Mathematics, the language of all things
The term "mathematics" is derived, of course, from the Greek mathēmatikē (μαθηματικά), and this word, in turn, is derived from the verb manthanein which means to learn.
Mathematics: The Science Toolbox
The mathematical is a tool built on the basis of a set of formal languages, and used to raise, the less ambiguous as possible, problems and solutions in various fields of human endeavor.
What is a Formal Language?
Well, to understand what a Formal Language is, let's first define Natural Language . It is known as Natural Language to the languages that have developed, spontaneously, in groups of humans throughout the planet, with the purpose of communicating with each other. English, Spanish, French, etc., are natural languages and their expressions can be interpreted in different ways, they take a different meaning, depending on the context in which they are said (They are Context dependent).
A formal language is a language —symbols and rules—formally specified, to be used in contexts and for very specific communicative purposes [2]. In this category fall, for example, computer programming languages and mathematics.
And why is that good for math?
The main advantage that the grammar and syntax of mathematics is based on formal languages is that its vocabulary does not change regardless of the language —or natural language— in which the mathematical solutions are presented. The meaning of what is conveyed will be the same regardless of the context.
A relatively young language
Until the 1920s, mathematics was supposed to have its birth among the ancient Greeks, but as experts have managed to decipher ancient documents, we have located mathematical developments dating back more than three millennia before our era. Mathematics, at that time, was used in elementary practices of counting, measuring and describing the shapes of objects.
However, Modern Mathematics, what we know today, with all the symbols and formalities of our days, was consolidated a little more than 300 years ago.
Historians tell us that in many cultures, influenced by the needs of practical activities, as commerce and agriculture, mathematics has developed far beyond basic counting. In complex societies this growth has been greater and they have had the opportunity to take advantage of the achievements of previous mathematicians.
Although five thousand years of mathematics seems like an eternity, most of the powerful abstract mathematical theories in use today originated in the 19th century [1].
But is mathematics a language to understand all things?
Mathematics is an indispensable complement to the physical sciences and technology, and in more recent times it has assumed a similar role in the quantitative aspects of the life sciences.
Mathematics are tools to understand things and facilitate the transfer of knowledge to other humans, and why not? to other non-humans - whether they are animals from this planet or beings from another galaxy.
Most of our science and technology would have been literally unthinkable without mathematics
The basis of the development of today's civilization
The language of mathematics has changed the way the world thinks — and you don't have to be an engineer to understand this statement. Most of our science and technology would have been literally unthinkable without math.
Scientists and engineers consider mathematics the tree of knowledge: formulas, theorems and results hang like ripe fruits, with which the scientists who pass, nourish their theories. Mathematicians, on the other hand, view their field as a growing rainforest, nurtured and shaped by the forces of human civilization, with a rich and ever-changing variety of intellectual flora and fauna.
Both views are the product of the perception that one has of the language of mathematics, as a rugged and rough, abstract terrain that separates the mathematical rainforest from the domain of ordinary human activity.
Computers and mathematics
This dense jungle of mathematics has been nurtured for millennia by practical application challenges, but it is in recent years that computers amplify the impact of those applications. Together, computation and mathematical applications have spread, with the interaction of humans from all over the planet speaking the same " Formal Language " forever changing, and for the better, the morphology of mathematics.
The existence of computers has been made possible by the application of theories of mathematicians such as Turing , Cantor , Boole and Von Neumann , whose works were criticized and branded as useless abstractions of irrelevant practical application [3]. However, today computers are to mathematics what telescopes and microscopes are to science.
References
[1] Mathematical Sciences: A Unifying and Dynamic Resource (National Academy of Sciences, Washington, DC, 1986).
[2] Alexandru Mateescu and Arto Salomaa, "Preface" in Vol.1, pp. v–viii, and "Formal Languages: An Introduction and a Synopsis", Chapter 1 in Vol. 1, pp.1–39
[3] G. H. Hardy, A Mathematician's Apology (Cambridge Univ. Press, Cambridge, 1940).