Chapter 22 This guy is just an undergraduate!

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After reviewing the first few problems, Professor Wang Zhong glanced at Zhang Yuan and slowly said, "Your handwriting is quite good, very neat. Not like some people who use computers so much that they can't even write, like chicken scratch."

Xu Yunjing, standing near, blushed. Could he be talking about her?

No!

It must be about someone else.

Wang Zhong didn't pay attention to Xu Yunjing's expression. In his understanding, answering the simple initial problems correctly was something expected from a student.

Looking further, the moderately difficult problems were also answered correctly.

The solutions were well-reasoned, though the approach seemed a bit odd, not quite the conventional method...

Overall, they were still correct.

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

Upon closer inspection, this young man was quite good-looking, rather handsome, and somewhat resembled his father in his youth.

The days and nights of struggle together between teacher and student over thirty years ago had long passed, yet seemed so near.

Time flies by so quickly!

Elderly people always tend to be a bit nostalgic. As he reviewed the test paper to this point, he thought to himself, since these questions were already answered correctly, the young man had some capability, so he wouldn't investigate any longer if there had been any favoritism.

Among 500,000 people, it's impossible for everyone to be a born saint; there's bound to be a trace of Earthly habits remaining, which can only be slowly corrected in the future.

Social interactions are such that if there were none at all, it would be too cold, too lacking in security; but if it became a society ruled by human emotions, bureaucratism would prevail, which would certainly be a disaster for a civilization.

Continuing to look further.

Oh, those few harder problems…

Also correct!

Not bad, very not bad!

These problems, even some quite intelligent students might not necessarily get right.

The stern expression on Wang Zhong's face began to soften, a sign that his mood improved.

He had misjudged the young man, with this level, he didn't need any favoritism; an astronaut exam would be a breeze.

Seeing Professor Wang's expression relax, Xu Yunjing also let out a sigh of relief, swallowing back the "wrong test paper" she had been hesitant to voice for so long.

Since this guy got it right, I suppose I needn't say anything more? Whatever!

The last problem…

Hmm, this…

A fine layer of sweat appeared on Professor Wang's brow, and his expression became serious.

Xu Yunjing curiously observed from the side, but really couldn't understand the proof of this problem. Furthermore, during the exam, she was utterly defeated by it, unable to solve it at all.

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

Actually, he knew in his heart, as the questions were of his own making, the answers couldn't be found online.

"Yes," Zhang Yuan replied.

"Xu Yunjing, did you understand it?"

"Huh?"

Xu Yunjing was stunned, suddenly called upon, her mind in disarray.

"In the exam, it seems you didn't answer this problem, did you?"

With a flushed face, covering her embarrassment for a long time, she finally uttered two words.

"No."

"Zhang Yuan, tell her your problem-solving approach."

Zhang Yuan thought for a moment, and said, "This constructed L-function has the following properties… it involves mapping the category of sheaves to the contravariant functor of H, decomposing through any special cohomology theory…"

Xu Yunjing pretended to listen intently, while also eyeing her newly met junior fellow.

Speaking of mathematical thinking, excellent mathematicians master several methods.

The first method: if a problem is difficult and cannot be solved directly, one can attempt to consider its equivalent problem.

To give a simple example, Fermat's Last Theorem and the Taniyama-Shimura Conjecture are an example of equivalent problems. Mathematician Wiles proved the famous Fermat's Last Theorem by demonstrating the Taniyama-Shimura Conjecture.

The second method: if the problem is difficult, and an equivalent problem also cannot be found, one can attempt to think about a broader issue.

What does that mean? Still taking Fermat's Last Theorem as an example, the "abc conjecture" is a stronger, broader conjecture. If the abc conjecture were true, then Fermat's Last Theorem would be trivial, provable in just five sentences.

Easier said than done.

The vast majority of people just solve problems without delving into the deep mathematical essence, and drawing inferences from one example is not something everyone can do.

After Zhang Yuan explained for quite a while, Professor Wang nodded in satisfaction and asked, "Do you understand now?"

Xu Yunjing hesitated for a moment, then quietly replied, "Um... I should have understood."

"Did you really understand?"

Wang Zhong furrowed his brow and slowly said, "Then repeat it back to me."

"..."

With a blush, she felt like ten thousand grass-mud horses were galloping through her mind, feeling extremely troubled, she stuck out her tongue, "... Not entirely. I only got the gist."

According to Xu Yunjing's very reluctant understanding, the proof of the last problem used a very cutting-edge L-function, akin to piloting a bomber and suddenly dropping a nuclear bomb!

It directly blew the problem to smithereens...

Not just this problem was obliterated, but the whole category of similar problems were resolved in one fell swoop.

This was a typical high-dimensional crushing method, full of the aesthetic of sheer force.

Wang Zhong furrowed his brow, knowing that the graduate student he was currently mentoring couldn't be considered a genius. Xisha University, after all, was not among the top two universities, so it was inevitable that the quality of students was slightly lower.

"If you don't understand, just leave it at that, no one's blaming you. Don't pretend to understand when you don't in the future."

He turned back to Zhang Yuan and said, "Very good problem-solving thinking, but isn't it overkill? Have you read through those papers? Motivic-L functions, this is cutting-edge mathematics, isn't it?"

Zhang Yuan replied shyly, "I've only read some introductions. Cutting-edge mathematics is still difficult for me to understand. But since I know the properties of these functions, I just used them effortlessly."

Used effortlessly?

Xu Yunjing muttered inside: Why can't I use them effortlessly?

Professor Wang couldn't help but laugh, saying, "Using the most advanced mathematical theories to solve a math problem on a test? Can you use theorems you don't understand? Do you just trust other people's research results like that? What if they're wrong?"

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

But in reality, his heart was filled with appreciation.

What does research require?

Innovation!

Not those who stick rigidly to the norm and follow rules step by step!

How many people are great at solving problems but turn out to be trash when it comes to actual research? Because they can only circle within existing frameworks. When they hear about cutting-edge mathematics, they have only one response: I can't do it, I can't understand it, it's like a heavenly book!

They don't even dare to pay attention to it, let alone possess the spirit of exploring the unknown, unraveling the mysteries!

"You're right," Zhang Yuan felt he was indeed at fault.

Wang Zhong's expression became slightly gentler, cautious not to indiscriminately dampen the young man's confidence, "In academics, one should be more down-to-earth. Although doing so can't be considered wrong, it isn't very solid. However, solving the problem is better than not solving it at all, so for this exam paper, I'll give you 99 points."

Zhang Yuan nodded understandingly, acknowledging his mistake, "I'm sorry, I self-studied these courses. I deeply understand my own lack of knowledge, my foundation is not solid, which is why I want to pursue further studies..."

"Self-study..."

Wang Zhong snapped back, a statement caught abruptly in his throat.

What was going on?

Suddenly, he remembered, this fellow was just an undergraduate!

…

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