We explain what mathematical thinking is and what its characteristics are. Also, its history and importance for science.
What is mathematical thinking?
Generally, by mathematical thinking or mathematical reasoning we refer to a form of reasoning capable of carrying out operations of a logical and abstract type through the use of a formal language, which in this case is the math.
Mathematics (a word from the Greek word μαθηματικά, “knowledge”) Can be defined as a formal system of reasoning logical, which studies the properties and relationships between imaginary entities such as numbers, geometric figures or relational symbols.
The famous French philosopher René Descartes defined it as “the science of order and measure”, while Galileo Galilei understood it as “the language of nature”.
Mathematical thinking is governed by a set objective but abstract laws, that is, they do not depend on the nature, nor from the subjectivity of the person who reasons, but from the very system of signs and relationships that makes up mathematics.
It is an exact mode of reasoning, which is not open to interpretation. It constitutes one of the models of representation of the reality more complex and ancient of the humanity, only surpassed by verbal language.
From its bosom they have arisen Sciences whole, like the physical, which is nothing other than the application of mathematical thinking to forces real world observables, or disciplines of enormous scientific utility such as statistics, logic, etc.
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History of mathematical thought
Mathematical thinking is really old in the history of humanity. In the prehistory Earlier, judging by evidence found in South African sites, 70,000 years ago the first forms of mathematical thought existed.
Thanks to him, primitive humans developed simple systems for tracking the number of animals in a herd (none, one, two or many, basically). On the other hand, women kept a sort of menstrual record that traced 28 to 30 marks on a stone or bone.
There is also later evidence of this type of reasoning in the Egyptian civilization of the 5th millennium BC. But only between 3,000 to 2,600 BC. The first known mathematics appeared in northern India and Pakistan, with the emergence of the Indus Valley Culture.
There, his own numerical and metric system was born, prior to the one developed in ancient China during the Shang Dynasty (1600 to 1046 BC), one of the oldest known. Finally, in 539 a. C., the Assyrian-Babylonian Mesopotamian cultures developed their own system, which together with the Arabs and the Egyptians, gave birth to the Hellenistic ones.
In that period, the greek antiquity produced many of the mathematical reasoning that we still use today, the work of great philosophers such as Pythagoras, Thales of Miletus, Eratosthenes or Archimedes of Syracuse.
This knowledge, transmitted to the Roman Empire and from there to the Christian nations and the rest of the West, is the basis of the mathematics we practice today.