The Nutrition Isn't Keeping Up

The male student from the School of Mathematics, who was called upon by Shen Qi, went up on stage. The young man confidently picked up the chalk and began to write furiously.

The boy used his high school algebra knowledge 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 opened the parentheses and expanded them one by one, and the positive and negative x to the power of 1, 2, and 3 canceled each other out.

What followed was a series of smooth and effortless movements, and the boy arrived at 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 and obtained 1 - 2 + 3 - 4 + 5 - 6 +... = 1/4

Although the absolute value of the numbers keeps increasing, they cancel each other out due to the presence of positive and negative signs, resulting in 1/4.

This is the conditional convergence method. That's how the male student from the School of Mathematics did it. He continued to double the sum of the even-numbered digits, then divided both sides of the equation by -3, and finally derived 1+2+3+4+5+...=-1/12.

"Thank you, student." Shen Qi was satisfied with the boy's answer, then turned to the whole class and asked, "Euler added an infinite number of positive integers and got a negative number. What exactly was he trying to express?"

One student said, "Infinity means not knowing whether it's positive or negative."

"OK, correct answer. Euler initially gave infinity a meaning that was not very significant for mathematics at the time, but it has great significance for mathematics and physics more than 200 years later." Shen Qi wrote a few simple formulas on the blackboard.

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

Let D=25

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

"D stands for dimension, so a shocking result was achieved: based on Euler's formula from the 18th century, we discovered that in 25-dimensional space, the mass of a photon is 0!" Shen Qi's lecture was very abrupt, leaping from the 18th century to the 20th century in an instant.

"That's awesome?"

"I'm not getting enough nutrition, I'll drink some nutritional supplements."

The students thoroughly enjoyed listening, but not everyone could immediately follow Shen Qi's teaching approach.

"Euler's formula does not contradict the theory of Theory of Relativity proposed in the first half of the 20th century, and it is also consistent with String Theory proposed in the second half of the 20th century. Now we will move on to the part about higher-dimensional space." Shen Qi's lectures are imaginative. He introduced Euler's formula with a novel, asked a student to prove Euler's formula in the form of an Olympiad math competition, and then transitioned to 25-dimensional space, Theory of Relativity String Theory.

"String Theory applies to spaces of 25 dimensions or less, Superstring Theory applies only to spaces of 9 dimensions or less."

"To put it another way, according to Superstring Theory, the space we inhabit is not ordinary three-dimensional space, but hyperspace."

"In hyperspace, in addition to coordinates defined by ordinary numbers, there exist additional dimensions, represented by Grassmann numbers."

"Type I Superstring Theory mentions 32-dimensional rotational symmetry."

"Gateway field theory stipulates that the rotational symmetry of a circle is the gauge symmetry of the Electromagnetic Force."

"Furthermore, in the Yang-Mi equations theory, which extends the gauge field theory of Electromagnetic Force, the rotational symmetry of higher-dimensional spaces is equivalent to gauge symmetry."

"Once the particles predicted by Supersymmetry are discovered, it will open up a new path for verifying Superstring Theory, which will refresh humanity's understanding of space."

"Some students mentioned the LHC and the Higgs Boson. I want to clarify that the discovery of the Higgs Boson proved that the symmetry between the Electromagnetic Force and the Weak Force can be spontaneously broken. It is the 'God particle,' but we still need more convincing evidence than 'God.'"

Shen Qi's lectures became increasingly profound; this was no longer just Advanced Algebra, but a comprehensive course integrating algebra, Theory of Relativity, and high-dimensional physics.

The students, who were taking notes, stopped and simply sat and listened to the lecture.

A young lecturer muttered to himself, "Professor Shen's lecture was very engaging, touching on the ultimate theories of mathematics and physics. But can first-year students fully understand it?"

"If first-year students could understand this, they could become professors right after graduation," a teaching assistant thought to himself. "First-year students can't possibly understand anything; this lecture is packed with information."

Explaining a technical term involves many more technical terms, requiring the learner to have a very deep theoretical knowledge base.

It is obvious that even outstanding first-year undergraduate students at Yenching University would find it difficult to accumulate such a massive amount of knowledge and information.

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

The students' expressions were a dance of excitement and bewilderment, a mix of fascination and dazedness.

They thoroughly enjoyed listening to it, but the students couldn't quite articulate exactly why they enjoyed it or what made it so enjoyable.

With 10 minutes left before class ended, Shen Qi rushed to finish, unleashing lightning-fast hand speed at the last moment to fill the blackboard with symbols at an unimaginable pace.

These days, multimedia teaching is the norm, and teachers are used to playing PowerPoint presentations. "Packing the blackboard" has gradually become a synonym for key points and important exam questions.

When Shen Qi gives reports or speeches, he always uses PowerPoint presentations, but when it comes to teaching, he prefers the traditional blackboard method.

The blackboard mode has several advantages. First, it allows students to practice handwriting. Second, it gives students time to think and digest the knowledge while the teacher writes on the blackboard.

Looking at the blackboard full of mathematical symbols, most students were still in a daze, not knowing what Professor Shen had written, but in short, they felt it was very impressive.

The boy who had just given the demonstration slammed his fist on the table and stood up, extremely excited. "This... this is the Riemann zeta function!"

Shen Qi looked at the boy. "Wow, you're pretty good, kid. Yes, this is the Riemann zeta function, so what?"

"So... so..." This boy knew the answer but not the reasoning, yet he was still the smartest student in the entire classroom.

"So we've returned to the topic of this lesson—mathematics. No matter how fancy the concepts, they ultimately rely on mathematics for explanation. What's written on the blackboard is the proof of Euler's formula for adding infinite positive integers to a negative number using the Riemann zeta function. Substituting this result into the energy formula for photons, you'll find..."

"Oh, class is over. This is the homework I'm leaving for you. Please think about a very basic math problem after class: If the real part of a function of a complex number s is greater than 1, what result can you derive?" Shen Qi ended the Advanced Algebra with the Riemann zeta function. The amount of information in this class was indeed very large, but it didn't matter. As long as the students could understand the last 5 minutes, that was enough. The essence of the whole class was in the last 5 minutes.

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

Then you'll have to ask your teacher.

After class, the students surrounded Shen Qi, humbly seeking his advice.