When people interact for a long time within a certain field of activity, they begin to look for a way to optimize the communication process. The system of mathematical signs and symbols is an artificial language that was developed to reduce the amount of graphically transmitted information and at the same time completely preserve the meaning in the message.
Any language requires study, and the language of mathematics in this regard is no exception. In order to understand the meaning of formulas, equations and graphs, it is necessary to possess certain information in advance, to understand terms, a notation system, etc. In the absence of such knowledge, the text will be perceived as written in an unknown foreign language.
In accordance with the needs of society, graphic symbols for simpler mathematical operations (for example, the designation of addition and subtraction) were developed earlier than for complex concepts like an integral or differential. The more complex a concept, the more complex a sign it is usually denoted.
Graphic Design Models
In the early stages of the development of civilization, people associated the simplest mathematical operations with the familiar concepts based on associations. For example, in Ancient Egypt, addition and subtraction were indicated by the pattern of walking legs: the lines in the direction of reading they indicated “plus”, and in the opposite direction - “minus”.
Figures, perhaps, in all cultures were initially indicated by the corresponding number of dashes. Later, symbols began to be used for recording - this saved time, as well as space on tangible media. Often, letters were used as symbols: such a strategy has become widespread in Greek, Latin, and many other languages ​​of the world.
The history of the emergence of mathematical symbols and signs knows the two most productive ways of forming graphic elements.
Converting Verbal Representation
Initially, any mathematical concept is expressed by some word or phrase and does not have its own graphic representation (in addition to the lexical one). However, performing calculations and writing formulas in words is a lengthy procedure and takes up unreasonably much space on a material medium.
A common way to create mathematical symbols is to transform the lexical representation of a concept into a graphic element. In other words, the word denoting the concept, over time, is reduced or transformed in some other way.
For example, the main hypothesis of the origin of the plus sign is its abbreviation from Latin
et , the analogue of which in the Russian language is the union “and”. Gradually, in cursive, the first letter ceased to be written, and
t was reduced to a cross.
Another example is the “X” sign, which means the unknown, which was originally an abbreviation of the Arabic word “something”. Similarly, signs occurred to indicate the square root, percent, integral, logarithm, etc. In the table of mathematical symbols and signs, you can find more than a dozen graphic elements that appeared in this way.
Custom character assignment
The second common option for the formation of mathematical signs and symbols is the purpose of the symbol in an arbitrary way. In this case, the word and graphic designation are not related to each other - the sign is usually approved as a result of the recommendation of one of the members of the scientific community.
For example, signs of multiplication, division, equality were proposed by mathematicians William Otred, Johann Rahn and Robert Record. In some cases, several mathematical signs could be introduced into science by one scientist. In particular, Gottfried Wilhelm Leibniz proposed a number of symbols, including the integral, differential, derivative.
Simple operations
Such signs as “plus” and “minus”, as well as symbols denoting multiplication and division, are known to every student, despite the fact that there are several possible graphic signs for the last two mentioned operations.
We can confidently say that people knew how to add and subtract many more millennia BC, but standardized mathematical signs and symbols denoting these actions and known to us today appeared only by the XIV-XV centuries.
However, despite the establishment of a certain agreement in the scientific community, multiplication even nowadays can be represented by three different signs (diagonal cross, dot, asterisk), and division by two (horizontal line with dots above and below or an oblique line).
Letters
For many centuries, the scientific community has used exclusively Latin to exchange information, and many mathematical terms and signs find their origins in this language. In some cases, graphic elements were the result of the reduction of words, less often - their intentional or accidental transformation (for example, due to a typo).
The percent designation (“%”) most likely comes from the erroneous spelling of the abbreviation cto (cento, that is, the “hundredth”). Similarly, the plus sign occurred, the history of which is described above.
A much larger number of characters was formed by intentionally shortening the word, although this is not always obvious. Not every person recognizes the letter R in the sign of the square root, that is, the first sign in the word Radix (“root”). The integral symbol also represents the first letter of the word Summa, but intuitively it looks like a capital f without a horizontal line. By the way, in the first publication, publishers made just such a mistake by typing f instead of this symbol.
Greek letters
As graphic designations for various concepts, not only Latin, but also Greek letters are used. In the table of mathematical symbols you can find a number of examples of such a name.
The number Pi, which is the ratio of the circumference of a circle to its diameter, comes from the first letter of the Greek word for a circle. There are several less well-known irrational numbers, denoted by the letters of the Greek alphabet.
An extremely common sign in mathematics is “delta”, which reflects the magnitude of the change in the value of the variables. Another common sign is "sigma", which performs the function of the sign of the sum.
Moreover, almost all Greek letters are somehow used in mathematics. However, these mathematical signs and symbols and their meaning are known only to people engaged in science professionally. In everyday life and everyday life, this knowledge is not required for a person.
Signs of logic
Oddly enough, many intuitive characters were invented recently.
In particular, the horizontal arrow replacing the word "therefore" was proposed only in 1922 by David Hilbert. The quantifiers of existence and universality, that is, signs read as: "exists ..." and "for anyone ...", were introduced in 1897 and 1935, respectively.
Symbols from the field of set theory were invented in 1888-1889. And the crossed out circle, which is known to any high school student today as a sign of an empty set, appeared in 1939.
Thus, signs for such difficult concepts as an integral or a logarithm were invented centuries earlier than some intuitive symbols that are easily perceived and acquired even without preliminary preparation.
Math symbols in English
Due to the fact that a significant part of the concepts was described in scientific works in Latin, a number of names of mathematical signs and symbols in English and Russian are the same. For example: Plus (“plus”), Integral (“integral”), Delta function (“delta function”), Perpendicular (“perpendicular”), Parallel (“parallel”), Null (“zero”).
Some concepts in two languages ​​are called differently: for example, division is Division, multiplication is Multiplication. In rare cases, the English name for a mathematical sign gets some distribution in the Russian language: for example, a slash in recent years has often been called a “slash” (English Slash).
symbol table
The easiest and most convenient way to familiarize yourself with the list of mathematical signs is to look at a special table that contains the signs of operations, symbols of mathematical logic, set theory, geometry, combinatorics, mathematical analysis, linear algebra. This table shows the basic mathematical signs in English.
Math characters in a text editor
When performing various kinds of work, it is often required to use formulas that use characters that are absent on the computer keyboard.
Like graphic elements from almost any field of knowledge, mathematical signs and symbols in Word can be found in the Insert tab. In versions of the 2003 or 2007 program, there is the “Insert Symbol” option: when you click on the button on the right side of the panel, the user will see a table in which all the necessary mathematical characters, Greek lowercase and uppercase letters, various types of brackets and many more are presented.
In versions of the program released after 2010, a more convenient option is developed. When you click on the "Formula" button, you go to the formula designer, where you use fractions, enter data under the root, change the register (to indicate the degrees or serial numbers of variables). All characters from the table above can be found here.
Is it worth learning math symbols
The mathematical notation system is an artificial language that only simplifies the recording process, but cannot bring an understanding of the subject to an outside observer. Thus, memorization of signs without studying the terms, rules, logical connections between concepts will not lead to the mastery of this area of ​​knowledge.
The human brain easily assimilates signs, letters and abbreviations - mathematical notations are remembered by themselves when studying the subject. Understanding the meaning of each specific action creates such strong
associative ties that signs denoting terms, and often formulas associated with them, remain in memory for many years and even decades.
Finally
Since any language, including artificial, is open to changes and additions, the number of mathematical signs and symbols will certainly grow over time. It is possible that some elements will be replaced or adjusted, while others will be standardized in the only possible way, which is relevant, for example, for multiplication or division signs.
The ability to use mathematical symbols at the level of a full school course is practically necessary in the modern world. In the conditions of rapid development of information technologies and science, widespread algorithmization and automation, the possession of the mathematical apparatus should be taken for granted, and the development of mathematical symbols as its integral part.
Since calculations are used in the humanitarian sphere, and in economics, and in the natural sciences, and, of course, in the field of engineering and high technology, an understanding of mathematical concepts and knowledge of symbols will become useful for any specialist.