Logic

In order to ensure that Ou Ye could fully understand his thought process and logic, Shen Qi expanded the original 100-word thesis outline to 800 words.

During the revision of the outline, Shen Qi and Ou Ye communicated frequently.

Shen Qi: "In the main body of the paper, you need to convert two quadratic forms into a sum of squares. You need to add a citation here. Ou Ye, do you know what to cite?"

Ou Ye: "Bundle."

Shen Qi: "Very good, you've made rapid progress. When summarizing, you'll also need to cite relevant information to correspond to the invariant factors mentioned earlier. Do you know what to cite?"

Ou Ye: "Collection."

Shen Qi: "Very good, you're a smart girl."

The waiter refilled Shen Qi's water, but he couldn't understand a word of what Shen Qi and Ou Ye were talking about.

When ordinary college student couples come to coffee, the most common topics of conversation are clothing, food, housing, and transportation: which restaurant has the best food, how beautiful your dress is and how it suits your style, whether it's Christmas and we should go on a trip, or just stay in a hotel locally, and so on.

The young couple drinking plain water—their daily conversations fall into a different category. Are they students from Tsinghua University or Peking University?

Among Shen Qi's peers, only Ou Ye could understand his logical theories, and Ou Ye was slowly beginning to grasp them.

Only Shen Qi could grasp the core points of Ou Ye's way of expressing himself, and Shen Qi was gradually adapting to it.

In short, the everyday conversations between these two are incomprehensible to ordinary people. Even if they could understand them, it wouldn't matter, as they wouldn't know what they were trying to do or what their purpose was.

Shen Qi paid the bill, copied the thesis outline onto a USB drive, and handed it to Ou Ye: "I'm going into seclusion. You won't see me for half a month to a month. I've delegated the class monitor duties to Zhou Yu'an. If there's anything urgent, you can call me."

Ou Ye took the USB drive and said, "One last thing."

Shen Qi said expressionlessly, "Speak."

Ou Ye: "Give me the handwritten copy of question 26."

Shen Qi remained expressionless. "Oh."

Ou Ye: "Are you crazy?"

Shen Qi gave a forced smile, "Heh."

"Hehe." Ou Ye was amused by Shen Qi, and she showed a clear smile, which was quite obvious to her.

"Look, your smile is so charming, you even have two shallow dimples. Ou Ye, why do you always have such a blank expression? Not crying, laughing, or getting excited for a long time can easily lead to facial paralysis. You should smile more often from now on, do you hear me?" Shen Qi offered his sincere advice.

Ou Ye gave a forced smile, "Oh."

"Ou Shen, I'm completely out of my element, but I admire you the most. Your original 'Oh' is so charming, I could never learn it in my entire life." Shen Qi stood up, shook his head with a smile, went back to his dormitory to get a copy of the handwritten manuscript of question 26, and handed it to Ou Ye.

The handwritten manuscript records Shen Qi's initial logical thinking and solution process, which has some reference value for Ou Ye.

In the following days, Shen Qi went into seclusion. He left his dormitory at 6 a. m. and returned at midnight. His roommates had no idea where he went or what he did.

While working out the proof for question 23, Shen Qi encountered a new problem: he needed a new method to solve the generalized nonlinear complementarity problem with linear inequality constraints.

Shen Qi pondered this problem for three days and three nights without success; he had no clue what to do.

The original problem number 23 set by Sun Erxiong was not difficult; it was simply a matter of proving a Jacobian determinant.

During 48 hours of frantic problem-solving, Shen Qi experienced his first intellectual leap. He suddenly had a brilliant idea: to hypothesize a new proof, prove the validity of this new proof, and then use that proof to find the Jacobian determinant.

Over the past three days and three nights, Shen Qi has experienced a second intellectual leap. He believes that his newly created proof still needs further refinement. While it is fine for solving problems, there are many aspects that deserve further consideration when written as a paper.

Constantly overturning and rebuilding, negating and affirming, Shen Qi would sit in a corner of Yenching University for a whole day, and then for three days and three nights straight, except for eating, sleeping and going to the toilet.

The biggest challenge for Shen Qi is whether there exists an algorithm to form a linearized quadratic model with ellipsoidal constraints for the generalized Jacobian matrix of the semi-smooth equation system based on the generalized complementarity problem.

What was originally a simple Advanced Algebra problem became increasingly complex and profoundly thought about by Shen Qi, to the point that even he himself could not solve it.

Mathematics, and all Natural Science, advance through constant overturning and re-verification.

Some succeeded and went down in history.

Someone went insane and was sent to a mental hospital.

Shen Qi was hungry; he wanted to eat.

In a daze, Shen Qi drifted to the cafeteria, to the noodle window, and waited in line for his meal.

While waiting for his meal, Shen Qi noticed a large rectangular basin inside the window, filled with many large, white steamed buns.

These steamed buns are stacked in a peculiar way, exhibiting clear mathematical arrangement characteristics.

"So, besides librarians and typists, there are also academic experts hidden among the people, including cafeteria cooks." Shen Qi couldn't help but take a few more glances at the cafeteria cook. His tall white hat highlighted his intelligence, and his bright eyes gleamed with intelligence. He must be an expert, and there must be some compelling reason why he was working in the Yenching University cafeteria.

When it was Shen Qi's turn to get his food, he took out his meal card and faced the cafeteria worker.

"Hello, student, what would you like to eat?" the driver asked with a smile, his manner very friendly.

Shen Qi wasn't in a hurry to order. He pointed to the pile of steamed buns inside the window and said, "They are non-linear."

"Absolutely, student. The big steamed buns are definitely unfilled; those with fillings are baozi," the vendor replied, then asked, "How many steamed buns do you want?"

Shen Qi humbly inquired, "Master, may I ask which prestigious university you graduated from, and which master you studied under?"

The chef revealed his educational background. "I graduated from New Oriental Culinary School, and the chef who taught me how to steam buns Li Baota."

Indeed, true masters rarely reveal their true identities easily. Shen Qi continued to probe, "You effortlessly presented the local nonlinear characteristics of the quadratic model at point xk, demonstrating a very solid theoretical foundation. Hiding in the Yanda cafeteria, you must be researching some major project. Have you made any initial progress?"

Well, another bright young man has gone mad. This isn't uncommon at Peking University. The chef didn't dare ask too many questions, focusing instead on his catering business. "Young man, are you going to buy the steamed buns or not?"

"Buy, buy five steamed buns." Shen Qi swiped his card and bought the buns.

Find a table and sit down. Shen Qi ate a large steamed bun, then tore it into four pieces.

Shen Qi's technique for tearing the steamed bun was very sophisticated, clearly calculated meticulously, with each piece of bun being almost identical in size.

Shen Qi arranged the bread fragments into three columns, representing a kind of matrix.

Observing the matrix of steamed buns on the table, Shen Qi fell into an even more perplexing logical dead end: If ▽G(x)^-1▽F(x) is a P-matrix, then my previous assumption is invalid?

Suppose that ▽G(x) is invertible, every principal minor of it is nonnegative, and every stationary point of φ satisfies H(x)=0.

Following this logical deduction, if ▽G(x)^-1▽F(x) is a P-matrix defined in Linear Algebra, then is V∈H(x) nonsingular?

This has obvious logical errors; it doesn't make sense!

Shen Qi became increasingly confused. The topic of his paper, based on question 23, became more and more profound as he explored it. He proposed a hypothesis, refuted it, proposed it again, and refuted it again.

Logic is invincible, because to defeat logic, another kind of logic is needed. Shen Qi was trapped in a dead end of logical self-consistency. He had never been so confused. He didn't know which kind of logic was truly effective.

A student couple sat at the same table, their love evident as they ate and drank from each other's milk tea.

The girl spotted Shen Qi not far away and said curiously to her boyfriend, "That person looks really strange."

The boy glanced at Shen Qi, then smiled nonchalantly, "I saw him too. He looks like a dog, a math dog."

"How did you know he was in the math department?" the girl asked.

"I'd recognize him even if he were ashes, Shen Qi." The boy, a sophomore majoring in materials science in the School of Engineering, had recently lost to Shen Qi in the 5000-meter race. "Ignore him, he's a lunatic. There's not a single normal person in the math department. Come on, let's eat, and then we'll go see a movie."

The girl didn't go to the stadium to cheer for the engineering students; she didn't know Shen Qi before, but she does now.

While eating the chicken wings her boyfriend picked up for her, the girl couldn't help but steal glances at Shen Qi. She thought that although this math geek was a bit strange, he was quite handsome and charming when he was seriously thinking about problems.