How to use an algorithm │ The History of Mathematics with Luc de Brabandère

Algorithms are nothing new, they've been making your life easier for centuries.

Subscribe now to ‘The History of Maths’ on the YouTube channel ‘What makes it tick?’

An algorithm is a method. The Greek 'meta hodos', 'hodos' means 'the way'. An algorithm is a way to do something. If you want to bake a cake, what do you do? You follow a series of steps. You take eggs and flour and then you cook, and you mix etc. And at the end you have the cake. This is an algorithm, of course one of the simplest ones, but that's what we do all the time.

Imagine, I want to know the day of the week I was born. I was born 27 May 48. Which day of the week was it? How should I do it? I have a method. OK, I go, it's 71 years, but some years are leap years, and finally I got the answer. I was born on Thursday. It's not that difficult.

But if you compare with the cake, these paths have different alternatives.

Another example from logic. Imagine a room with two doors, two switches and only one light bulb. You have to allow each person coming this side, and coming this side, to switch it on. So, you need a piece of electronics. If it's on, the switch will be off etc. Not too difficult. But this algorithm has nothing to do with mathematics. It's logic.

My next example will show a new element: efficiency. Because in a simple example, you have just one way to get the answer. But imagine now I have a stack of 1000 cards with names. And I'm asked to sort the cards by alphabetical order. You immediately realise some methods are more efficient than others. Probably the least efficient way to do it is to take the first one, OK, and then the second one, OK, and I do the third one, and on and on and on 1000 times. That's not efficient.

Probably it's much more efficient first to sort only by the first letter, all As, all Bs, all Cs,and then you sort it here and there and then you put it together. Definitely, in this example, you have an efficient method, an efficient algorithm. That's the next step in thinking about algorithms.

But so far, all the examples I gave you are sure to get the answer I was born on Thursday and the cards are sorted by alphabetical order. There is a 100% guarantee of reaching the result.

Of course, today the algorithms we're talking about are not 100% guaranteed, because they are so sophisticated.

If you take for example face recognition or self-driving cars and all those kinds of algorithms, they are not pure mathematics. They include another way to think about data, and it is called a model.

Imagine I want to make a weather forecast, so next Sunday it’s gonna be sunshine. This is not the outcome of a formula, it's the outcome of a given model. Today's algorithms we're talking about with the Internet are more of this nature.

In the past, algorithms were a bit like machines, at each step you knew exactly how the algorithm was working, and you can nearly follow the machine, following the algorithm.

Today, we don't know exactly how those complex algorithms are working.

I think today an algorithm is a bit like a pill, an aspirin, for example. If you swallow a pill, an aspirin, you don't know exactly which molecule goes where into the body, with which kind of impact. You just feel better because you took this aspirin.

We are a bit in the same situation. The algorithms we use today, we don't know exactly how they work, we don't know exactly which path is followed by the machine, but in the end, just like with a pill, you realise there is a result and sometimes the result is tremendous.

Next time, we'll have a look at how the indivisibility of prime numbers forms the basis of encryption technology.

Subscribe now to follow the series ‘The History of Maths’ on the YouTube channel ‘What makes it tick?’