# If Maths Is a Language, Can It Evolve? I Would Like To Think So

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I would like to think of maths as a language, like so many other people.

Unlike the more "natural" or "human" languages, maths does not evolve. It accumulates, and its core stays the same. When languages evolve, they drop unnecessary expressions and become more "efficient". In other words, languages remove redundancies; they evolve towards not having more than one way to say anything.

In a sense, in an advanced language, there should not be more than one way to say the exact same thing. The equivalent of having more than one way to express the same sentiment in mathematics is an equivalence relation.

Therefore, is languages become more efficient by removing redundancies, and maths could be considered to be a language, are equivalence relations in maths inefficiencies caused by the notation? We could possibly redesign maths to lose some of the core equivalence relations, this could make things simpler to develop.

Here is what I mean: $| a - b |$ and $| b - a |$ are equivalent. Why then do we have two different ways of expressing the same thing? Could we have a more efficient way of expressing this? In others word, could we have a notation where the reflexive property is immediately apparent?

And here is a more subtle equivalence relation: Given $y=y(t)$, $\frac{dy}{dx}=y$ is the same as $y=ke^t$. Could we have a new form of notation where such equivalence relations are immediately noticeable? And would that notation help us progress? I would like to think that we can, and that it would help us progress.

In fact, I would like to think that more than one such notation is possible, and that the same mathematical constructs could be delineated by several notation, each notation making different theories and lemmas easy to notice. I would like to see a future of maths where maths is not a language, but several, and each serving different purposes.

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