Nine most wonderful theorems in mathematics: 1 and Bayes theorem.
2. Porter's periodic theorem
3. Closed image theorem
4. Bernstein theorem
5. Fixed point theorem
6. Briansan theorem
7. Brown Theorem
8. Bezu theorem
9. Bossuke-ulam Theorem
Theorem in five interesting mathematical miracles 1: A drunken man can always find his way home, but a drunken bird may never get home.
Suppose there is a horizontal straight line, starting from a certain position, there is a 50% probability of going left 1 m and a 50% probability of going right 1 m. What is the probability that you will eventually return to the starting point if you wander indefinitely like this? The answer is 100%. In the process of one-dimensional random walk, as long as the time is long enough, you can always return to the starting point.
Theorem 2: If you lay a local map on the ground, you can always find a point on the map, and the point on the ground below this point is exactly the position it represents on the map.
In other words, if you draw a map of the whole mall on the floor of the mall, you can always make an accurate "you are here" mark on the map.
Theorem 3: You can never straighten the hair on a coconut.
Imagine a sphere with hair on its surface. Can you comb all your hair flat, without leaving a lock of hair like a comb or a lock of curly hair like hair? Topology tells you that this is impossible. This is called the hairball theorem, which was first proved by Brouwer. In mathematical language, it is impossible to have a continuous unit vector field on the sphere. This theorem can be extended to higher dimensional space: there is no continuous unit vector field for any even dimensional sphere.
Theorem 4: At any moment, there are always two symmetrical points on the earth, and their temperatures are exactly the same as atmospheric pressure.
Polish mathematician Ulan (Stannis? Aw Marcin Ulam) once guessed that given a continuous function from an n-dimensional sphere to an n-dimensional space, two points symmetrical to the center of the sphere can always be found on the sphere, and their function values are the same. 1933, Polish mathematician Bolsuke proved this conjecture, which is the Bolsuke-ulam theorem in topology.
Theorem 5: Given any ham sandwich, there is always a knife that can cut it, so that ham, cheese and bread are just divided into two equal parts.
More interestingly, the name of this theorem is really called "Ham Sandwich Theorem". It was written by mathematician Arthur? Si Tong and John? Proved by John Tukey in 1942, it is of great significance in measure theory.