Are mathematicians inventing mathematics, or are we simply discovering the workings of the universe?
The mathematical language, just like any other language, has been invented in order to express our thoughts in a universal way, thus facilitating communication between scientists. We have invented concepts – numbers, shapes, sets, symbols, and so on – by abstracting them from the world around us. Additionally, axioms of mathematics (statements that are regarded as being self-evidently true) have been established and in doing so we have been able to discover the complex connections among the concepts that we’ve invented, hence creating the theorems of mathematics.
Mathematics has the powerful ability to describe, explain and predict phenomena in the physical world. These phenomena have always been present – they have not been invented. For example, a right hand triangle has always had sides that obey the equation:
The mathematician, Pythagoras merely discovered this fact through observation and calculations, and formulated an equation to express this relationship using accepted mathematical language.
Many of those who argue that mathematics is invented suggest that mathematics is a human construct and without us there would be no mathematics; the reason that mathematics is suited to describing the physical world is because we’ve invented it to do just that. In contrast, the structures of mathematics are intrinsic to nature, and if we did disappear, mathematical truths would still hold.
Although this question is rather philosophical, it has always fascinated me. To me, Mathematics is a mixture of both inventions and discoveries; in order to make discoveries to understand the way our physical world works, we have to invent mathematical language that describes these phenomena.
Let me know what you think! M x