Studying mathematics (3)

1 Name: Anonymous Scientist : 2008-08-08 09:42 ID:yU4x5T3I

First of all, before I truly delve into my problem, I want to make something very clear. I'm quite geeky. But I'm not a geek. While my mind is more than happy to pursue the complexities of the universe, my heart is quite content just painting and drawing. It's this duality of purpose that has kept me from moving forward, but that's not the reason I'm posting.

It's mathematics.

Like I said, my heart may not be into it, but my mind is. Not only that, but I once made a promise to a friend that I would like to keep. I won't go into details, but let's just say the "queen of sciences" is involved.

Thus, my predicament.

I'm quite good with numbers, don't get me wrong. Pre-calc was easy and until I dropped out, I was doing quite well at Calculus. However, no matter how hard I look, I don't see the purpose of math. Or rather, I don't see why it is studied as a "stand-alone" science. You see, to me, math is more of a "support science". It's there to help the other sciences out, not to be studied for it's own sake. In that sense, it is useless. Obscure beauty that only a rare few can see.

And even fewer understand.

So where am I going with this? I want to study math. Not only that, but eventually, I even want to appreciate it. However, I have no idea how to do that. So, I come to you with a few questions that will hopefully steer me in the right direction:

  1. How did you guys began to appreciate, even enjoy, math? What made it fun for you?
  2. Some of the areas of math that I would like to explore are fractals, cryptography, game theory, econometrics, statistics, actuarial science, number theory, and how mathematical concepts relate to real-world phenomena. Can you suggest other topics that would be of interest to someone like me?
  3. Once you go into the applied fields; statistics, computer science, financial engineering, economics, is it still math, or something else entirely?
  4. Can a purely mathematical background take me to areas such as computer science, meteorology, finance, engineering, operations research, information theory, and such, or would I need to pursue a more "specific" degree in order to truly understand these subjects?

Finally, I have spent some time looking at research papers written by some of the world's top mathematicians. To be perfectly honest, most of them didn't make the slighest bit of sense to me. As I move past Calculus, will this situation change (and perhaps I will even start getting some good research ideas of my own), or it's a case of, if I don't get it now, there is a good chance that I won't get it later?

With this thread, I hope to get more insight into what makes math enjoyable. Answers to my questions, as well as some advice, would be appreciated. Thanks. And sorry for the long post.

2 Name: Anonymous Scientist : 2008-08-08 10:48 ID:+YKjPK2K

The thing that always makes me shit bricks is when underlying mathematical structures turn out to be the same for two areas of investigation that were previously considered unrelated. For example the fact that mathematical proofs are computer programs and information entropy and physical entropy are so closely related as to be almost the same thing. Note also that information theory and probability theory unify perfectly under a bayesian interpretation (see here and here for easy introductions, see also Probability Theory: The Logic of Science) which gives us a rigorously formal definition of 'evidence', and shows us what we're actually doing when we do a statistical test.

I was going to say some stuff about economics and biology, but this post is already quite long so I'll just say that although you might think you understand evolution, if you don't understand the way allele frequencies change across a population through time, then you don't really get evolution. Oh and when I hear political firebrands blathering about the economy when they obviously know nothing about it, I have to lol.

3 Name: Anonymous Scientist : 2008-08-08 13:18 ID:+YKjPK2K

>>2 again

Consider also that you can build logic gates out of pretty much anything (cool video here, adding machine <a href=""here), so you can build turing-complete computers out of anything, and all turing-complete computers are equivalent and that all mathematical operations can be derived from a few simple logical operations.

If it's the case that all physical phenomena can be modelled mathematically, then it implies that the laws of physics are turing-equivalent.
This thread has been closed. You cannot post in this thread any longer.