[Mika]

If the math is already done, you don't have to wait for mathematicians to solve certain types of problems in order to progress through those fields. And with sufficient mathematical background, one can go through the implications of an hypothesis much quicker. Hence, mathematical prowess is one of the indicators of how fast one can advance in relevant fields. I didn't mean to imply it was the only one, if that's what you are suggesting.

Thanks for clarification.

As a practical example, the math behind black holes was mostly done by the time physicists proposed their existence.

This is actually not true. Schwarzschild was the first who published solution for Einstein field equations in General Relativity, noting that something particularly interesting would happen if enough mass was concentrated on small enough volume (his choice of metric is simple and quite easy to understand). The solution literally came from the trenches of WWI. But this is not what I would consider Maths. Different metrics and manifolds were analyzed by mathematicians years before Einstein had started to formulate General Relativity. Later on, behavior of charged and rotating black holes have been analyzed, the work required different kinds of metrics to solve the field equations. But this again, isn't maths in the sense I understand maths. Though Einstein was quoted saying something like once mathematicians got their hands on his Theory of Relativity, he hasn't been able to recognise it since...

Also, regarding "theoretical" vs "practical" knowledge, it's kind of pointless to make that distinction. Specially when most research can be dependent on its results to see which is which. As an example, there's the computer science problem of P vs NP. If the answer is P != NP, then the practical application of this doesn't seem to be much (at least compared with the alternative), and it's what most researchers lean towards. However if the answer is P = NP...

My point was that current scientific world seems to concentrate heavily on theoretical side. But it also works the other way: independent observations can themselves lead to new theoretical knowledge. For some reason, good old dumb luck is never mentioned in the books of Physics, even though I suspect that quite a lot of the current technology is actually based on it. The thing is, somebody just noticed something peculiar when something almost normal was supposed to happen and was lucky enough to think that for a couple of minutes longer.

By the way, the mathematical problem you describe sounds like a generalization of an inversion problem. Is that it? If yes, my hutch feeling is that anything including inversion is more complex problem, and for that reason cannot be executed quickly. I have no desire to try proving this, though.

Rest assured, though, if some mathematician proves otherwise, I'll be among the first ones to butcher and apply (with crude simplification and approximations) his carefully thought out clean mental constructs and just barely mention the guy's name in as small font as possible in the References-section, just like generations of Physicists used to do before me.

[Pyro MX]

Should I consider maths as art for a moment. Will I suddenly like it because it's art now? I doubt so. And will people like it more should the subject be presented as such? That remains to be proven. But in my experience, no matter which teacher I had, I failed to like it. As simple as this. And at this point, I think it's invariable to the way it was thought to me. Maths, as is, doesn't seem to be a subject I personally like.

I don't consider maths to be useless, far from it - it's all about how deep you are in the matter and what you learn. I wouldn't mind taking advanced math classes if I knew in what way it is linked the domain in which I study (and I'm strictly talking about math classes here). Up to now, what I've been answered in math classes is "Well, programming and computers is basically maths". And that is just plain blatantly false. It involves maths depending what you're working on, but conceiving software is far more than "just maths". The thing is, I'm not a mathematician, and probably won't be one soon. Don't waste my time showing things I'' forget two weeks after the exams. And the problem is, I may do so while what I saw in classes was indeed important for me to know, but because it was presented in a way that seemed completely pointless to me, I won't have the reflex of correctly studying the matter.

And that may be a problem. Kids are being shown things that may appear pointless to them, and some times, with reason. School is also about doing stuff you won't necessarily like. And everybody should go trough that kind of situation regardless of the subject that is being studied. And in my past professional experience, I had to do stuff I didn't necessarily like. The difference between this and maths, is that when I'm finished doing my math problem, I don't feel satisfaction. The problem was pointless, and the solution was as pointless as the problem.

[Snail]

I suck at Maths but I think it's interesting, but I do get satisfaction when I successfully find an answer to a problem.

[Lucika]

"Suppose I am given the sum and difference of two numbers. How
can I figure out what the numbers are themselves?"

As he mentioned, these are those things that might be able to make math more interesting than it is right now. Sadly, these are only given to those who are already on upper level and finish the regular worksheet in 20 minutes or so.
I know. I am one of them.

Spoiler:

Though the question above is incredibly simple: (sum+difference)/2; (sum-difference)/2

[TESLA]

To be fair,

I do believe with maths, there is an element of natural intelligence to it.
Some people get it, others dont.
Others simply do have an interest in it. They might prefer to study history or music, etc. We all have different tastes and orientations.
But the big influence is the teacher. If the teacher knows his/her stuff & is passionate about his/her job  then kids will enjoy the subject and are more likely to learn from it.

[Lucika]

To be fair,

I do believe with maths, there is an element of natural intelligence to it.
Some people get it, others dont.
Others simply do have an interest in it. They might prefer to study history or music, etc. We all have different tastes and orientations.
But the big influence is the teacher. If the teacher knows his/her stuff & is passionate about his/her job  then kids will enjoy the subject and are more likely to learn from it.

I agree. A horrible teacher was able to present such levels of epic suckage that I seriously disliked my favourite class (history) under her, and in contrast, the presence of a new biology teacher suddenly improved my grades.
The teacher is very important.

[brandx0]

I believe in the simplicity and beauty of math, as shown by this very educational video, it reminds me of being back in high school!

http://www.youtube.com/watch?v=drE5cHe6c3s