8.The third crisis of mathematics

One day, the barber in Swill village hung out a piece of signs: "I will cut hair in the village for people who don’t give themselves a haircut, and I only give these people a haircut." Then people in the village asked him, "Who will cut your hair?" The barber t was speechless.



Who can cut my hair?



If he cut his hair himself, he would belong to people who cut hair themselves. However, the sign said that he would not give this kind of person a haircut, so he can't cut hair himself. If another person gave him a haircut, he didn't give himself a haircut. Then the sign clearly said that he would give all the men who didn’t give themselves a haircut. Therefore, he should cut his hair. Thus, in both kinds of situation, what the barber said is self-contradictory.

This is the famous paradox, known as the "Russell paradox". It is raised by the British philosopher Bertrand Russell, who represented a famous paradox of set theory by using an interesting story generally.

In 1874, the German mathematician Cantor founded the set theory. The theory soon penetrated to most of the branches of mathematics, and became the basis of the branches. By the end of the nineteenth century, almost all mathematics are based on the basis of set theory. At this time, some contradictory results of the set theory appeared, particularly in 1902 when Russell proposed the barber story which reflected the paradox. It is very simple, clear, and popular. So, the foundation of mathematics is moved, this is the so-called third "mathematical crisis".

So you can see science is not always right. Many theories which are truth now may be turned out to be wrong someday. It is the pursuit of process that keeps our human beings going. This story also shows us that mathematics is not dull, it can also be interesting, do you think so?