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Let's face it, no mathematician asks himself of what use is the discipline he works in every day, it's clear to him. But the thing is, it's not clear for everybody since the layman often asks the mathematician "what use is math ?". In this blog I'll attempt to answer this question with a bit of originality through... physics !
« Philosophy is written in this grand book - I mean the Universe - which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles and other geometrical figures, without which it is humanly impossible to understand a single word of it. » G. Galilei, Il Saggiatore (The Assayer), 1623.
By the term "philosophy" used in this famous quote, we must of course understand "natural philosophy", which we now call "physical sciences". Note also that at the time of Galileo, mathematics were mainly about geometry and its figures. Nowadays, mathematics are also driven by rules about abstract objects depicted by symbols, "characters" of a formal language which is not what Galileo referred to.
A common paraphrase of this quote says that « Nature is a book written in mathematical language ». In my view, this interpretation insinuate a now foolhardy realism. If we were to distort the author's words, I would prefer to think that « Nature is a book that we know how to decipher only through mathematical language ».
This way, the role of mathematics is clear : they are an improvement and an extension of our thinking, and are then at the basis of our understanding of the world.
Of course this point of view is debatable, and I invite you to criticize me !
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