The day is almost over, at least here in Germany, and I didn’t think I would get to flip the page today, but then I saw Garret’s link. Reading the article got me philosophizing on nature, math, the universe and everything.
“[T]he mathematical picture of nature, in the form of an insistent group of equations describing atoms and stars, makes possible such things as electric light, the exploration of space, and the destruction of Hiroshima. This powerfully suggests that mathematics captures truths about the world, and that we would all do well to understand it better therefore.”
The article reminded me of the essay I wrote half a year ago. It was about why mathematics is part of education. (And it reminded me that I have never really gotten around to translating it to English…) One of the points that were important to me is also mentioned in the article:
“The amazing fact is that the physical universe, for all its great diversity, can be described with precision and power in terms of a small number of equations. Galileo himself called mathematics “the language of nature,” and Sir Arthur Eddington remarked that a study of physics gives us a “knowledge of mathematical structures”. Does this mean that reality is fundamentally mathematical? Is mathematics, indeed, reality?”
There are two interesting questions, I think:
- Is mathematics something that is invented or discovered?
- What came first – nature or mathematics?
From the second question you can see that I believe mathematics to be part of nature and therefore to be discovered, not invented.
In some cases, a certain branch of math has been developed to help describe a phenomenon discovered by physicists because they needed a mathematical tool for it in order to describe and understand it better.
But often enough, it is the other way round. Some mathematicians play around with a theory, discover new ways of solving problems – and a few years later, physicists discover something new and find it can be described by the mathematical means that had been “invented” just for fun!
This doesn’t mean, of course, that everything in the world can be put into formulas and equations, but mathematics sure help you to understand many things and lets you see analogies that would be invisble otherwise.