I've read arguments and statements in internet arguing about Mathematics being a science or a language. To me, certain branches of Mathematics fit more with the definition of language and others with the definition of language. For example, equations are part of the branch Algebra, if you write the equation = F = m • a , that's a representation of a relation in Physics and it's a good representation of reality for low speeds, but if you write F = m • a^2 that has no connection with reality at all, so here the definition of Mathematics as a language makes more sense to me. You can use that language to write relations which are connected with reality or not, so the equations (language) themselves couldnt be considered science . An argument I've seen in favor of Mathematics being a language and not a science it is it doesnt rely in empirical evidence, here that argument seems to fit the situation.

However, if you go to the branch of Mathematics Geometry for example, there are properties of geometric figures which are true 100% of the times, and you can test them empirically. This makes Mathematics looks more like a science and it doesnt comply with the argument that Mathematics doesnt rely in empirical evidence.

So seeing these things, considering the different branches of Mathematics seems to be so different not only superficially, but in the most deep of its nature, it made me wonder if all branches of Mathematics were always considered to be part of the same discipline "Mathematics", or were there a time where different branches were seen as different sciences or disciplines.

Were all the branches of Mathematics always considered part of a single discipline "Mathematics"?

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    $\begingroup$ In my opinion, you are completely correct in your inferences, although you could already get people to argue with you about it. :) Indeed, "mathematics" was not considered to be a single, monolithic thing historically, and really isn't nowadays, either. In history, the distinction between "geometry" (with Euclidean-style arguments) and "calculus" (with seemingly less-justified means of deduction), was huge. I will tell what I know, a bit later, if no one more knowledgeable responds after a bit. $\endgroup$ Nov 20 at 21:45
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    $\begingroup$ "there are properties of geometric figures which are true 100% of the times" So they thought until hyperbolic geometry arrived $\endgroup$ Nov 21 at 1:13
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    $\begingroup$ Logic is still considered by many to be not completeuly a part of math. $\endgroup$
    – markvs
    Nov 21 at 7:08

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