispensable in mathematics. In this sense, the old greek mathematics is very different from the old greek math. That's how the ancient greeks began a new era of mathematics。
Mathematics and life 5: history, modernity and methods of math
