I Just Want to Be a Quiet Top Student

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

The boys use their knowledge of middle school algebra 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

Boys open the brackets and expand them one by one, and the positive and negative x's 1st, 2nd, and 3rd powers cancel each other out.

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

It is recorded in "History of Number Theory" that Euler took x=-1 in the above formula at that time, and got 1-2+3-4+5-6+...=1/4

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

This is the conditional convergence method, which is what the boys in the math school do. He continues to double the sum of the even digits, divides both sides of the equation by -3, and finally derives 1+2+3+4+5+ ... = -1/12.

"Thank you, classmate." Satisfied with the boy's answer, Shen Qi turned to all the students and asked, "Euler added infinitely many positive integers to get a negative number. What exactly did he want to express?"

Some students said: "The so-called infinity means that we don't know whether it is positive or negative."

"OK, the answer is correct. Euler originally gave infinity a meaning, which was of little significance to mathematics at that time, but it was of great significance to mathematics and physics more than 200 years later." Shen Qi wrote a few simple formulas on the blackboard.

Shen Qi substituted the Euler's formula -1/12 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 the dimension, so shocking results have been produced. Based on Euler's formula in the 18th century, we found that in the 25-dimensional space, the mass of photons is 0!" From the 18th century to the 20th century.

"So hanging?"

"I can't keep up with my nutrition, I'll drink some nutrition express."

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, and it is also consistent with the string theory proposed in the second half of the 20th century. Next, we will enter the part of high-dimensional space." Euler's formula, let a student prove Euler's formula in the form of Olympiad competition, and then transition to 25-dimensional space, relativity and string theory.

"String theory is applicable to spaces within 25 dimensions, while superstring theory is only applicable to spaces within 9 dimensions."

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

"In hyperspace, in addition to the coordinates determined by ordinary numbers, there are additional dimensions expressed by Grassmann numbers."

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

"Gauge field theory dictates that the rotational symmetry of a circle is the gauge symmetry of the electromagnetic force."

"In addition, in the Yang-Mie equation theory that expands the gauge field theory of electromagnetic force, the rotational symmetry of high-dimensional space is gauge symmetry."

"Once the particles predicted by supersymmetry are discovered, it will open a new way to verify superstring theory, which will refresh human's cognition of space."

"A classmate mentioned the LHC and the Higgs boson. I want to explain that the discovery of the Higgs boson proves that the symmetry between the electromagnetic force and the weak force will be broken spontaneously. It is the 'God particle' ’, but we still need more convincing evidence than ‘God’.”

...

The more Shen Qi taught, the more advanced it became. This is no longer advanced algebra, but a comprehensive course that combines algebra, relativity, and high-dimensional physics.

The students were taking notes, but now they are doing nothing, just sitting and listening to the class.

A young lecturer muttered in a low voice: "Professor Shen's lecture is very enjoyable. It touches on the ultimate theory of mathematics and physics, but can the first-year students fully understand it?"

"If the first-year students can understand it, they can become professors directly after graduation." A teaching assistant next to him thought that the first-year students can understand the thread, and the amount of information in this class is too large.

If a technical term is to be explained, more technical terms will be involved, which requires the lecturers to have extremely deep theoretical knowledge reserves.

Obviously, even the first-year undergraduate students of Yanda University who are outstanding among their peers have difficulty accumulating such a huge amount of knowledge and information.

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

The expressions of the students are excitement and bewilderment dancing together, obsession and dementia flying together.

It sounded cool, but the students couldn't tell exactly where it was, and where it was.

With 10 minutes to go before the end of get out of class, Shen Qi forcibly ended it. At the last moment, he showed his hand speed and filled a blackboard with symbols at an unimaginable speed.

These years are all about multimedia teaching. Teachers are used to playing PPT lectures. "Knocking on the blackboard" has gradually evolved into a synonym, representing key content and important test points.

Shen Qi's reports and speeches are also played in the form of PPT. Only in class, he likes the traditional blackboard mode.

The blackboard mode has several advantages. First, it can practice calligraphy. Second, it gives students a certain amount of time to think. When the teacher writes on the blackboard, students have time to digest and absorb knowledge.

Looking at the mathematical symbols on the blackboard, most of the students are still in a state of obsession + dementia. They don't know what Professor Shen wrote. All in all, they feel very powerful.

The boy who came to the stage to give a proof just now clapped the case, he was very excited: "This... this is the Riemann zeta function!"

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

"So... so..." This boy knew what happened but he didn't know why, but he was still the smartest student in the classroom.

"So we're back to the subject of this lesson—mathematics. No matter how extravagant things are, they must ultimately be explained by mathematics. What is written on the blackboard is to use the Riemann zeta function to prove that positive integers add infinitely to negative numbers. Pull the formula, substitute this result into the photon energy formula, and you will find..."

"Oh, class is over. This is the homework I left for you. Please think about a basic math problem after class. The real part of the function of the complex number s is greater than 1. What kind of result will it deduce?" Shen Qi ended this advanced class with the Riemann zeta function. The amount of information in this class is really large, but it doesn’t matter, as long as the students can understand the last 5 minutes, the essence of the whole class is the last 5 minutes.

What if the students didn't understand the last 5 minutes?

Then you have to ask the teacher.

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