7 junio, 2024

Mathematical language: what it is, origin, characteristics, elements, examples

What is mathematical language?

He Mathematical Language It is the set of symbols through which mathematical relations and operations are expressed. Some examples of these symbols are x (multiplication), + (addition), (subtraction), (less than or equal to), (square root).

Mathematical relationships are expressed through equations, which are like short sentences in mathematical language. For example: X + 7 = 10where X does not symbolize multiplication, but represents a variable.

Mathematical language is distinguished from language in words by being strictly objective. Each mathematical symbol represents a concrete object, such as a number or a relation, without the possibility of its being interpreted in different ways.

Mathematical language has applications in virtually all sciences, including biology and chemistry. But it is of fundamental importance in engineering, astronomy, physics and computing.

Origin of mathematical language

The mathematical language was born to satisfy the need to count, measure and record business operations.

In ancient Mesopotamia, small clay objects of different shapes were used to record amounts of grain and hours of work. The cone represented a small measure, while the sphere and the disk symbolized a regular and large measure, respectively.

Sumerian tables

Around 2700 BC, the Sumerian civilization used clay tablets to record simple mathematical calculations carved in cuneiform. These tables were not only used for accounting, but also for teaching mathematics.

Greek antiquity

The mathematical language experienced its first great development thanks to the geometers of ancient Greece. Among the Greeks, the study of mathematics did not respond to commercial needs, but was cultivated for the sheer pleasure of learning.

This led them to be interested in geometry rather than arithmetic. In this field they made fundamental contributions, especially Thales and Pythagoras, who formulated two of the first theorems of mathematical language, both related to triangles.

That of Pythagoras demonstrates the relationship between the longest side (hypotenuse) and the equivalent sides (legs) of a right triangle.

That of Thales establishes a relationship between a triangle and the lines that cut parallel to any of its sides.

Mathematical language features

use symbols

The mathematical language does not use words, but symbols, that is, graphic marks that correspond to concrete concepts. For example, the symbol ∏ corresponds to a specific number: 3.1416.

Read from left to right and top to bottom

Mathematical symbols are read from left to right, like language with words, but it is also read vertically. This is the case with fractions, such as ⅗, ⅕, ⅓ or ⅘.

There are also numerous mathematical formulas expressed, so to speak, on two levels, such as the Taylor function: .e^x=1+x/1!+x^2/2!+x^3/3!+ ⋯,-∞

is objective

Words have meaning and connotation, so they can be interpreted in different ways and take thought along different paths.

On the contrary, the symbols of mathematical language are objective, that is, they refer to a concrete and precise meaning, which can be a number or a formula, with no possibility of its being interpreted in another way.

it’s formal

Mathematical language expresses universal relationships and measurements in the abstract, without referring to any concrete reality.

For example, the Pythagorean theorem, which establishes a constant relationship in right triangles, can be applied to any object of material reality that has this shape, but before that it exists as such, that is, as a formula or equation that expresses a proportion in mathematical language.

It has been developed over millennia

The language of mathematics has become increasingly broad and complex over the centuries.

Some important milestones in its development are Euclidean geometry (300 BC), the invention of algebra by the Persian mathematician Muhammad Al-Khwarizmi (750) and the adoption in Europe of the Arabic numeral system (approximately 1100).

Elements of mathematical language

Mathematical language is made up of three types of meaningful units: symbols, equations, and graphics.


They are like the letters of the mathematical alphabet, with the difference that they do not represent sounds, but concepts, operations, variables or constant relationships. Examples of symbols are ^ (extension), √ (square root), or ∞ (infinity).


They are like sentences in mathematical language, only instead of being made up of subjects and actions they are based on equivalence relations indicated by the symbol = (equals).

An example of an equation is the Pythagorean theorem: a2 + b2 = c2.


Especially in the case of statistics and physics, some mathematical calculations can be represented through graphs, such as the Gaussian curve or bell. Charts help to recognize patterns or trends in results.

applications of mathematical language

Mathematics is the mother science: practically all the other sciences use it, to a greater or lesser extent. Even biology and chemistry resort to it in specific cases.

In the same way, we can say that mathematical language is the fundamental language of all science, and its applications are numerous:

– In Astronomy: to measure the intensity of the brightness and the distance that separates us from the stars, to predict the trajectory of comets and asteroids.

– In Engineering: to know how aerodynamic a design is, to determine how much force is needed to move a vehicle, be it a car, a plane or a rocket.

– In Statistics: to determine the probability that an event will be repeated, or to identify recurring patterns in a large mass of data.

– In Computer Science: to express algorithms, which are mathematical formulas that tell computing devices how to respond in various situations.

– In chemistry: to calculate the proportions of the chemical substances that make up a solution.

– In medicine: for the design and manufacture of complex medical equipment, such as MRI equipment.

Examples of mathematical language

– 1/3 + 2/3 = 1

– 8 x 6 = 48

– 17 + 5 – 8 = 14

– 10/5 = 2

– √4 = 2

– 0 + 4 = 4

– 3 x 9 = 27

– 3 + 7 – 2 = 8

– 18 – 8 = 8

– 2/7 + 4/8 = 11/14 = 0.78571


(2010). Mathematics. Britannica Student Encyclopedia. Vol 8.
(2016). Gaussian Bell Method in the Master MBA. Taken from master-valencia.com.
Folkerts, M., Fraser, Craig G., Berggren, John L., Gray, Jeremy John, & Knorr, Wilbur R. (2020). mathematics. Encyclopedia Britannica. Taken from britannica.com.
Hernandez Malacara, Z. (2019). Mathematics: a language to describe nature. Intertexts, Year 10, No. 30.
Serrano Gomez, W. (2005). What constitutes natural and mathematical languages? sapiens. Vol. 6, No. 1.

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