Is Maths Invented or Discovered

The question over whether or not mathematics was a concept invented, or discovered, has been one long debated throughout history. On one hand, it seems almost intuitive to suppose that mathematics is discovered: after all, numbers exist regardless of whether or not an intelligent enough species were capable of quantifying, expressing and playing with these intrinsically existent numbers. On the other hand, when studying the intricacies of mathematics, it seems almost as if that it is simply a game, following rules; and when necessary, can be utilised in such a way that it may be able to reflect some aspects of the real world. Yet taking a more holistic point of view, the theory that mathematics is invented and follows basic rules, is, to some extent, fallible. This is because although to some it may appear that some of the rules of mathematics (such as square roots, squares, BEDMAS, exponents) are simply true because of definition, they are in fact true because in it’s most innate beginning, we built these ‘rules’ upon the very rational and real properties and functions of the ‘discovered’ numbers. The concepts of ‘squaring a number’ or ‘multiplying before adding’ often seem abstract; yet when you actually examine these concepts, it becomes clear that this process of simplification (that squaring a number is just that number times itself; or multiplying two numbers is just the first number adding itself the second number of times) is the reason behind why mathematics is endowed with this stigma of being abstract. Certainly there exists many abstract components of maths, such as negative numbers and imaginary numbers; and there really is no counterargument to how, or perhaps why, these concepts exist concretely in reality. That doesn’t, however, therefore immediately justify the argument that maths is simply a game, with rules. To me, this rather reductive perspective of looking at it completely disregards the very concrete foundations of mathematics; almost ignoring the fact that maths has played such an important role in representing reality. YET AGAIN, fundamentally, everything mathematics has built to represent and accurately reflect is because we humans have quantified and brought into existence quantifiable units, numbers, and expressions for such concepts. Mathematics and numbers can be used to accurately express the speed of light, speed of cars, lengths of polygons, angles of a shapes, etc; but the only reason they are able to do this with such eerie real life accuracy is because we’ve created these¬†real life concepts,¬†founded upon mathematical foundations. Speed isn’t an inherent concept. It’s something us as humans have artificially created; defined as distance (another artificial creation) over time (controversially another creation). Because speed and similarly, other concepts such as speed, are founded upon mathematical reasoning (that speed will always equal to the measurable distance of something divided by the time it takes for an object to cross this distance), it would thus be illogical and irrational to argue that mathematics works independently of reality, if this reality is indeed founded upon mathematics. This really does not make a lot of sense; please excuse my poor train of thought; this was a very stream-of-consciousness piece; and i keep getting confused with what i’m trying to say; and i can’t be bothered to properly organise my thoughts so sorry

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