After reviewing the first few problems, Professor Wang Zhong glanced at Zhang Yuan and said slowly, "Your handwriting's pretty good. Very neat. Unlike some people who use computers so much they've forgotten how to write, and end up with chicken scratch."
Xu Yunjing, standing nearby, blushed. He couldn't be talking about her, could he?
No!
He definitely meant someone else.
Wang Zhong didn't pay attention to Xu Yunjing's expression. In his view, getting the first few easy questions right was simply what any student ought to do.
He looked again. The questions of moderate difficulty were also answered correctly.
The proof was pretty good, though the approach was a little strange, not quite like the usual methods...
Still, it was correct.
Wang Zhong took a long breath and looked up at Zhang Yuan. The anger in his heart slowly faded.
Taking a closer look, the young man was actually quite handsome, and even looked a little like his father had when he was young.
The countless days and nights teacher and student had spent working hard together more than thirty years ago were long gone, yet somehow felt close enough to touch.
Time really did fly!
Old people tended to be a little nostalgic. As he reviewed the exam, he thought to himself that since the young man had answered these questions correctly and clearly had some ability, he wouldn't investigate whether Zhang Yuan had pulled strings to get in.
Among half a million people, it was impossible for every single one to be a born saint. Some habits from their time on Earth were bound to linger; they could only be corrected gradually.
If there were no human connections at all, society would be too cold and people would feel insecure. But if it became a society ruled by personal connections and rife with bureaucracy, that would be a catastrophe for civilization.
He continued reading.
Huh, those difficult questions near the end...
He got them right too!
Not bad, very impressive!
Even some fairly clever students might not be able to answer these questions correctly.
The stern expression on Wang Zhong's face began to soften, a sign that his mood was improving.
He'd misjudged the young man. With this level of ability, he had no need to pull strings. Passing the astronaut exam would be a breeze.
Seeing Professor Wang's expression soften, Xu Yunjing breathed a sigh of relief. The words "They gave you the wrong exam paper" had been stuck in her throat for ages, but she swallowed them again.
Since this guy had answered everything correctly, I probably don't need to say anything, right? Whatever!
The last question...
Hmm, this...
A fine sheen of sweat appeared on Wang Zhong's forehead, and his expression grew serious.
Xu Yunjing watched curiously from the side. She really couldn't make sense of the proof for this question. Besides, she'd been thoroughly beaten by it during the exam and hadn't been able to solve it at all.
"Did you work this out yourself?" Wang Zhong couldn't help asking.
He knew the question was his own, so there was no way the answer could have been found online.
"Yes," Zhang Yuan replied.
"Xu Yunjing, did you understand it?"
"Huh?"
Xu Yunjing froze, caught off guard by the sudden question, her mind in a muddle.
"You didn't answer this question during the exam, did you?"
She blushed and hemmed and hawed for a long while before finally managing two words.
"No."
"Zhang Yuan, explain your approach to her."
Zhang Yuan thought for a moment, then said, "This L-function we constructed has the following properties... We decompose the natural contravariant functor from the category of smooth projective varieties to H using any given special cohomology theory..."
Xu Yunjing pretended to listen attentively while sizing up the junior student she'd only just met.
When it came to mathematical thinking, excellent mathematicians all mastered several approaches.
The first approach: if a problem was difficult and couldn't be solved directly, they could try to think about an equivalent problem.
For a simple example, Fermat's Last Theorem and the Taniyama–Shimura conjecture were equivalent problems. By proving the Taniyama–Shimura conjecture, the mathematician Wiles proved the famous Fermat's Last Theorem.
The second approach: if the problem was difficult and the equivalent problem couldn't be solved either, they could try thinking about a broader problem.
What did that mean? Take Fermat's Last Theorem again. The abc conjecture was a stronger, more general conjecture. If the abc conjecture were true, Fermat's Last Theorem would be child's play—just five sentences would be enough to prove it.
It was easy to say, but difficult to do.
Most people simply solved problems without grasping the deeper mathematical principles behind them. Not everyone could apply what they'd learned to new situations.
After Zhang Yuan had explained for a while, Professor Wang nodded with satisfaction. "You understand it now, right?"
Xu Yunjing paused, then answered quietly, "Um... I think so."
"You really understand?"
Wang Zhong frowned and said slowly, "Then explain it back to me."
"..."
Blushing, she imagined ten thousand mud horses stampeding through her heart. All she could do was stick out her tongue in frustration. "...I don't really understand. Just the general idea."
As Xu Yunjing understood it, the proof for the last question used a very cutting-edge L-function. It was like flying a bomber in and suddenly dropping a nuclear bomb!
It blew the problem to smithereens...
Not only was this particular problem blown to bits; all problems of the same type were solved in one fell swoop.
This was a classic example of crushing something from a higher dimension, a display of brute force with its own kind of beauty.
Wang Zhong frowned. He knew that the graduate student he was currently supervising wasn't really a genius. Xisha University wasn't one of the top two universities, after all, so it was only natural that the students were a little less capable.
"If you don't understand, then you don't understand. No one will blame you. Don't pretend you do in the future."
He turned to Zhang Yuan. "This is a very good approach, but it's a little overkill. Have you read those papers? Motivic L-functions are cutting-edge mathematics."
Zhang Yuan said sheepishly, "I've only read some introductory material. Cutting-edge mathematics is still too difficult for me to understand. But I know the properties of these functions, so I used them without thinking."
Used them without thinking?
Xu Yunjing wondered to herself, Why can't I do that?
Professor Wang couldn't help smiling. "You used cutting-edge mathematical theory to solve an exam problem? You can use a theorem you don't understand? You trust other people's work that much? What if it's wrong?"
That was his usual way of doing things. He never praised anyone...
But in truth, he was full of admiration.
What did research require?
Innovation!
Not people who simply followed procedures and rules!
So many people were good at solving problems, yet useless when it came to actual research. They could only go around in circles within the existing framework. The moment they heard the words "cutting-edge mathematics," they had just one reaction: I can't do this. I won't understand it. It's practically gibberish!
They didn't even dare to pay attention to it. They had none of the drive to venture into the unknown and explore the mist!
"You're right..." Zhang Yuan felt that what he'd done really wasn't right.
Wang Zhong's expression softened a little. He didn't want to recklessly discourage the young man and damage his confidence. "When it comes to scholarship, you should be more rigorous. What you did isn't wrong, but it isn't rigorous enough. Still, solving the problem is better than failing to solve it, so I'll give you 99 points on this exam."
Zhang Yuan nodded, readily admitting his mistake. "I'm sorry. I studied all of this on my own. I'm well aware that my knowledge is lacking and my foundations aren't solid, which is why I want to pursue graduate studies..."
"Self-taught..."
Wang Zhong came to his senses, the words suddenly catching in his throat.
What was going on?
It suddenly came back to him. This guy was still only an undergraduate!
Before you continue