The boy named by Shen Qi came to the stage, and the young man picked up the chalk with confidence, brushed and brushed the book.

The boys used their knowledge of algebra in middle school to create a series of regular equations:

（1-x）(1+x)=1-x^2

（1-x）(1+x+ x^2)=1-x^3

（1-x）(1+x+ x^2+ x^3)=1-x^4

The boy opens the brackets and expands them in turn, and the 1st, 2nd, and 3rd powers of plus or minus x cancel each other out.

After that, there is a wave of flowing operations, and the boy gets the equation: 1+2x+3x^2+4x^3+......=1/(1-x)^2

According to the History of Number Theory, Euler took x=-1 in the above equation at that time to obtain 1-2+3-4+5-6+......=1/4

Although the absolute value of the number keeps getting larger, it cancels each other out due to the presence of plus and minus signs, so 1/4 is obtained.

This is the conditional convergence method, which is what the math boy did, he continued to expand the sum of even digits to 2 times, and then divided both sides of the equation by -3, and finally deduced 1+2+3+4+5+......=-1/12.

"Thank you, classmate. Shen Qi was satisfied with the boy's answer, and turned to all the students and asked, "Euler uses an infinite number of positive integers to add up to get a negative number, what does he want to express?"

One student said: "The so-called infinity means that I don't know whether it is positive or negative." ”

"OK, that's correct. Euler's original meaning to infinity was of little significance to mathematics at the time, but significant to mathematics and physics more than 200 years later. Shen Qi wrote a few simple formulas on the blackboard.

Shen Qi substituted the -1/12 Euler formula into the energy formula of the photon, so the energy of the photon = 2-(D-1)/12

Let D = 25

then 2-(25-1)/12=0

"D is dimension, so the shocking result is produced, based on the 18th century Euler's formula, we found that in the 25th dimensional space, the mass of the photon is 0!" Shen Qi's lecture was very jumpy, and he suddenly traveled from the 18th century to the 20th century.

"So hanging?"

"I can't keep up with nutrition, so I drink some nutrition fast. ”

The students enjoyed listening to it, but not everyone could immediately follow Shen Qi's teaching ideas.

"Euler's formula does not contradict the theory of relativity proposed in the first half of the 20th century, but also coincides with the string theory proposed in the second half of the 20th century. Shen Qi's lecture was imaginative, and he introduced Euler's formula in a book, and asked a student to prove Euler's formula in the way of an Olympiad competition, and then transitioned to 25-dimensional space, relativity, and chord theory.

"String theory applies to space within 25 dimensions, and superstring theory only applies to space within 9 dimensions. ”

"To put it another way, according to superstring theory, the space we live in is not ordinary three-dimensional space, but hyperspace. ”

"In hyperspace, in addition to the coordinates determined by ordinary numbers, there are additional dimensions represented by Glassmann numbers. ”

"In Type I superstring theory, rotational symmetry in 32 dimensions is mentioned. ”

Gauge field theory, on the other hand, states that the rotational symmetry of a circle is the gauge symmetry of the electromagnetic force. ”

In addition, in the theory of the Yang-Meter equation, which expands the gauge field theory of electromagnetic forces, the rotational symmetry of high-dimensional space is the gauge symmetry. ”

"Once we discover the particles predicted by supersymmetry, it will open a new way to test superstring theory, which will refresh the human understanding of space. ”

"Some students mentioned the LHC and the Higgs boson, and I would like to explain that the discovery of the Higgs boson proves that the symmetry between the electromagnetic force and the weak force can spontaneously break, and it is a 'God particle', but we still need more convincing evidence than 'God'. ”

……

Shen Qi is getting deeper and deeper, this is no longer advanced algebra, but a comprehensive course that integrates algebra, relativity, and high-dimensional physics.

The students were taking notes, but at the moment they didn't do anything but sit and listen to the lecture.

A young lecturer muttered, "Professor Shen's lecture is very enjoyable, touching on the ultimate theory of mathematics and physics, but can first-year students fully understand it?"

"If first-year students can understand, they can go straight to becoming professors after graduating from undergraduate. A teaching assistant next to me said that the first-year students can understand a yarn, and the amount of information in this class is too much.

If you want to explain a technical term, then there will be more technical terms involved, which requires the participants to have a very deep theoretical knowledge.

Obviously, even the first-year undergraduate students of Yan University, who are outstanding among their peers, have a hard time stockpiling such a huge amount of knowledge and information.

Shen Qi didn't care whether the students could understand it or not, he just taught in his way.

The students' expressions are exciting and confused, and obsession and dementia fly together.

It's cool and crooked, but the students can't tell exactly where it is cool and where it is.

With 10 minutes left to get out of class, Shen Qi forced the end to it, and at the last moment, he used his hand speed like light, and wrote a blackboard symbol at an unimaginable speed.

In the past few years, it has been multimedia teaching, and teachers are accustomed to playing PPT handouts, and "knocking on the blackboard" has gradually evolved into a synonym, representing key content and important test points.

Shen Qi makes reports and speeches, and they are all played in the form of PPT, but in class, he likes the traditional blackboard mode.

The blackboard mode has several advantages, one is that it can practice words, and the other is to give students a certain amount of time to think, when the teacher writes the blackboard, students have time to digest and absorb knowledge.

Looking at the mathematical symbols on the blackboard, most of the students are still obsessed + demented, I don't know what Professor Shen wrote, all in all, I feel very powerful.

The boy who came to the stage to testify just now stood up, and he was very excited: "This ...... This is the Riemann zeta function!"

Shen Qi looked at the boy: "Yo, you're very strong, young man, yes, this is the Riemann zeta function, so what?"

"So...... So...... "The boy knew what was going on, but he was still the smartest student in the room."

"So we came back to the topic of this lesson--- math, and no matter how fanciful things are, they ultimately have to rely on mathematics to explain. What is written on the blackboard is Euler's formula that uses the Riemann zeta function to prove that positive integers are infinitely added to get negative numbers, and substituting this result into the energy formula of the photon, you will find ......"

"Oh, class is over, this is the homework I left for you, please think about a most basic mathematical problem after class, the real part of the function of complex numbers s is larger than 1, what kind of result will be derived?" Shen Qi ended this high generation class with the Riemann zeta function, this lesson is indeed very informative, but it doesn't matter, as long as the students can understand the last 5 minutes, the essence of the whole lesson is the last 5 minutes.

What if the student doesn't understand the last 5 minutes?

Then you'll have to ask a teacher.

After class, the students surrounded Shen Qi and humbly asked for advice.