On Mathematics

by Carlos Pedro Gonçalves


In formulating the question “what is mathematics?” it is important to notice that the intellectual matrix and structure that underlies our concept of mathematics is Greek. This should not be confused with a statement that mathematical activity started in Greece, it does mean, however, that our usage of the term mathematics and our conception of what it means to “do mathematics” has a Greek root.

Thus, in trying to answer the question “what is mathematics?” we should, perhaps, first look at the Greek root of the word mathematics, which is mathematike which comes from manthein (to learn, to study), meaning learning, study, science. It is also important to look at the expression mathematike tekhne, which places mathematical activity as science techne, in Latin being translated to ars mathematica.

As a science techne, the mathematical activity tries to find the quantities, structures and patterns exemplified by the things, and builds an abstraction of these quantities, structures and patterns that allows the study of these quantities, structures and patterns in themselves, in their nature and generative mechanisms.