For a lot of people, mathematics is just a bunch of formulas. They somehow learnt how to apply a certain rule or theorem, but they have no clue why. This makes mathematics abstract and elusive while it does not have to be puzzling at all if the roots of the mathematical concepts are understood.
The greatest mathematicians had a severe struggle in understanding the world as it is. Difficulties in real life gave them the urge to develop a better understanding of the world through mathematics. Theory to understand the concepts of the world had to be developed. This mathematical foundation with its formulas is used to study physical phenomena in all different kind of fields of research such as astronomy, biology, physics, and chemistry.
One of the greatest mathematicians of all time is Isaac Newton. Newton was interested in the question why the orbits of the planets are ellipses rather than circles. In order to do so, he wanted to understand the relation between an object, the forces acting on the object and the resulting motion. He did not only succeed but also developed the formulas, known as the three universal laws of motion, which are the foundation for classical mechanics and are every day used both in practise as in many research areas.
If Newton was not fascinated by the planets, he might not have developed these laws. The same holds for many other scientists such as Pythagoras, Fibonacci, and Euler. All those people wanted to know more about the world around them and used mathematics to describe this. Understanding where certain formulas stem from helps getting a grasp of mathematical concepts and makes it less abstract. So, the next time when you try to find the roots of a function, remember that Fermat already described minima and maxima in 1629 when he wanted to find the centers of gravity of various plane.
This is a blog I wrote as an assignment for my Masters. I got a lot of comments that I am too philosophical for someone who studies applied mathematics. In stead of being interested in waves which might bring us closer to understanding the origin of the universe, I just had to study water waves because they are 'more real'. I disagree and feel like the combination of good thinking and the skills I learn at the University is a very usefull one.