Chapter 120 Inviting Me to Participate
"The tangent line through a point on any curve can be reflected by studying the properties of the derivative. The derivative can be used to determine the increase or decrease of the function and determine the curvature direction of the function graph."

"And the degree of bending is called curvature."

……

"So acceleration in physics is actually curvature in geometry."

Friday, April 2005, 4, in the lecture hall of Qinghua School of Mathematics and Science.

Xu Yuan sat in the first row, listening to Tang Shihong's lecture on differential geometry at the podium.

At the same time, my hands were not idle.

Quickly calculating the relevant content on the draft paper.

After formally coming into contact with differential geometry, he developed a great interest in it and almost always had a book on Riemannian geometry in his hand for study.

With the help of his solid mathematical foundation, he made rapid progress in learning differential geometry in the deep learning state.

It can be said that he has already mastered what Tang Shihong is talking about now.

However, considering that self-study alone would not be able to cover some areas, he would come to the classroom to attend classes from time to time during this period. Although strictly speaking he would officially start his doctoral studies after the summer vacation, the normal regulations of the department were obviously not applicable to him.

At this time, Tang Shihong on the podium looked at the time, paused temporarily, picked up the cup on the table and drank a sip of tea.

Then he picked up the chalk again, faced the blackboard, and wrote a differential geometry problem on it.

"Let the curve r(s) have curvature and torsion x, τ, and the unit tangent vector t(s) of r(s) be the unit sphere..."

"Proof: The curvature and torsion of the curve r(s) = t(s) are respectively..."

After quickly finishing the last mathematical symbol, Tang Shihong turned around and faced the students below the stage with his usual kind smile on his face.

"I'll give you this question today. Who is willing to come up and answer it?"

But as the words fell, the classroom became very quiet and no one chose to raise their hand.

There were not many students attending Tang Shihong's class, but they were all graduate students at the School of Mathematics.

Under normal circumstances, even if no one was scrambling to answer the question, at least one or two people would raise their hands.

After all, it is beneficial to successfully answer questions on stage.

But today, he didn't know what happened. After waiting for about half a minute, it was still quiet, which made Tang Shihong have doubts in his mind.

He thought that the questions this time were not very difficult and he should be able to answer them.

Surprised, he had to add, "The credits you get for solving the problems today can be doubled." He used a tempting tone when saying this.

According to his usual habit of teaching graduate students, he would sometimes give credits to students who successfully solved his problems. Although the credits were only a few tenths each time, it greatly motivated the students.

Therefore, the atmosphere in his class is very good.

However, this trick doesn't seem to work today. Even when the credits were doubled, no one took the initiative to go to the podium.

Just when he really began to doubt whether the questions were too difficult, he noticed that everyone's eyes were on Xu Yuan in the front row.

I immediately understood the key.

"It's because they saw Xu Yuan here that everyone else dared not show their heads."

I muttered to myself, not knowing what to say about this. I didn't expect Xu Yuan's coming to the class would have a counterproductive effect.

Xu Yuan's successive solutions to difficult mathematical problems in the fields of number theory and partial differential equations were published in the Annals of Mathematics, and he was even evaluated by Professor Deligne as the Prince of Mathematics in today's mathematics community. There is no doubt that Xu Yuan's name has become completely famous at Qinghua University and even other universities.

Even though he has just graduated from college, he is not someone that an ordinary graduate student or even a doctoral student can get away with.

So when everyone saw that Xu Yuan didn't raise his hand, they naturally didn't dare to step forward.

After figuring out the cause of the current situation, Tang Shihong had no better solution.

He had no choice but to turn his gaze to Xu Yuan.

"Xu Yuan."

"Come up and explain this question to everyone."

Without saying a word, he immediately called on Xu Yuan to come up to the stage to answer the question.

Xu Yuan was calculating on a piece of draft paper and was not paying attention to what was going on on the stage until he heard Tang Shihong's shout.

He raised his eyes and took a look before he realized what was happening and stood up.

"Oh well."

He didn't think much about it. After all, it was just a question and it wasn't difficult for him.

Just as Xu Yuan walked up to the podium, took the chalk from Tang Shihong and carefully examined the questions on the blackboard, more than a dozen graduate students in the audience couldn't help but whisper to each other.

"If our great scholar doesn't raise his hand, who else would dare to raise their hand?"

"That's a good point, but it's a shame to waste such a good opportunity to earn extra credits."

"Professor Tang, do you have any ideas for this question?"

"How many minutes do you think our great scholar will take to answer the question on stage?"

"It's hard to say. After all, he just started learning differential geometry."

……

Tang Shihong naturally listened to all the discussions of the graduate students in the audience, but his eyes were full of trust when he looked at Xu Yuan, with a faint smile on his face.

Others don't know the real situation, but he knows Xu Yuan's abnormal learning and comprehension speed.

Although I have only been exposed to differential geometry for a short time, I have absolutely no problem with the current knowledge.

And the facts turned out to be just as he expected.

At this moment, Xu Yuan was completely immersed in the question. He used abstract thinking to unravel the key information, and the solution emerged in his mind without much thought.

The next second, without any hesitation, he picked up the chalk to prove it.

"Analysis s is not necessarily the arc length parameter of the curve F(s), it can be calculated using the conclusion of the known binormal vector." "P(s)=-=xn, |P"(s)|=K"

"i"(s)=(xm)=x'n+K→≈K'n+K(-xt+τb)......"

Yes.

"x2t(-3kK')+K(2k'τ+Kτ')"

"So the curvature and torsion of the curve r(s) = t(s) are respectively..."

Xu Yuan did not pause at all throughout the whole process. It can be said that he completed the entire proof of the problem in one breath. Only after he finished writing the last mathematical symbol did he let out a sigh of relief and put the chalk on the podium.

at the same time.

The dozen or so graduate students who had been watching Xu Yuan solving the problem suddenly widened their eyes.

Although they thought that with Xu Yuan's mathematical level, since he had no hesitation in going up to the stage to solve the problem, he should be able to complete the solution to this differential geometry problem.

But the speed of this solution is really too fast.

If any one of them were to go up there, it would be impossible to do it.

You have to know that differential geometry is highly abstract, and coupled with the complexity of tensors and tensor operations, as well as the intersection of differential form processing with other fields, it can only be said that learning it is quite difficult.

Especially Riemannian geometry.

Not only are the concepts complex and difficult, but the calculations are also prone to errors.

Even if you have a good foundation in mathematics, it is difficult to learn on your own.

But Xu Yuan obviously had not attended many relevant courses, which means that he could solve this problem so easily and quickly because of his previous self-study.

How could they not be shocked by such a terrifying talent?

"That's the answer. I just got some ideas."

“It’s so scary.”

"If I hadn't seen it with my own eyes, it would be hard to believe that someone could teach differential geometry to this extent by themselves!"

"Self-study is not the point. What's important is how long someone has studied for."

"No wonder he was able to publish two papers in the Annals of Mathematics. Master Xu is truly worthy of being Master Xu."

……

Just as everyone in the audience was expressing their admiration and worship from the bottom of their hearts, Xu Yuan turned his gaze to Tang Shihong in front of him.

"Professor Tang, I've finished writing."

"The idea is ingenious and the proof process is complete and accurate, very good." Upon hearing this, Tang Shihong did not hesitate to praise him.

To be honest, he didn't expect Xu Yuan to answer so quickly without even thinking.

All I can say is that being able to solve two difficult problems consecutively during the undergraduate stage shows that one's mathematical talent is truly something that others cannot envy.

Then Xu Yuan just returned to his seat and heard the bell for the end of get out of class ringing. The time had reached twelve o'clock.

Tang Shihong naturally had no habit of delaying the class, so he immediately announced the end of the class.

Perhaps it was because Xu Yuan's performance was too eye-catching. As soon as he packed up his things and walked out of the classroom, he saw his classmates surrounding him. They were all very enthusiastic and almost asked about his well-being.

"Do you want to go to dinner together, Xu Shen?"

"The east window on the second floor of the cafeteria has a new one. I heard it tastes good. Let's go try it."

"I'm happy to treat you today."

Xu Yuan felt everyone's enthusiasm and was at a loss whether to laugh or cry. He did not expect that it would be even more difficult to cope after the graduate students were let go.

Fortunately, just as he was thinking about how to reply, he saw a familiar figure walking towards them.

Several graduate students who had originally invited Xu Yuan to dinner immediately stood up straight and greeted him politely when they saw him coming.

"Hello, director."

"I have something to ask Xu Yuan, you guys go eat first." Liao Fangyi said to the graduate students expressionlessly. After they came to him, he looked at Xu Yuan and smiled, "Finally I found you, Xu Yuan."

"Director, do you want to talk to me about something?" Xu Yuan asked in doubt.

Liao Fangyi did not keep the question in suspense and answered Xu Yuan's question on the spot.

"It should be said that Mr. Yang wants to talk to you about something."

"Mr. Yang?!"

Xu Yuan exclaimed.

Ever since he was called to meet Mr. Yang because Wang Xiaoyun joined the Qinghua Institute for Advanced Studies, they haven't met since.

The main reason was that he was busy working on his graduation thesis during this period and could not spare the time to ask the other party about physics problems.

But he thought that Mr. Yang would not ask Liao Fangyi to call him over just for this. He thought that he must have other important matters to tell him.

So he didn't ask any more questions, replied to Liao Fangyi, and went to the office of the dean of Qinghua Institute for Advanced Studies together.

Since it was his second time there, Xu Yuan was familiar with the route. After taking some time to get there, he saw Mr. Yang sitting in his office chair.

"Xu Yuan, you came just in time. I have something to inform you."

When Mr. Yang saw Xu Yuan coming in, he immediately put on a smile and stood up, then walked over and got straight to the point.

Soon after hearing this, Xu Yuan was quite surprised. He didn't expect that Mr. Yang would give him such a surprise.

"We are going to hold a mathematics exchange event with the Chinese University of Hong Kong, and Professor Qiu specifically invited me to attend."

……

(End of this chapter)