Why+study+Maths?

Neil Marshall Our Deputy Headmaster and Head of Mathematics Ponders….. Imagine a dream where there are many pillars—some low, some high—all of which are too high to step up to, and all of which are wide enough to stand upon.Now imagine someone dreaming this dream. That person looks at one of the pillars and asks, "Has anyone been on top of that pillar?" Then one of the Inhabitants of his dream answers, "No, nobody has been on top of that pillar." Then the person looks at another of the pillars, which has a set of stairs next to it, and asks, "Has anyone been on top of that pillar over there?". The answer is, "Yes, some-one has, and has left behind a set of steps. You may take those steps and climb up on top of the pillar yourself, if you wish."And this person continues, and sees more pillars. Some of them stand alone, too high to step up to, and nobody has been to those. Others have had someone on top, and there is always a set of steps which the person left behind, by which he may climb up personally. And the steps go every which way—some go straight up, some go one way and then another, some seem to almost go sideways. Some are very strange. Some pillars have more than one set of steps. But all of them lead up to the top of the pillar.The person dreaming may well have the impression that one gets atop a pillar by laying down one step, then another, then another, until one has assembled steps that reach to the top of the pillar. And, indeed, it is possible to climb the steps up to the pillars that others have gone to first.But that impression is wrong.And the person sees what really happens when the guide becomes very excited and says, "Look over there! There is a great athlete who is going to attempt a pillar that nobody has ever been atop!"And the athlete runs, and jumps, and sails through the air, and lands on top of the pillar.And when the athlete lands, there appears a set of stairs around the pillar. The athlete climbs up and down the stairs a few times to tidy them up for other people, but the stairs were produced, not by laying down slabs of stone one atop another, but by jumping.Then the guide explained to the dreamer that the athlete had learned to jump not only by looking at the steps that others had left, but by jumping to other pillars that already had steps, instead of using the steps.Then the dreamer woke up.What does the story mean?The pillars are mathematical facts, some proven and some unproven.The pillars that stand alone are mathematical facts that nobody has proven.The pillars that stand with steps leading up to them are mathematical facts that have been proven.The steps are the steps of proofs, the little assertions. As some of the steps are bizarre, so are some proofs. As some pillars have more than one path of steps, so some facts have more than one known proof.The leap is a flash of intuition, by which the mathematician knows which of many steps will take him where he wants to go.As the steps appeared when the leap was made, so the proof appears when the flash of intuition comes. The athlete then tidied up the steps, as the mathematician writes down and clarifies the proof, but the proof comes from jumping, not from building one step on another.The athlete was the mathematician. Finally, the athlete became an athlete not only by climbing up and down existing steps, but also by jumping up to pillars that already had steps—one becomes skilled at making intuitive leaps, not only by learning existing proofs, but also by solving already proven problems as if there were no proof to read.