What mathematical theorems are intuitively right, but difficult to prove?

Many mathematical laws have been deeply rooted in people's hearts, such as proving that three things exercise their rights, and those that complement the angle and two straight lines are parallel. These are all from our lives, but it is easy to form a mindset. As my most annoying teacher said, just recite. It's really incomprehensible. Just memorize it. Below we list which forces are intuitively correct, but it is difficult to prove.

Two straight lines are parallel

This theorem was told to us by our primary school teacher. I vaguely remember that he told a joke at that time. What kind of thread do monkeys like least? The answer is parallel lines. Because there was no intersection (banana), I thought it was fun at that time, so I remember it now. I still remember that he said at that time that a scientist spent a long, long line to prove this theorem, and the two lines never crossed. But this theorem is really difficult to prove. Must we continue painting?

Theorem: The number is 1

For any positive integer n, if n is an even number, divide by 2; If n is odd, multiply it by 3 and add1; Repeat the above steps for the obtained number, and finally you will always get 1. It seems obvious that it can be proved by studying elementary algebra and elementary number theory, but countless Daniel mathematicians have stumbled on this 3x+ 1 conjecture.

Many mathematicians are studying this theorem, but in the end no one has worked out why. Moreover, data users began to doubt life, and it seems that this theorem has not been solved until now.

There are many wonderful theorems. I have seen the coloring theorem in some magazines before. You can go and have a look if you are interested.