Is there creativity in Maths? │ The History of Mathematics with Luc de Brabandère

Take a look at some brain teasers to see if you have the right approach to maths.

Subscribe to watch the rest of our series, ‘The History of Maths,’ on the YouTube channel ‘What makes it tick?’

This last video is about creativity and mathematics.

Quite often, people are in an either/or mode: it's mathematics or creativity. Absolutely not. There is a beautiful combination of the two skills. And sometimes if you want to be a good mathematician, you have to be extremely creative. Don't go too fast into the calculation.

Let's take a first example: I have a box here. Imagine I want you to give me the distance between here and here. This means a diagonal that goes through the box. Probably you go: ‘Oh, I know the formula of Pythagoras. I'm going to use it’. And, of course, you get the answer.

But there is a funny way to do that. You take a table and you put the box on the table in the corner. Then you move the box one length. You create here an empty space and you can measure the distance. As you can see, sometimes you can have an answer with a completely different approach, a bit counterintuitive.

Another good example is, imagine a shelf in your library with Encyclopaedia Britannica, 10 volumes. Each volume is 5 cm thick, with 2 x 0.25 cm for the cover. My question is: what's the distance between the first page of volume 1 and the last page of volume 10? If you go too fast, we say, OK, minus 0.25 twice and the answer is 49.5. No, you went too fast.

Take a volume, look: Where is page 1? It's on the right side, not on the left side on the shelf.

So; the correct answer is 40.5 cm. The message is the same: don't go too fast in calculus - look first.

Another beautiful exercise: take Wimbledon - 64 players competing to win the game. The question: How many games, final included? It's not too difficult, it's 32 + 16... and of course you have the answer. But there is a quick way to get the answer: ‘What's the goal of a game?’

To get rid of 1 player. So, if you want a winner, you have to get rid of 63 players. So, it means there are 63 games played. This is extremely rapid even if you have a million players. The answer is 999999 games. This is creativity and mathematics.

One more: let's take those 12 numbers. I want you to select some of them to make a 100 by addition. You simply have to add the numbers. And you may take one number once. There is a way to get it, you try everything. And of course, you get the results.

But again, there is a quick way to get the result, to look at the numbers and to notice there is something strange in those numbers. They are all multiples of 3. But two, only two of them are not multiples of 3, and we were supposed to get 100 and 100 is not a multiple of 3. So, you will need those two numbers that are not multiples of 3. And now I'll let you find the answer.

Watch the full series on the YouTube channel ‘What makes it tick?’