The number theory class in the afternoon is two classes connected together.

There is a 10-minute break for students to use the restroom.

During the break, some students communicated with Liu Yichen, and Liu Yichen was happy to communicate with these peers.

After all, these students are all very good students, the best among their peers, and none of them has an IQ below the line.

During the two classes, Liu Yichen lectured very fluently. He taught one chapter in one class and two chapters in the two classes.

It can be said that this kind of lecture is very fast, but what is surprising is that no one in the entire classroom found it difficult to understand or laggards, but listened with concentration, as if everyone understood what Liu Yichen said.

Liu Yichen spent a lot of time writing this number theory textbook. When he was in high school, the number theory he came into contact with was elementary number theory, such as the fundamental theorem of arithmetic!

However, the exposure is not deep, and this number theory is also elementary number theory, but it is much deeper than in high school, including the fundamental theorem of arithmetic, Euclid's proof of infinite prime numbers, the Chinese remainder theorem, Euler's theorem, Gauss's two

Sub-reciprocity law, the quotient-high theorem of the Pythagorean equation, the continued fraction solution method of the Pell equation, etc.

Liu Yichen had already learned all these elementary number theory knowledge when he was in high school. However, for normal high school students, unless they have participated in Mathematical Olympiad training classes or competitions, they would not be exposed to it, let alone understand it in depth.

.

Liu Yichen has quite a lot of experience in these matters.

While teaching his theories to these students, Liu Yichen was also silently absorbing experience from them.

These experiences may be of little use to him, but he believes that one day these valuable experiences will come in handy.

Furthermore, Liu Yichen found that teaching these students was a very pleasant and relaxing thing, and he felt very happy inside.

In this focused atmosphere, the class gradually came to an end.

After closing the book, Liu Yichen simply assigned homework and then announced the end of get out of class.

When he announced the end, the classroom burst into warm applause.

Liu Yichen also smiled and nodded to these students and walked outside the teacher.

"It's so awesome. I didn't even turn to the textbook during the whole process. I just talked about it incessantly. Mathematics suddenly became simpler, no longer boring, and became interesting. I found that I am no longer afraid of mathematics.

"The girl who got the first opportunity to ask questions said excitedly to her friend with her eyes shining.

"That's right. We don't even know who wrote the textbook. He is the author. Do we still need to read it? But I didn't expect that Mr. Liu's lectures would be so good. I really look forward to him giving a lecture and giving an academic report." This girl

friends, began to look forward to it.

"Next time you have his class, remember to tell me that I will come to your school to take classes." The girl has decided that she will come to Kowloon University to take classes more often in the future.

Although Ludao University is also a famous university in the country, it used to be the best university in Fujian Province and the only 985 university in Fujian Province.

But now, this girl discovered that the difference between her school and her best friend's school was not just a tiny bit, but a big difference.

"You can consider finding a boyfriend in our school. You are so beautiful, why are you afraid that you can't find him? Another day I will introduce you to a top student who studies well and is handsome." The girl's best friend followed her with a half-smile but not a smile.

The girl said.

"Is there any teacher Liu who is handsome? Is there any student who is better than Teacher Liu? If so, you can consider it~~" the girl said thoughtfully, holding her chin.

Phew~~

The girl's best friend almost spat out a mouthful of blood.

How can it be!?

I couldn't find it even with a lantern.

...

When Liu Yichen walked out of the classroom and was about to go downstairs, Zhang Wei appeared out of nowhere, came over to greet him, and said enviously: "It seems that you are quite popular with the students, too

It’s enviable.”

Zhang Wei is also a professor in the Department of Mathematics. He not only teaches undergraduates, but also leads graduate and doctoral students. He is the backbone of the Department of Mathematics.

Liu Yichen touched his chin and said, "Maybe it's because he's handsome. You don't have to envy him. You can't envy him!"

Zhang Wei only felt that he had been hit hard and almost vomited blood.

Among them, Liu Yichen is undoubtedly the youngest and the most handsome.

Next, if there is someone who is somewhat handsome, it is Xu Chenyang, but Xu Chenyang is over thirty, already middle-aged, his belly has grown, and he has turned into a greasy uncle.

Everyone else looks very average.

To be honest, although this group of young mathematicians all have experience as lecturers abroad, in their lectures, professional students listen well. If students from non-mathematics departments listen to their lectures, they will be confused.

Misty, even the best lullaby.

Liu Yichen also knew this, but he didn't care.

After all, Zhang Wei and the others teach students in the Department of Mathematics. They don’t need humor, liveliness, and progression from the shallower to the deeper. They only need to cultivate students’ mathematical thinking, lead students to understand the wonder and beauty of mathematics, and allow students to maintain

If you have curiosity and love for mathematics, that’s fine.

After all, the mathematical ability of students in the mathematics department is not comparable to that of students in other departments, and their mathematical skills are very solid.

"How is it? Is there any progress in the research on the standard conjecture?" Liu Yichen asked as he walked towards the mathematics department.

"Small progress, not too outstanding." Zhang Wei frowned: "Sometimes I even suspect that the standard conjecture may not be correct, and it may be proven or not in the end!"

Mathematical conjectures are like this. Until they are fully proven, no one knows whether this mathematical conjecture is proven to be true or not.

"No matter what the situation is, its value is still astonishing. This is a huge treasure worthy of our full efforts to explore." Liu Yichen thought for a moment and said.

If the standard conjecture is proven, it means that the Riemann Hypothesis has also been proven in the field of algebraic geometry. The achievement of proving the Riemann Hypothesis is probably the greatest mathematical achievement in mathematics in the past half century.

If it is proven that the standard conjecture is wrong, it will also prove that the Riemann Hypothesis is negative, which will undoubtedly be a disaster for mathematics at that time.

In the history of mathematics, there have been three mathematical crises.

The first mathematical crisis occurred in ancient Greece between 580 and 568 BC. The mathematician Pythagoras established the Pythagorean School. At that time, people had limited understanding of rational numbers, and the concept of irrational numbers was even more limited.

They knew nothing about it. The numbers mentioned by the Pythagoreans originally referred to certificates. They did not regard fractions as one kind of number, but rather regarded them as the ratio of two certificates.

At that time, Hibersus, a member of the school of thought, discovered through logical reasoning based on the Pythagoras theorem (Pythagorean theorem) that the diagonal length of the political and legal system with side length l is neither an integer nor a ratio of integers that can be expressed

The discovery of Hibersos directly impacted the Pythagorean creed and the traditional views of the Greeks at that time.

As a result, Hibersos was thrown into the sea and drowned.

In order to solve this problem, later generations introduced the concept of irreducible quantities in geometry to solve this problem.

The second mathematical crisis occurred in the 17th century. At that time, after the birth of calculus, the mathematical world was in chaos due to the elaboration of the theoretical basis of calculus. There were theoretical contradictions in calculus. Infinite small quantities are the basis of calculus.

One of the basic concepts.

In some typical derivation processes, Newton, the main founder of calculus, used the infinitesimal amount as the denominator for division in the first step. Of course, the infinitesimal amount cannot be zero; in the second step, Newton regarded the infinitesimal amount as zero and removed those that contained it.

terms, thereby obtaining the desired formulas. The application in mechanics and geometry has proved that these formulas are correct, but its mathematical derivation process is logically contradictory.

The focus is: Is the infinitesimal quantity zero or non-zero? If it is zero, how can we use it as a divisor? If it is not zero, how can we remove the terms that contain the infinitesimal quantity?

This mathematical crisis lasted until the 19th century, when Cauchy developed the limit theory in detail and systematically. Cauchy believed that treating infinitesimal quantities as definite quantities, even zero, was unjustifiable because it would conflict with the definition of limits. Infinitely small quantities

It should be as small a quantity as it needs to be, so in essence it is a variable, and it is a quantity with zero as the limit. So far, Cauchy has clarified the concept of infinitesimals of the predecessors and liberated infinitesimal quantities from the constraints of metaphysics.

, thus the second mathematical crisis was basically resolved.

The third mathematical crisis occurred at the end of the 19th century. At that time, the British mathematician Russell divided sets into two types. However, upon further deliberation, Russell's paradox was formed: s is composed of all sets that are not its own elements, then s belongs to s

?

In layman's terms, Xiao Ming said one day: "I always lie!" Ask Xiao Ming whether he lied or told the truth. The scary thing about Russell's paradox is that it does not involve the advanced knowledge of aggregation like the maximum ordinal paradox or the maximum cardinality paradox.

, it is very simple and easily destroys set theory!

In order to solve this mathematical crisis, mathematicians are actively looking for solutions. One of them is to base set theory on a set of axioms to avoid paradoxes. The first person to do this work was the German mathematician Zermelo.

He proposed seven axioms and established a set theory that would not produce paradoxes. After improvements by another German mathematician, Fuzker, a set theory axiom system without contradictions was formed. It is the so-called zf axiom system.

It was only then that the mathematical crisis abated.

And if the standard conjecture is disproven, it will cause the fourth mathematical crisis, and many theories that were previously considered correct will be overthrown and reconstructed.
Chapter completed!