This guy is still just an undergraduate!

After reviewing the first few questions, Professor Wang Zhong glanced at Zhang Yuan and spoke slowly, "Your handwriting is quite good, very neat. Unlike some people who use computers so much they've forgotten how to write, leaving marks like a dog's scratchings."

Standing to the side, Xu Yunjing felt her face flush. Surely he couldn't be talking about her, right?

No way!

It must be someone else.

Wang Zhong paid no mind to Xu Yunjing's expression; in his view, answering the first few simple questions correctly was merely a student's basic duty.

He looked further and saw that the medium-difficulty questions were also answered correctly.

The proof was decent, though the line of reasoning was a bit strange, differing from the standard approach...

Regardless, it was still correct.

Wang Zhong took a long breath and looked up at Zhang Yuan, the anger in his heart slowly dissipating.

Looking closely, the young man actually looked quite good, rather handsome, and a bit like his father when he was young.

Those days and nights of struggling together as teacher and student over thirty years ago felt like a long, long time ago, yet also as if they were right before his eyes.

How time flies!

The elderly are always a bit nostalgic. As he reviewed the paper to this point, he thought to himself that since the questions were answered correctly and the young man clearly had some level of skill, he would stop investigating whether he had pulled strings to get in.

With 500,000 people, it was impossible for everyone to be a born saint; there would always be some residual habits from Earth that could only be corrected slowly over time.

If one were completely devoid of social graces, it would be too cold and insecure; but if it turned into a society of cronyism where bureaucracy ran rampant, it would inevitably be a catastrophe for a civilization.

He continued reading.

Huh, those difficult ones at the back...

They were correct too!

Not bad, very good indeed!

Even some of the brighter students might not necessarily be able to solve these problems.

Wang Zhong's stern face began to soften, a sign that his mood was improving.

He had misjudged the young man. With this level of ability, there was no need to pull strings at all; passing an astronaut exam should be a breeze.

Seeing Professor Wang's expression soften, Xu Yunjing also breathed a sigh of relief, swallowing back the "you gave me the wrong test paper" that had been lingering in her throat for so long.

Since this guy had already answered them correctly, I probably don't need to say anything, right? Whatever!

The last question...

Hmm, this...

A fine layer of sweat broke out on Professor Wang's head, and his expression turned serious.

Xu Yunjing watched curiously from the side; she really couldn't make heads or tails of the proof for this question. Moreover, she had been thoroughly crushed by it during the exam and hadn't been able to solve it at all.

"Did you do this yourself?" Wang Zhong couldn't help but ask.

In truth, he knew full well that he had written the questions himself, so it was impossible to find the answers online.

"Yes," Zhang Yuan replied.

"Xu Yunjing, did you understand that?"

"Ah?"

Xu Yunjing was stunned. Being suddenly called upon left her head in a mess.

"It seems you didn't answer this question during the exam."

She blushed, stammering and hedging for a long time before spitting out two words.

"I didn't."

"Zhang Yuan, you explain the problem-solving logic to her."

Zhang Yuan thought for a moment and said, "This constructed L-function has the following properties... the natural contravariant functor from the category of smooth projective varieties to H, which can be decomposed through any special cohomology theory..."

Xu Yunjing pretended to listen intently while sizing up this junior she had just met.

When it comes to mathematical thinking, excellent mathematicians master several methods.

The first method: If a problem is very difficult and cannot be solved directly, one can try to think about its equivalent problem.

To give a simple example, Fermat's Last Theorem and the Taniyama-Shimura Conjecture are a pair of equivalent problems. The mathematician Wiles proved the famous Fermat's Last Theorem by proving the Taniyama-Shimura Conjecture.

The second method: If the problem is very difficult and the equivalent problem cannot be solved either, one can try to think about a more generalized version of the problem.

What does that mean? Taking Fermat's Last Theorem as an example again, the "abc conjecture" is a stronger, more generalized conjecture than Fermat's Last Theorem. If the abc conjecture is true, then Fermat's Last Theorem is trivial, and it could be proven in just five sentences.

It is easy to say, but difficult to do.

The vast majority of people just solve problems; they don't grasp the profound mathematical essence within. Not everyone can draw inferences about other cases from one instance.

After Zhang Yuan explained for a long time, Professor Wang nodded with great satisfaction, "You understood, right?"

Xu Yunjing hesitated for a moment and replied in a low voice, "That... I think I understood."

"Did you really understand it?"

Wang Zhong frowned and said slowly, "Then repeat it back to me."

"..."

She blushed, feeling as if ten thousand grass mud horses were stampeding through her heart, and could only stick out her tongue in great distress, "...I didn't quite get it. I only understood the general idea."

According to Xu Yunjing's very reluctant understanding, the proof for the final question used a cutting-edge L-function, which was equivalent to flying a bomber and dropping a nuclear bomb!

It blew the problem to smithereens...

It wasn't just this one question that was blown to pieces; all questions of the same type were solved in one fell swoop.

This was a typical high-dimensional crushing method, filled with a violent sense of beauty.

Wang Zhong frowned, knowing that the graduate student he was currently mentoring couldn't really be considered a genius. After all, Xisha University wasn't one of the top two universities, so it was inevitable that the quality of students would be a bit lower.

"If you don't understand, then forget it. No one is blaming you; don't pretend to understand when you don't in the future."

He turned his head and said to Zhang Yuan, "A very good line of reasoning for the proof, but it's a bit of an overkill. Have you read those papers thoroughly? The motivic-L function is the most cutting-edge mathematics, isn't it?"

Zhang Yuan said sheepishly, "I've only read some introductions; cutting-edge mathematics is still too hard for me to understand. But I know the properties of these functions, so I just used them as I went along."

Used them as he went along?

Xu Yunjing muttered to herself: Why can't I just use them as I go along?

Professor Wang couldn't help but chuckle and said, "Using the most cutting-edge mathematical theory to solve a math problem on an exam? Can you just use a theorem you don't understand? You trust other people's research results just like that—what if they're wrong?"

This was his usual style; he never praised anyone, anyway...

But in reality, his heart was filled with appreciation.

What does scientific research require?

It's innovation!

Not those guys who follow the rules and stick to the beaten path!

How many people are great at solving problems but are trash when it comes to actual research? It's because they can only spin in circles within existing frameworks. The moment they hear about cutting-edge mathematics, they have only one reaction: I can't do it, I don't understand it, it's practically gibberish!

They don't even dare to pay attention to it; they completely lack the spirit to open up the unknown and explore the fog!

"You're right..." Zhang Yuan felt that he was indeed in the wrong.

Wang Zhong's expression softened slightly, not wanting to recklessly discourage him and destroy the young man's self-confidence. "When doing academic work, one still needs to be grounded. Doing it this way, while not exactly wrong, isn't solid enough. However, solving the problem is better than not solving it at all, so I'll give this exam paper 99 points."

Zhang Yuan nodded and admitted his mistake very tactfully: "I'm sorry, these are all courses I've self-studied. I deeply realize the shortcomings in my knowledge level and that my foundation isn't solid, which is why I want to pursue graduate studies..."

"Self-studied..."

Wang Zhong snapped back to reality, a sentence suddenly choking in his throat.

What is going on?

He suddenly remembered that this kid was still just an undergraduate!