Monday, December 24, 2007

Invented or discovered?

Is math invented or discovered? It is a very ancient question. It dates back to the ancient Greek mathematicians. They believed that everything is a number - and they took this philosophy very serious. In fact, according to a legend the man who discovered that is irrational payed for this with his life. He proved that while sailing in the sea with his friends, and when he told them, they threw him out of the boat. For them such a proof was totally unacceptable.

In our days this sound weird. Killing for money and power is more or less common. But killing because of a mathematical question? This is not something you hear all the time.
But anyway, back to the question. If math is invented what does it mean? Does it mean that it is a mere game of thought? But if so why there are wrong answers? And if it is only a game of thought, then why it actually describes something real? Take E8 for example. Some people believe that it describes the shape of our universe and also all the particles are described in this symmetry.
The math is build on a logical basis. In fact, it is an old joke that math professors are the only one who can say that what they teach is always true and correct and it will stay so. But it does not explain why so often pure mathematics is found to either be useful in natural sciences or to describe something that exists in the real world.

If math is discovered, what is this strange "universe" that we are discovering then? The term Mathiverse is sometimes used for this. Also in some mathematical jokes we are told about things like "function city", "fractal forest" and so on. But are they real? Well the functions are real, but I really doubt that they have a city to live in. I cannot prove this of course, so all I can do is to say what I think about it, and it is fine if you think differently.

Personally, I believe that math is discovered. But I don't believe that we can talk about mathematical "entities" as if they were humans - they don't have cities, and they don't drink tea. So for me the term Mathiverse is just a reference to a very real set of objects. They are real because we can use them, and they are important because a lot of what we have depends on how well we understand them. Even the fact that you are reading it now is only possible because someone understood math well enough to build this monitor.

By the way the in the first paragraph is brought to you by a script that integrates latex to blogger (unfortunately there is no official way to type formulas here). You can get it here, and you can find its author here.

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