Can you cross a square? Is someone lying or

not? Discover the strange paradoxes revealed by maths. Subscribe to follow the series, the

history of maths, on our YouTube channel now. Sometimes, when you are a logician or a mathematician,

you face strange problems. Problems you really don’t know how to solve. Those problems

are called paradoxes. Let’s start with logic. If I tell you I am

a liar, and if this is true, I am not a liar. If this is not true, then I am a liar. You cannot

escape the loop. This is called a paradox. In mathematics, you also have paradoxes. A

famous was Zeno. He told his friends it’s impossible to cross a square. It’s impossible

to go from A to B. Yes, he said, because if you want to go from A to B, you first have

to go half way. And then, half way. And then, half way. You never can reach the other end

of the square, because you can go as far as you want, there is still a little distance,

you have to start with half way. That was Zeno’s paradox. And paradoxes in logic were “solved” by Bertrand Russel and the new kind of logic. Paradoxes in mathematics,

at least this one, were solved by, at the same time, Leibniz and Newton with the invention of calculus,

and you will see in the next video how they did it. Let’s have another example of a beautiful paradox in mathematics. Let’s take a right

angle triangle again, A, B, C. I will prove to you that AC=AB + BC. You say “No, it’s not

possible”. Yes, and I will prove it to you. Let’s start with A C. I propose to build this

like a stair, like this, and you replace the straight line by your stair. If you look at

the sum of the horizontal pieces, it’s exactly the distance here (BC). If you look at the

sum of the vertical pieces, it’s exactly the distance here (AB). Now, if you go to a very,

very thin stair, with very limited pieces of steps, you’ll finally have AC=AB + BC. It’s

another paradox and it’s important because mathematicians make progress when they embrace

paradoxes. Next time we will explain how that scourge

of school children, calculus, was invented.

1 st like 1st comment & i rank as no. 1 student who hates MATHS LIKES FU…D MY FRIENDS 😉