"We should not be surprised to find that mathematics must be considered a language. By definition, whatever has symbols and propositions is called a language, a form of representation for this something going-on which we call the world and which is admittedly not words. Several interesting statements can be made about mathematics considered as a language. First of all, mathematics appears as a form of human behavior, as genuine a human activity as eating or walking, a function in which the human nervous system plays a very serious part. Second, from an empirical point of view a curious question arises: why, of all forms of human behavior, has mathematizing proved to be at each historical period the most excellent human activity, producing results of such enormous importance and unexpected validity as not to be comparable with any other musings of man?"
Alfred Korzybski, Polish-American philosopher, scientist, engineer, mathematician, linguist, logician, author of Science & Sanity: An Introduction to Non-Aristotelian Systems and General Semantics, and is remembered most for developing the theory of general semantics (1879-1950).
Also consider The Lousy Linguist’s Why Linguists Should Study Maths.
YES! ETERNALLY YES! Math is a language. I wish it were taught that way, with more theory and application so that younger students could see the beauty in it and the purpose. Imagine how boring English classes would be (Sorry for the English language centric POV, feel free to insert any other language) if you only learned grammar and a small amount of vocabulary. You were never given a story to read, though you maybe were hurriedly told that they existed and if you learned the rules of grammar perfectly you might be able to read one some day.
Because that is how math is taught most of the time.
Even if math isn’t applied—it’s still expressing an idea. It’s way more than just numbers. The Greeks didn’t really use numbers, at least not the way we do. Open up a copy of Euclid’s Elements. It’s propositions written out with ratio and magnitude. They are logic problems that also teach you the rules of Euclidean geometry. You might be sitting there wondering why anyone would bother learning Euclidean Geometry as written by Euclid at this point? Well. If you want to study Newton’s Principia—you need to be grounded in Euclid and Apollonius’s Conic Sections. Newton relied heavily on both to construct his proofs. The whole thing is written geometrically, even though it introduces the principles of The Calculus. (There is a reason we use Leibnizian notation and not Newtonian. Newton’s is impossible to use in any sort of useful way. It’s good if you want to write incredibly cryptic propositions that three other people can comprehend.)
In the Western world—algebra didn’t come in to use until Descartes was like, “Huh. If I put this geometry on a graph with numbers I can do things with it.” (He went to tutor the Queen of Sweden in math to avoid joining the army. He died of a lung infection in her drafty castle. So if you loathe algebra there is some satisfaction for you.)
If we were taught geometry and logic first, then algebra and calculus—with explanations of why these branches of math were needed, how they grew and what people wanted to do with them? I think math would make more sense to people and would be more interesting.
Do you know why they tried to find Calculus for so many thousands of years? (Archimedes tried and got sort of there, but not really.)
Imagine a line. Square it. When you square a line you literally get a square. Imagine a circle. Square it. Well, you can’t using simple geometry, or even complicated geometry. Algebra won’t do it either. Calculus does. It finds the area under a curve. Obviously the applications of Calculus extend way far beyond this, but that’s what the original search was driven by. Squaring the circle. It was such a Holy Grail kind of quest that Dante uses it as an analogy at the end of The Paradiso for seeing and becoming one with God in Heaven.
I just realized I can’t “read more” cut this. I am sorry if your eyes are glazing over. But I love math. I love it so much.
(Source: mymindtank, via imaginarycircus)