Chapter 82 - 79: How Are Li Dong’s Grades?
Riemann? Bernhard Riemann?
Li Dong, of course, knew what that name meant.
The star student of Gauss, the Prince of Mathematics.
When you mention Riemann, if you’re a physics student, the first thing that comes to mind is definitely Riemannian geometry.
The mathematical cornerstone of Einstein’s General Relativity.
But if you’re a mathematician, the first thing you think of when you hear that name is the ultimate nightmare that has stumped countless top geniuses for over a century—the Riemann Hypothesis!
To put it bluntly, this thing is the ultimate secret behind the distribution of prime numbers.
Prime numbers are like the "atoms" of the numerical world; all integers can be formed by multiplying primes.
But on the number line, the positions where prime numbers appear seem completely random, with no discernible pattern.
Back in the day, Riemann came up with the Riemann zeta function and casually left behind a sentence.
He proposed that the real part of all non-trivial zeros of this function lies on a critical line with a value of 1/2.
If this hypothesis were proven, it would mean that those seemingly chaotic prime numbers actually have a hidden pattern behind them.
The problem was, Riemann just threw out the hypothesis without a care for the lives of those who came after him.
For over a hundred years, from David Hilbert to Godfrey Hardy, and even Sir Atiyah, how many brilliant mathematical titans have broken their teeth on this tough nut?
’Gauss, you old coot, you went through all this trouble, exploiting a bug in the group’s rules just to send me a file... Don’t tell me you want me to prove the Riemann Hypothesis?’
Li Dong swallowed hard, feeling completely unconfident.
Even if he collected the halos of all the great minds in the group and maxed out his Concentration, Logic, and Memory, he still wouldn’t be sure he could solve a Millennium Prize Problem like this!
’Fine, even if this group had some awesome function that could give me that kind of ability, but...’
Other mathematical titans have been stuck on it for over a hundred years. What about him? Could he even live to be a hundred?
’I can’t just go and fleece Mendel for all his halos, get into life sciences, and double the human lifespan just to prove a math theorem, can I?’
Li Dong’s mind raced with ridiculous complaints.
However, the mention of Riemann made Li Dong suddenly think of something. ’Wait a minute, Riemann was also a grandmaster-level figure who defined an era. With his historical status, getting into this Cyan Dragon Study Group should have been more than easy for him. How come I’ve never seen him in the group?’
Li Dong opened the group member list and carefully scrolled through it from top to bottom.
Sure enough, there was no [Bernhard Riemann].
Frowning, Li Dong continued to check against a list of historical scientists.
’Huh? The father of computer science, Alan Turing, isn’t here either?’
’Let’s see... That Indian genius who played life on cheat mode, Ramanujan, doesn’t seem to be here either!’
Li Dong wasn’t too disappointed to find that Ramanujan wasn’t in the group.
’It’s fine that he’s not here. If that guy were in the group, I wouldn’t be able to communicate with him anyway.’
Ramanujan’s math might have been incredible, but... the formulas he came up with were just too ugly! They had absolutely no mathematical beauty.
More importantly, the guy solved problems purely by intuition. If you asked how, he’d say the goddess Namar taught him in a dream. He never wrote out his derivations—completely unreasonable!
’Hmph, not even writing out the steps. People like that are the worst...’
Li Dong scoffed internally, completely ignoring how he himself had omitted eighty percent of the calculation steps on the blackboard at Jiangcheng Sixth Middle School, driving the star students below crazy.
Just as Li Dong’s expression flickered uncertainly, Sun Xiang, who was walking beside him, noticed something was off.
Sun Xiang thought Li Dong was still feeling conflicted and pressured by his earlier question.
He patted Li Dong’s shoulder.
"Li Dong, don’t feel burdened."
"What I said earlier wasn’t meant to force you to come to Zhejiang University."
"As your teacher, of course I hope you go to the school you truly want to attend."
The pat from Sun Xiang brought Li Dong back to his senses, and he immediately understood Teacher Sun’s good intentions.
’That unknown file from Gauss still has four months left to transfer. It’s useless to think so much about it now. I’ll just wait until it’s done. Maybe I’m just scaring myself for no reason?’
"It’s nothing, Teacher Sun. I just spaced out for a moment. Let’s head back to the hotel. We have to return to Jiangcheng early tomorrow morning."
The two of them walked out of the Zhejiang University Zijingang Campus side by side, melting into the Hangzhou night.
...
「The next day, at Jiangcheng Sixth Middle School, in the Advanced Class.」
Migo, sitting in the third row, had been feeling a lot of pressure lately.
The pressure wasn’t from his studies, but from his own sister, Misha.
For the past few weekends, whenever Misha had a chance, she would ask him about some of the toughest high school math problems, wanting him to help her with the solution strategies.
To Migo, those problems weren’t actually that difficult.
It was just that the concepts they tested were rather obscure and required very advanced techniques!
For example, things like the application of Taylor expansion remainders in limit problems involving inequality scaling. Even if it appeared on the college entrance exam, it would at most be the very last step of the final major question.
Migo really wanted to tell her the truth. ’Sis, studying this stuff gives you very little return for your effort.’
But he knew his sister too well; she had a strong sense of pride.
Besides, every time Misha finished asking about a problem, she would always add, "How have Li Dong’s grades been at your school lately?"
It seemed his sister had set Li Dong as her target...
As for how his grades were? When Migo thought about that, the corner of his mouth couldn’t help but twitch.
’Sis, you’re asking me how his grades are? You might as well go ask Senior Qin Yan, who just got back from the national training team!’
At that very moment, at a study desk diagonally in front of Migo’s seat,
Qin Yan was staring intently at a piece of scratch paper.
On the paper was the effective potential energy model for a "rotating loop-small ball dynamic system" that Li Dong had casually derived in the physics lab before he left for Hangzhou.
Li Dong had provided the Lagrangian and the isomorphic conclusion, but... the extremely crucial step of solving the nonlinear ordinary differential equation with elliptic integrals was missing!
Qin Yan had been trying to solve it for two whole days! He attempted to use the mathematical tools he was so proud of to fill in the missing steps, but... he was on the verge of a mental breakdown.
’Sigh, Brother Dong is really something else...’
When Li Dong first transferred to the Advanced Class, Migo, as an acquaintance, had actually admired this Brother Dong quite a bit.
But some people, when they show off to the point of complete cluelessness, become truly infuriating!
’If you’re going to solve a problem, just solve it. Why do you skip steps? And if you’re going to skip steps, why do you look at us with that ’it’s-so-obvious’ expression?’
Although Migo knew in his heart that Li Dong didn’t do it on purpose, and he didn’t hate him for it, the chosen ones of the Advanced Class had privately and unanimously formed an "Anti-Show-off Alliance."
At that moment, the math teacher, Teacher Cai, had just finished going over a practice test at the front of the class.
"You all did pretty well on that last test, but to wake up the students in our class who are preparing for the Olympiad, I have a final problem from the CMO finals a few years back. See if you have any ideas."
With that, he wrote a problem on the blackboard.
[Given a positive integer n, find the largest real number C such that for any non-negative real numbers x1, x2, ..., xn satisfying x1+x2+...+xn = 1, the following holds: Σ(1≤i
The whole class looked at the blackboard, and this time, they were truly woken up.
This type of inequality problem, finding the maximum value of a homogeneous symmetric polynomial, appeared to have few conditions, but it was often full of traps.
If you chose the wrong approach, you could fill three whole sheets of scratch paper and still not find the constant C.
Migo stared at the blackboard, his brow furrowed.
’The variables are symmetric, and it’s asking for the maximum constant C. This is essentially an extremum problem for a multivariate function on a simplex.’
He felt that he could probably solve this problem, but it would take a significant amount of time and trial and error.
Migo picked up his pen and began working on his scratch paper. ’Using the Lagrange multiplier method directly would be too computationally intensive, not a good idea... The core concept for the first step has to be the SMV theorem, or maybe try pushing the variables to the boundary, assuming only two variables are non-zero...’
Just as Migo had written down the preconditions for the local adjustment method on his scratch paper,
"Excuse me."
A familiar voice suddenly came from the classroom doorway.
Li Dong, wearing a backpack and looking travel-worn, appeared at the entrance.