We explain what mathematical thinking is and what its characteristics are. Also, its history and importance for science.
What is mathematical thinking?
Mathematical thinking or mathematical reasoning is a form of reasoning capable of carrying out logical and abstract operations through the use of a formal language, which in this case is mathematics.
Mathematics (word from the Greek word μαθηματικά“knowledge”) can be defined as a formal system of logical reasoning, which studies the properties and relationships between imaginary entities such as numbers, geometric figures or relational symbols.
mathematical thinking It is governed by a set of objective but abstract laws that is, they do not depend on nature, nor on the subjectivity of the person who reasons, but on the system of signs and relationships that make up mathematics. It is an exact mode of reasoning which is not open to interpretation. It constitutes one of humanity's most complex and oldest models of representing reality, surpassed only by verbal language.
The famous French philosopher René Descartes defined mathematics as “the science of order and measurement,” while Galileo Galilei understood it as “the language of nature.” Entire sciences have emerged from mathematics, such as physics, which is nothing more than the application of mathematical thinking to the observable forces of the real world, or disciplines of enormous scientific utility such as statistics, logic, etc.
History of mathematical thought
Mathematical thinking is really ancient in the history of humanity. In the earliest prehistory, judging by evidence found in South African sites, 70,000 years ago the first forms of mathematical thinking existed .
Thanks to it, early 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 kind of menstrual record that made 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. C. But just between 3,000 to 2,600 BC. C. the first known mathematics appeared in northern India and Pakistan, with the emergence of the Indus Valley Culture.
There, its 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 BC. C., the Assyro-Babylonian Mesopotamian cultures developed their own system, which, together with the Arabs and the Egyptians, gave birth to the Hellenistic ones.
In that period, Greek antiquity produced many of the mathematical reasonings 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.
References
- “Mathematical reasoning” on Wikipedia.
- “Mathematical thinking: 10 strategies to stimulate its development” in Educrea (Chile).
- “Development of Mathematical Thinking” (video) at Universidad Rey Juan Carlos (Spain).
- “Mathematical thinking” at Jorge Tadeo Lozano University of Bogotá (Colombia).
- “Mathematical thinking and processes” at EAFIT University (Colombia).
