Chapter 170 - 166: This Isn’t Scientific
Li Dong stood at the lectern, looking down at the university students whose eyes were filled with a thirst for knowledge. Some of them were already starting to yawn.
’It must be because I was too late,’ he thought, feeling a pang of guilt. ’Everyone’s gotten tired of waiting...’
So, he decided to skip the pleasantries and get right to it.
"Today, I’d like to start by talking about prime numbers."
Li Dong wrote a string of numbers on the whiteboard behind him: 2, 3, 5, 7, 11... 23, 29...
"These are all prime numbers."
"They can only be divided by 1 and themselves. In the world of integers, they’re the most stubborn bunch."
A few soft chuckles rippled through the audience.
"But the question is, how are they distributed?"
Li Dong looked at the audience.
"Look at this string of numbers. 2 and 3 are right next to each other, and 3 and 5 are very close too. But between 23 and 29, the gap suddenly widens to six."
"As we go further, the gaps between primes become larger and more erratic."
"It’s as if God casually scattered a handful of beans—some places dense, some places sparse, seemingly without any pattern."
He paused.
"But is there truly no pattern at all?"
Li Dong wrote a function on the whiteboard.
ζ(s)=Σ 1/nˢ
"In 1859, Riemann told us that the secret to the distribution of prime numbers is hidden within the zeros of this function."
"This function is called the Riemann zeta function."
He pointed at the summation symbol.
"Its definition is very simple: just sum the reciprocals of all positive integers raised to the power of s. It’s addition so simple even a grade-schooler could understand it."
"And yet, this simple sum has tormented the entire mathematical world for over one hundred and sixty years."
The graduate students in the audience began to nod repeatedly.
They had all encountered this material before, but Li Dong’s explanation was just so accessible.
Instead of immediately bombarding them with a wall of symbols, he laid out the problem as clearly as if he were telling a story.
A graduate student, sitting toward the middle of the auditorium, whispered to the person beside him.
"Hey, I think he’s explaining this really well."
"This guy’s the real deal."
The surrounding undergraduates who were just auditing the class were also surprised.
’Huh? Maybe... this isn’t so hard after all?’
Even Lin Xue, sitting in the third row, thought to herself, ’Hey, I think I can actually understand this.’
Li Dong, on stage, looked at the receptive faces in the audience and felt a warm glow inside.
It wasn’t like at Seventh Middle School, where the students would just stare at him with dead eyes whenever he explained a math problem.
’Zhejiang University really is a great school,’ he thought.
His confidence surged, and he started to delve deeper into the topic.
"Alright, since we’re on the topic of the zeta function’s zeros, let’s talk about what those zeros actually look like."
Li Dong drew a vertical dashed line on the whiteboard.
"This is the critical line, Re(s) = 1/2."
"The Riemann Hypothesis states that all non-trivial zeros of the zeta function lie on this line."
He dotted a few points on the dashed line.
"The first zero is located at imaginary part 14.134..., the second at 21.022..., the third at 25.010..."
"To date, the most handsome person alive has verified the first 10²³ non-trivial zeros."
Li Dong ignored the whispers from the audience calling him shameless and continued.
"That’s an astronomical number—a one followed by twenty-three zeros—and every single one of them falls obediently on this line. Not one of them has wandered off."
He paused for a moment here.
"But have you ever considered a deeper question?"
"We know these zeros lie on the line."
"But what about the distribution of the gaps between them?"
"The gap between 14.134 and 21.022 is about 6.9, while the gap between 21.022 and 25.010 is only about 4... Is there some statistical law governing these spacings?"
Li Dong spoke at a measured pace, but every sentence was a hook, reeling in the audience’s attention.
"In 1973, Montgomery provided an answer."
He wrote the definition of the pair correlation function on the whiteboard.
The expression for F_T(α), the weight function w(u) = 4/(4+u²), the normalization process...
"Montgomery proved that for |α|
"What does this mean?"
Seeing that no one in the audience spoke, Li Dong continued.
"It means that the distribution of prime numbers and the distribution of particle energy levels in quantum physics follow the same mathematical law."
"God used the same hand to scatter both sets of beans."
The auditorium fell silent for two seconds.
Then, for reasons they couldn’t quite explain, several graduate students felt goosebumps prickle their skin.
’Prime numbers and quantum mechanics? The same hand?’
They were starting to wonder if God might actually exist...
The undergraduates were starting to get lost, but they couldn’t help but feel... they had to keep listening.
A few even secretly pulled out their phones and started recording.
Li Dong didn’t notice any of this. He was completely lost in the joy of teaching.
He pressed on, now completely forgetting Professor Cai Tianxin’s advice: "Don’t go too deep..."
"Montgomery proved the case for |α|
"For fifty-three long years, number theorists the world over have thrown themselves at this problem, yet none have managed to break past this theoretical impasse."
"But I did."
He said it plainly, with no intention of showing off. He was simply informing these graduate students—most of them older than him—of the latest cutting-edge results.
But some in the audience who were unaware of the context gasped, unsure for a moment whether to believe him.
Of course, those who had seen the paper on arXiv knew it was almost certainly true. After all, not a single major figure in the field had come forward to call it nonsense.
Li Dong started writing formulas on the whiteboard.
"My proof is divided into four parts."
Starting with the Riemann explicit formula, he deconstructed the contributions of the zeros and the prime powers term by term.
...
Line after line of formulas filled the board.
Each step of the derivation was clean and efficient, with no extraneous symbols or redundant calculations.
Then he began to discuss the interval of |α| from 2 to 3 and the contribution of prime squares.
Then, for the interval from 3 to 4, the contribution of prime cubes combined with a Fourier optimization framework...
By this point, the audience had begun to split.
The undergraduates were completely lost, but strangely, not a single one of them left.
They were having an experience unlike any other.
Even though they couldn’t understand the meaning of each symbol, they could feel the rhythm flowing between the formulas.
They couldn’t bring themselves to leave!
Because humanity had spent a hundred and sixty years just to touch the edge of this problem.
And now, this young man on stage, not even twenty years old, was sketching it out for them with a piece of chalk.
The graduate students were still holding on.
They could follow about seventy percent of the derivation. While some of the leaps in logic would require further thought later, they were able to grasp the overall framework.
But the more they grasped, the more shocked they were.
Because Li Dong’s train of thought...
...was something they had never even conceived of.
Sitting in the first row, Cai Tianxin and Xu Hongwei glanced at each other, both seeing deep surprise in the other’s eyes.
They had read the paper Li Dong posted on arXiv about Montgomery’s Conjecture on Association.
It wasn’t just them; many of the top mathematics professors in the country had read it.
And they all thought they had understood it.
But now, listening to Li Dong explain it...
...it seemed they hadn’t truly understood it at all.
How could one describe the feeling?
It was as if the result was the same, the destination identical.
But the path taken was completely different.
When modern number theorists read the paper, it was like taking a high-speed train to the destination.
The scenery flashed by, every stop was predictable, and the arrival was on schedule.
But the line of thought Li Dong was presenting on stage today...
...was like riding in a horse-drawn carriage.
He was using the methods of the nineteenth-century masters.
Riemann’s explicit formula, Chebyshev’s estimations, the Hardy-Littlewood circle method...
All of them were the most classic, most foundational tools of number theory.
No safety net from the theory of automorphic forms, no technical shortcuts from spectral decomposition, not even any of the sieve method variations developed in the twenty-first century.
It was all just brute-force calculation.
But the problem was...
...his horse-drawn carriage was faster than a high-speed train.
Because it wasn’t being pulled by horses.
It was being pulled by a unicorn.
Modern methods were developed precisely because classical methods had run out of steam.
The remainder terms were uncontrollable, the estimates weren’t precise enough, and ultimately, one had to resort to more abstract, higher-dimensional algebraic tools to circumvent the obstacles.
It was like building a high-speed railway: when you hit a mountain, you dig a tunnel; when you cross a river, you build a bridge.
It consumed immense time and resources, but at least it got you to your destination.
Classical methods, on the other hand, were like a horse-drawn carriage on an old road. You had to go over any mountains and wade through any rivers.
It was too slow and too exhausting, so everyone abandoned it.
But Li Dong’s carriage could fly...
How do you even argue with that?
Mountains? Rivers? They might as well not have existed. It just flew right over them.
And that was what truly shocked Cai Tianxin and Xu Hongwei.
It wasn’t that Li Dong had used classical methods to achieve a result that modern methods could not.
It was that Li Dong had made classical methods themselves radiate a power they should not possess.
It wasn’t logical.
But that’s exactly what was happening.
This was the part they hadn’t truly grasped from the paper.
A path everyone had thought was a dead end for ages.
Li Dong hadn’t just walked it; he had turned it into a breathtaking spectacle.
Xu Hongwei took a deep breath and glanced at Guan Yi in the third row.
Guan Yi’s expression was calm.
But Xu Hongwei knew his student.
That calm wasn’t composure.
It was the stillness of being utterly stunned.
...
「On the other side of the world.」
Late at night, Arthur Penrose sat on his sofa at home, watching a livestream on his phone.
Liu Ruochuan had told him in advance that Li Dong was giving a public lecture at Zhejiang University and asked if he wanted to watch it remotely.
Penrose had immediately said, "Of course."
Now, he was muttering to himself.
"Yes... yes, that’s it. It’s the exact same feeling..."
"I had this same feeling when I listened to his report at the ICCM..."
"This train of thought... it’s so much like the nineteenth-century masters."
He recalled how he felt the first time he read Li Dong’s paper. The feeling had been strange. The conclusion was correct, and the derivation was rigorous, but something had always felt... different.
Not that it was wrong, but... the style.
"Incredible."
Penrose said softly.
Then he picked up his phone and sent a message to someone far away in Los Angeles.
"Terry, are you watching the Zhejiang University livestream?"
A reply came a few seconds later.
"Watching now."
"Thinking the same thing I am?"
"Even more incredible than I imagined."
Terry sent another message.
"Classical thinking with modern tools. I finally understand how he wrote that paper."
Penrose smiled.
He was looking forward to his trip to Yan University more and more.