DiBeos

Here’s a classic question that you probably heard of before. It’s simple, but we will look at it from a completely different perspective that will show whether you really know how to think about mathematics:

What is 1 + 2 + 3 + … + 200 ?

Now, stop right there. How long do you think you would take to calculate the answer in your head? A variation of this question, which was finding the sum of the first 100 positive integers, was first asked to the young Friedrich Gauss when he was a schoolboy. His teacher was hoping it might occupy him for a nice half an hour, but unfortunately for him, Gauss managed to calculate the answer in seconds in his head.

Of course, we have no idea if this story actually happened to Gauss, but here’s the important thing: I don’t know how long it took you to find the answer, or if you even calculated it at all, but there’s a famous “trick” for finding the solution.

This is a great question, but there’s one danger in the way it’s usually taught. It can make mathematics look like nothing but a collection of tricks, as though the difference between understanding and not understanding something, is whether someone happened to show you the clever shortcut or the right method to solve stuff. But if you didn’t know this trick, how would you find the answer?

In mathematics, relying on tricks, or in more advanced mathematics, relying on following logical steps and methods, but not fully understanding why exactly you’re using them, is going to get you to a situation where it’s a matter of time before you get stuck.

Find out how to think like Gauss

If you’re serious about learning and expanding your knowledge, using an intuitive approach, check out our catalogue of PDFs. Each of them comes with a YouTube video, and they are built on intuition, concrete examples, rigorous explanations, and (only then) exercises with detailed solutions.