Mathematics [Taken from Live Spaces Blog, 05 mayo 2006, 21:54]

I'm supposed to write an essay with the following phrase as main subject: "What is mathematics?".

Mathematics is a subject in school with a bad reputation. Nowadays, kids grow up with the idea that Math is the "hard" class. Many kids don't seem to understand it, many don't see why they should, and by kids it is mostly abhorred. (Some kids who do kind of like Mathematics are coerced into disliking it, as a social adjustment. Kids who like Math and kids who dislike Math are almost never friends). They see it as a meaningless obstacle, as tons of exercises for homework where they must follow the even more meaningless little steps they learned in class, only to get to answers they couldn't care less about.

And they can't care. How could they? What does it matter to them if Mary ended up with 3 or with 5 sheep? It does not matter. Even if it were twelve thousand sheep. It has no relevance WHATSOEVER. However, there's one thing they DO care about. They want to get the answer right. And truly, from a kid's point of view, that's all (s)he wants. Otherwise he/she is thought of as WRONG.

The point that many kids miss is that, true, it DOESN'T matter if Mary got 3, 5, 10, 0, or 40 sheep or goats or dogs or strawberries... or if Joe DID catch up with Jane going at 60 km/h... it DOESN'T MATTER. But when a person grasps the whole ruling concept, and is able to correspond REAL-LIFE quantities to mathematical symbols, and REAL-LIFE events to operators, that person is able to predict REAL-LIFE results, such as going bankrupt or falling down a cliff. And THAT can be useful. Generalization/abstraction. A fundamental concept of Mathematics and Knowledge in general... it uses a single piece of information to generate complete families of concepts. Now if kids could understand THAT before doing the tons of exercises they do... they probably wouldn't even need those. (No, Neo. I'm trying to tell you that when you're ready... you won't have to.)

Mathematics is a powerful tool for many disciplines. Physics, Chemistry, Geography, Astronomy, Engineering, Computer Science, Accounting, Marketing, Economy... I can't think of any discipline unrelated to Mathematics. Even stuff like Poetry and Music have Mathematics embedded in them, since rhythm has already been quantified. Virtually all disciplines include a lil bit of Mathematics as their tool to produce results. Physics needs to model space with numerical coordinates. Chemistry needs to quantify and specify measurements, Geography needs geometry... you get the idea.

The trick Mathematics has to be SO popular is its universality. Mathematics tells us that 5 units added to 6 units will always bear 11 units. Always. It guarantees the truth of a universal prediction. "5 + 6 = 11" is TRUE WHEREVER, WHENEVER, HOWEVER, with WHATEVER units ever occurred. And "(senx)^2 + (cosx)^2 = 1". So disciplines take concepts like this for granted, specify convenient units and fields, and there they go. The tools to get their job done are imported from Mathematics and used as any other tool would be. Mathematics provides the world with standard symbols, standard operations, and standard concepts, over which virtually all sciences are constructed.

Mathematics is the only exact science. All other sciences I know of are not. Physics, probably the oldest natural science, tries to represent the workings of the whole universe. Chemistry deals with a subset of the universe: the classification and behavior of the millions and millions of different types of matter, alone and/or during interaction. Astronomy models the universe outside our Earth. Economy models a very small subset of the universe indeed: the distribution of stuff that human beings value. The list just goes on and on and on and: (http://phrontistery.info/sciences.html) on.

This last site says: 'Mathematics: "Study of magnitude, number, and forms"'. There. How's that? Is that enough? No, because this must be the size of an essay, and besides, I think it's formally and fundamentally wrong. It's probably the best-known definition... its popular definition. Numbers, forms, operations... they don't MAKE UP mathematics... they're the RESULTS of Mathematics!! But that's not all about Mathematics.

Unlike the natural or social sciences, Mathematics does not try to represent reality. That's not its job. I think Mathematics tries to represent Thought. It is an expression of the concepts we generate and process in our minds. Mathematics is not about numbers! Numbers are the symbols which Mathematics created to express the abstract concept of quantity. It's not about circles and polygons either... they're only Mathematics' impression of the simple, perfect concept of space and objects in our mind. Mathematics uses them so much because they are such essential concepts of our thinking. But there are SO MANY OTHER results of Mathematics (which are now also tools): Computation, Functions, Set Theory, Discrete Mathematics, Probability... you can even make more if you want to!

Up to this point, I've talked about what Mathematics does, but never said what it is. That's because I really don't know. If I had to give a definition, I'd say it is any way in which a person expresses any fully understood thought in a fully understandable way. And since nobody fully understands reality, what with all its complexities and chaos and interactions... the attempts to mathematize reality have resulted in the inexact Natural Sciences. And when a person tries to express him/herself, Poetry and Art occur.

These are my arguments and thoughts about what Mathematics is. Any questions?