Who's going to Ya Palace?

Isaac Barrow (1630- 1677) is a famous British mathematician. He is a professor of mathematics at Cambridge University and has made great achievements in geometry. He was also a famous priest and wrote a lot of famous sermons. He was modest and amiable, but he had an indissoluble enmity with Count Rochester, the favorite of the King of charles ii at that time. As long as we meet together, there will inevitably be a war of words.

Rochester is said to have ridiculed Reverend Barrow as "a musty seminary".

One day, Barrow prayed for the king and met Rochester.

Rochester bowed deeply to Barrow and said sarcastically, "Doctor, please help me tie my shoelaces."

Barrow replied, "I ask you to lie on the ground, sir."

"Doctor, I invite you to the center of hell."

"Sir, please stand opposite me."

"Doctor, I invite you to the deepest part of hell."

"No, sir, such an elegant palace should be reserved for people of your status!" Say that finish, barrow shrugged and walked away.

The mystery of the inscription

Diophantu, a famous mathematician in Alexandria, ancient Greece, only knew that he was from the 3rd century A.D., and his age and life history books were not clearly recorded. However, we can still learn a thing or two from his tombstone, which tells people all the year round that he is 84 years old.

The tombstone of Diophantine is like this:

Diophantine is buried here. If you understand the mystery of the inscription, it will tell you the life span of Diophantine. The gods gave him 1/6 of life as his childhood. After112 of life, he grew a beard, and then Diophanto got married, but he had no children, so he lived 1/7 of life again. Five years later, he had his first son, but his beloved son died young.

The will of mathematicians

The will of Arab mathematician Hua Razmi, when his wife was pregnant with their first child. "If my dear wife gives birth to a son for me, my son will inherit two thirds of the inheritance and my wife will get one third; If it is a girl, my wife will inherit two-thirds of the inheritance and my daughter will get one-third. " .

Unfortunately, the mathematician died before the child was born. What happened after that made everyone more troubled. His wife gave birth to twins, and the problem happened in his will.

How to follow the mathematician's will and divide the inheritance among wife, son and daughter?

Not a bathhouse.

Amy Nord, a German mathematician, got a doctorate, but she is not qualified to teach because she needs to write another paper before the professor will discuss whether to grant her the qualification as a lecturer.

Hilbert, a famous mathematician at that time, appreciated Amy's talent very much. He ran around asking for permission to be the first female lecturer at the University of G? ttingen, but there was still controversy at the professor meeting.

A professor said excitedly, "How can a woman be a lecturer?" If she is allowed to be a lecturer, she will become a professor in the future and even enter the university Council. Can women be allowed to enter the highest academic institutions of universities? "

Another professor said, "How do our soldiers feel when they come back from the battlefield and find themselves prostrating themselves at the feet of women?"

Hilbert stood up and firmly refuted: "gentlemen, the gender of the candidate should never be an argument against her becoming a lecturer." After all, the university Council is not a bathing hall! "

Can only be single for life.

When alexander humboldt, an outstanding German naturalist, visited Lobachevsky, the founder of Russian non-Euclidean geometry in Kazan, he asked the mathematician, "Why do you only study mathematics? It is said that you have a deep understanding of mineralogy and are proficient in botany. "

What, you only study math? It is said that you have a deep understanding of mineralogy and are also proficient in botany. "

"Yes, I like botany very much," Lobachevsky replied. "When I get married in the future, I will definitely build a greenhouse ..."

"Then get married quickly."

"But contrary to my wish, my interest in botany and mineralogy has made me a bachelor all my life."

seven bridges problem

In A.D. 1737, Euler received the "Seven Bridges Problem", when he was thirty years old. He thought, let's try it first. He started from the middle island area, arrived at the north area through the 1 bridge, returned to the island area from the No.2 bridge, entered the east area through the No.4 bridge, reached the south area through the No.5 bridge, and then returned to the island area through the No.6 bridge ... Now only the No.3 and No.7 bridges have not passed. Obviously, the only way to cross the third bridge from the island area is to cross the first bridge, the second bridge or the fourth bridge, but all three bridges have passed. This move failed. Euler again at a side:

Island northeast island south island north

This way of walking still doesn't work, because Bridge 5 hasn't crossed yet.

Euler can't even try a few tricks. This question is really not simple! He calculated that there were many moves, including * * *.

7×6×5×4×3×2× 1=5040 (species)

Boy, if we try this method and this method, when will we get the answer? He thought: you can't just try, you have to think of other ways.

Clever Euler finally came up with a clever way. He used A to represent the island area, B, C and D to represent the north, east and west areas respectively, and the seven bridges were represented by arcs or straight lines. In this way, the problem of seven bridges has been transformed into a problem in several branches of graph theory, that is, whether the above graphics can be drawn without a repetition.

Euler concentrated on studying this figure and found that at every point in the middle, there was always a line drawn to that point and another line drawn from that point. That is, except the starting point and the ending point, the line passing through the middle point must be even. Like the picture above, because it is a closed curve, the lines passing through all points must be even. In this picture, there are five lines passing through point A, three lines passing through point B, point C and point D, and none of them are even, which means that no matter from that point, there is always a line that has not been drawn, that is, a bridge has not arrived. Euler finally proved that it was impossible not to walk seven bridges at a time.

The talented Euler summed up 5040 different moves with only one step of proof, which shows the power of mathematics!

Here are Hilbert's 23 questions:

The first problem is the continuum hypothesis.

It has been solved. 1963 paul cohen, an American mathematician, proved by coercion that ZFC could not deduce the continuum hypothesis. In other words, whether the continuum hypothesis is established cannot be decided by ZFC.

The second problem is the compatibility of arithmetic axioms.

It has been solved. Kurt G?del proved Godel's incomplete theorem in 1930.

The third problem is how to prove that the volumes of two tetrahedrons are equal.

It has been solved. Max Dean, a student of Hilbert's, proved this impossible by counterexample.

The fourth problem is that it is too obscure to establish all metric spaces so that all line segments are geodesics. Hilbert's definition of this problem is too vague.

Question 5: Are all continuous groups differentiable?

It has been solved. 1953, Japanese mathematician Hidehiko Yamabe got a completely positive result.

The sixth question is axiomatic physics non-mathematics. Many people question whether physics can be completely axiomatized.

Question 7: If B is an irrational number and A is an algebraic number other than zero sum 1, is ab transcendental?

It has been solved. Solved independently by Gelfond and Schneider in 1934 and 1935 respectively.

The eighth question Riemann conjecture and Goldbach conjecture

Partially solved. 1966 China mathematician Chen Jingrun partially solved Goldbach's conjecture.

General reciprocity law in arbitrary algebraic number field

Partially solved. 192 1 Japan's masahiro takagi and 1927's Emil E.Artin in Germany each have partial answers.

Solvability of problem 10 indefinite equation

It has been solved. 1970, the Soviet mathematician Marty Sevik proved that, generally speaking, the answer is no.

Quadratic form of algebraic coefficient

It has been solved. The rational part is solved by Hasse in 1923, and the real part is solved by Higl in 1930.

Problem 12: Extended Algebraic Numbers

It has been solved. 1920, Takagi Sadako initiated Abel's domain theory.

Problem 13: Solving any seventh degree equation with binary function.

It has been solved. Andre Andrey Kolmogorov and Arnold proved that this is impossible.

The problem 14 proves the finiteness of a complete function system.

It has been solved. 1962 Japanese Masayoshi Nagata put forward a counterexample.

Question 15 Schubert's strict foundation of enumeration calculus (Schubert's enumeration calculus)

Partially solved. Some of them were strictly proved by Vander Waals in 1938.

Topological structure of algebraic curves and surfaces

unresolved

Question 17: Write the sum of squares fraction of a rational function.

It has been solved. Emil Artin solved the real closed domain in 1927.

Question 18: Can a non-regular polyhedron closely arrange space and spheres?

It has been solved. In 19 10, Bieber Bach made that "n-dimensional space is embedded by finite groups".

Question 19: Are all solutions of Lagrangian system analytical?

It has been solved. 1904 was solved by Sergei Bernstein.

Question 20: Do all variable problems with boundary conditions have solutions?

solve

Problem 2 1 Prove that there is a linear differential equation for a given peak group.

solve

Question 22: Unify analytic relations with automorphic functions.

It has been solved. 1904 was taken care of by Kobe and Poincare.

Long-term development of variational method

unresolved

1. In a topology class, Minkowski proudly declared to the students: "The most important reason why this theorem has not been proved is that only some third-rate mathematicians have spent time on it so far. Let me prove it below. " ..... At the end of this class, I didn't complete the certificate. In the next class, Minkowski continued to prove that several weeks had passed ... On a cloudy morning, Minkowski walked into the classroom. It was just a flash of lightning across the sky, and the thunder was deafening. Minkowski said very seriously: "God was angered by my pride, and my proof was incomplete ..."

2. During the period of 1942, Lefschetz went to Harvard to give a speech. Boekhoff is his good friend. After the lecture, someone asked him what interesting things he had done in Princeton recently. Lefschetz said that someone had just proved the four-color conjecture. Boekhoff seriously disbelieved, saying that if it was true, he would climb directly to Fine Hall in Princeton with his hands and knees.