Why bother with the maths?

An absolutely essential part of science is observation. So the theorists give us some idea (pretty good ones most of the time) about what to look for and the rest is about trying to observe those things. Of course, you could stab in the dark for something interesting. I think it's a far better use for time to actually have some idea about what you are looking for. So for this you'll need some sort of theory about roughly where you should be stabbing! But there are fundamental problems to the observation stage.

For starters, our senses are limited. Take studying electromagnetic radiation as an example. We "see" electromagnetic radiation as "light" Our eyes are sensors that pick up radiation in a very narrow range of values. We actually "see" a range outside that which our eyes can detect. This is the heat we feel coming from objects. This is just infrared radiation. We don't see it with our eyes but can sense it. To visualise the full range of electromagnetic radiation, we need machines that convert the stuff we can't directly sense to something we can.

Another problem for observation is that our intuitions are flawed. For example, our intuitive sense of space is in three dimensions. Up/Down, Left/Right, forward/back. However, we experience a 4th dimension, Time. We talk about direction of time by saying "Future and Past". We cannot intuitively sense time in a backward direction because we have no experience of it. Try to imagine 5 or more dimensions I guarantee you will fail. Our brains just cannot do it.

one area where intuition is some help though is in the sense of Beauty. A scientific theory or result is often seen as simple and beautiful. This beauty is often only apparent to those people who understand the universal language of beauty, Mathematics. It does not limit us because it does not rely on our senses or our intuitions. It liberates us from the shackles of human experience and allows us to see nature in all its glory.

But wait! isn't mathematics a human invention which will suffer from all the limitations of human intuition and sense? The answer lies in wether you believe we invented or discovered mathematics. Personally, I believe we are discovering although we have to be careful that our definition of beauty is not based on Human experience alone. Mathematics provides a description of beauty that steps away from what we perceive with our senses. This is what makes it such a valuable tool and why we should bother with Maths.