What's the use of learning about proofs?

"Prove that if all the sides of two triangles are congruent, then the triangles themselves are congruent."

What's the point of an exercise like this? You are asked to painstakingly go through a series of logical steps, only to prove something  that you could easily verify by looking at a few examples. What's more, people have known about congruent triangles for thousands of years, so it's hardly necessary to prove this statement yet again. Why should anyone, even those that don't want to become mathematicians, have to learn about mathematical proof?

Brain training

One reason why proofs are included in your syllabus is that they provide the best possible training in logical thinking. If you try to write down a logical train of thought as concisely as possible, you'll soon find yourself using a form of language that is very nearly mathematical: you'll end up with a sequence of steps and some precise description of how each step relates to the next. Mathematical proofs are examples of the purest form of logical reasoning and they provide the best way to train the logical part of your brain. The skills you learn here go quite a way beyond maths: they'll serve you well whenever you have to solve a problem or analyse a complex situation.

Communicating with machines

If there's one place where the logic of mathematical proof is applied directly to real life, it's in computer science. Any computer program is a closed chain of logical commands, without any gaps or contradictions. In fact, any computer program is based on exactly the same logical rules that are used in mathematical proofs.  If you're thinking of going into a field that involves programming - be it software design, computer game development or the development of the computer chips that control modern cars - you first have to get your head around mathematical logic.

Spotting lies

You'd be surprised at how often politicians or advertisers use flawed logical arguments to make a point. Often this has to do with mixing up cause and effect. An advertiser might say, for example, that 9 out of 10 people eating a certain breakfast cereal are healthier than the average person, and deduce that the cereal makes you healthy. But this deduction is not necessarily correct. It may well be that the people are eating the cereal for the very reason that they are concerned about their health. Eating the cereal is a consequence of them caring about their health and therefore being healthy people, rather than the other way around.

While being fooled into buying a cereal, or a face cream, or any other product might not be the end the world, such logical trickery can have much more serious consequences. Flawed arguments, often involving statistics, have actually landed innocent people in jail. To spot them you need a keen eye for logic and it's in your maths lessons that this eye is being trained.