Somewhat Troubled, Too
"The proof for this problem is very complicated, and there's not enough space on the blackboard," Shen Qi said.
"Shen Qi, your proof is very meticulous, but the process is indeed tedious. Anyway, you've already filled a blackboard with proofs; you should at least finish it," Professor Lu said, wanting to see Shen Qi complete the proof. "How many more blackboards do you need?"
Shen Qi thought for a moment and said, "1.5 to 2 blackboards should be enough."
"Please continue your proof." Professor Lu picked up the blackboard eraser and handed it to Shen Qi, then asked the students below the stage, "Did you all understand the first part of the proof that Shen Qi wrote on the blackboard, the derivation based on Fagnano's Theorem?"
Everyone shook their heads. "We don't quite understand."
Shen Qi explained, "Once I've written all the proofs, everyone will understand."
Some people say, "The problem is, if you erase the previous proofs and continue writing the later ones, we won't remember the previous ones either."
Professor Lu suggested, "You can write down what's on the blackboard in your notebooks. You don't need to copy everything; just extract the core steps."
Which steps are the core procedures?
"This, this, and this." Shen Qi tapped on several different parts of the blackboard.
Zhou Yu'an was quick-witted; he secretly took out his phone and took a picture.
Then the other students started to follow suit and take pictures.
Professor Lu turned to face the wall, turning a blind eye. "You have 10 seconds to extract the core steps from the blackboard."
Within 10 seconds, the students in the audience saved the first part of Shen Qi's proof on the blackboard using their mobile phones.
Having a mobile phone is great; data transfer is completed in seconds.
Copying a blackboard full of mathematical symbols by hand would take several minutes, possibly more.
"Then I'll wipe it," Shen Qi said to his classmates.
Students: "Wipe."
Professor Lu turned around, Shen Qi erased the first part of the proof on the blackboard and continued his investigation.
Next, Shen Qi processed the key equations using Euler method and multiplication theorem. This was a rather complicated process, though the amount of computation was not very large. The difficulty lay in switching between the derivation logics.
The most difficult part of mathematical analysis is not the calculation itself, but the inability to calculate it, not knowing how to calculate it.
It is obvious that the integral of dx/√[X] cannot be obtained using circular or logarithmic functions. Shen Qi needs to find an algebraic relation that satisfies the equation (22).
Shen Qi transformed the coefficients and lower limit of integration in the third integral radical by summing integrals of the form ∫dx/√[R(x)], which took up half a blackboard.
When Shen Qi obtained the algebraic functions for the common lower bound and the corresponding values at the two upper bounds, the blackboard was once again filled with writing, so densely packed that not a single word could be inserted.
Shen Qi's proof has reached this point, and some clever students in the audience have already grasped the core secret.
"I see, I see."
"I should have thought of that sooner, I should have thought of that sooner!"
"Shen Qi is awesome, his methods are incredibly awesome."
"So it's... Legendre's three types of integrals!" Zhou Yu'an slapped his thigh. Who could have come up with such a proof? Even Professor Lu probably couldn't have come up with it in such a short time.
"His logic is hard to understand, but it's impressive." Ou Ye took the initiative to say something to Zhou Yu'an. Through this proof problem, she also learned something from Shen Qi.
Zhou Yu'an: "Wow, this is the first time you've said something so long to me. Let me digest this."
Ring ring.
Just then, the bell rang, signaling the end of get out of class.
Shen Qi had filled two blackboards, but his proof was still incomplete; he was just a little short of completing it.
"This..." Shen Qi was at a loss. "Class is over. Let's call it a day, Professor Lu?"
Professor Lu waved his hand. "No, class will end after the proof is complete. There are only a few steps left."
Then Professor Lu personally picked up the blackboard eraser and helped Shen Qi erase half of the blackboard. "An incomplete proof, like a novel without an ending, is equally regrettable."
"Alright." Shen Qi unleashed his ultimate move, completing the final few steps of proof on the blackboard with lightning-fast hand speed.
The chalk writing was already somewhat messy, and ∫∞∈ looked like some kind of mysterious symbol, seemingly linked to a void magic circle from another dimension.
The students from the School of Mathematical Sciences were mesmerized, even somewhat captivated.
More and more students gathered at the classroom door. They weren't from the mathematics department; they were there for class, and the next period was College English.
"Who is he?"
What is he doing?
"Is he a student?"
"What... what are all these things?"
"Scribbles?"
"Math class?"
"Isn't this Shen Qi from the School of Mathematical Sciences?"
"As expected, mathematics is almost like metaphysics. He should summon his pet beast by now, right?"
The students and onlookers at the entrance watched the commotion and discussed it animatedly.
Finally, Shen Qi completed all the proofs, which took a total of 2.5 blackboards.
"Clarification." Shen Qi said to Professor Lu.
Professor Lu said, "If Shen Qi starts from the 24th equation and uses the algebraic relationships between lyolinear integrals, you can save half a blackboard, or even more."
"Professor Lu is absolutely right. I hadn't considered things thoroughly enough." Shen Qi nodded, humbly accepting Professor Lu's advice.
"You've done a fantastic job. To come up with this proof and complete it in such a short time is something I couldn't have done thirty years ago." Professor Lu greatly admired Shen Qi. After finishing, he said to the students at the door, "Excuse me, class is about to end."
"Is the proof that the bald professor gave really that impressive?" The student at the door asked, puzzled but intrigued.
"How the hell would I know? We're liberal arts students."
"What's wrong with Shen Qi? He's only been in school a few days and he's already showing off?"
"It's just technical showing off. I can't understand a word he wrote, but he seems really impressive."
"When someone's math skills are on display, the impact is devastating."
Professor Lu then turned to the students of the School of Mathematics and said, "Time is limited, so I won't go into detail about this proof today. We'll cover it in the next class. Class dismissed."
Then the math students left, and students from the foreign language department came in for the English class.
There were no classes in the Mathematics Department and the Department of Scientific and Engineering Computing in the morning, Shen Qi walked alone toward the Mathematics Building.
Upon entering the Mathematics Department building and finding Sun Erxiong, Shen Qi offered his thoughts. "Professor Sun, I don't know many people at Yenching University, but you're the closest to me. There are some things I'd like to tell you."
Sun Erxiong: "Speak."
"Professor Sun, you asked me to go to the large lecture hall to relearn the basic courses of mathematics, such as mathematical analysis, Advanced Algebra, and Analytic Geometry. I did as you said, and after a week of practice, I feel that Professor Lu, Professor Qu, and you, Professor Sun, all teach very well, but... I'm very embarrassed." Shen Qi with some distress.
"Oh?"
"I've already studied mathematical analysis, Advanced Algebra, and Analytic Geometry on my own several times, but I understand that professors have to cater to the majority of students. It's difficult for me in large lectures; if I don't perform well, I won't be able to showcase my abilities, but if I overdo it, it might cause resentment. A week is fine, but a semester or a year, I'm afraid it will have a negative impact and be detrimental to the unity within our mathematics department."