Chapter 109 - 106: I Hope You Don’t Cry Later
When Li Dong returned from Zhejiang University, Wang Hao was the only one in the dorm room.
Liu Qiang and Chen Nan were still off studying somewhere, who knows where.
Seeing Li Dong push the door open, Wang Hao put down his copy of *Algebraic Geometry* and looked at him.
But he had a strange expression on his face.
"Brother Dong, you’re back? Is everything taken care of?" Wang Hao asked tentatively.
Li Dong, looking a bit tired, nodded.
"Yeah, it’s all good. The rest is just a matter of waiting for time to verify it."
The T1 generation of the mutant Alpine Willow Chrysanthemum had successfully flowered and produced seeds. As soon as the phenotype data came in, Mendel’s century-old regret could be brought to a perfect close.
Wang Hao said, "Oh," then asked, feigning nonchalance.
"Hey, by the way, Brother Dong, I never got the chance to ask. How did you do on the math section of your college entrance exam?"
He had his own little reasons for asking this question.
Ever since he saw the zero data on Li Dong’s mobile workstation, his pride had been on the verge of collapsing.
If that was really a full-range verification, and it had reached the hundreds of billions or even higher, then Li Dong’s math skills were probably...
Li Dong was getting a cup of water. Hearing the question, he answered subconsciously.
"Oh, a perfect score."
’Just as I thought.’
Wang Hao pressed on.
"So your high school math... did you always get perfect scores?"
Only then did Li Dong find it a bit odd. He turned to look at Wang Hao.
"Yeah, always perfect scores. Haozi, why the sudden interest?"
This time, Wang Hao let out a long sigh in his heart.
It wasn’t that he was jealous of Li Dong.
Everyone who got into Yan University’s Yuanpei College was one of heaven’s chosen, all with outstanding grades.
But Wang Hao came from a background in math competitions and had even won a gold medal.
Though he was modest about it, deep down, he always felt that no one in dorm 404 was better at math than him.
But now, he was beginning to seriously doubt that.
A layman, seeing Li Dong’s program running into the hundreds of billions, might exclaim in shock.
"Brother Dong, your programming skills are insane!"
But Wang Hao, who truly understood what verifying the non-trivial zeros of the Riemann Zeta function entailed, knew better.
The underlying logic of this thing was, in fact, a mathematical algorithm.
Programming languages and the low-level memory management of C++ were merely tools to translate and execute this algorithm.
While pushing a computer’s performance to its absolute limit certainly required a high degree of computer science expertise, the core element that could brutally reduce the time complexity was still the mathematical algorithm.
"Sigh..." Wang Hao pointed to the mobile workstation on Li Dong’s desk, its lid still open, and asked in a strained voice.
"Brother Dong, that program of yours... is it really a full-range verification?"
On his way back, Li Dong had been completely preoccupied with the data from his biology experiment, thinking about how to structure his paper if he were to submit it to *Nature Plants* later.
When Wang Hao pointed it out, he finally remembered that he still had the non-trivial zero verification program running in his dorm room.
"Yes, it’s a full-range verification."
Li Dong replied hastily, forgetting about his water, and rushed over to the mobile workstation to wake the screen.
On the computer screen, the black console window was still running.
[Verified Zeros: 987,654,321,000...][Verified Zeros: 988,102,445,112...]
Nine times ten to the eleventh power!
Over nine hundred billion! It was about to break the 10^12 (trillion-level) barrier!
The moment Li Dong saw this data, he knew he had succeeded.
Using a single mobile workstation to run a full-range verification to the trillion level in just a few days—the superiority of this dimensionality reduction algorithm, derived from Riemann’s Manuscript, was now irrefutably proven!
However, as he reached for the mouse to check the specific memory stack status...
"HISSS—it’s so hot!"
The temperature of the workstation’s C-panel was alarmingly high.
And when he moved the mouse, the cursor was lagging severely.
’It must have reached the hardware’s physical limits.’
This time, Wang Hao didn’t come over to look.
He had been glancing at the data from time to time, and now he just wanted to be a quiet, blind man.
’I can’t let it run any longer. If it keeps going, I’ll even lose the earlier data.’
There were still a few key data points he hadn’t collected.
"The maximum gap between non-trivial zeros," "the maximum value of the Zeta function on the critical line," and "the extreme fluctuations of the argument function S(t)."
So, Li Dong pressed "Ctrl + C," a safe stop signal he had pre-programmed.
Then he entered a few commands: [Exporting Extreme Values to Log...]...
As the hard drive indicator light flickered, the statistical data supporting the core arguments of his paper was exported to a local .csv file.
Li Dong let out a long sigh of relief.
"All done?"
Wang Hao, the "blind man" who had been forcing himself not to look, asked in a sour tone.
Li Dong turned his head and nodded with great ease.
...
At two in the afternoon, it was time for the weekly *Advanced Algebra* class.
When Li Dong and Wang Hao walked into the large lecture hall in the Science Building just as class was starting, they assumed they would have to sit in the back again, just like last time.
But as soon as they entered, they saw two figures in the very center of the front row, waving frantically at them.
"Brother Dong! Haozi! Over here!"
Those two grinders, Liu Qiang and Chen Nan, hadn’t even returned to the dorm at noon. They had just scarfed down a few bites in the cafeteria and run straight to the Science Building to save seats.
"Not bad, Old Liu. These are great seats. We can probably see every single one of Professor Liu’s nose hairs from here,"
Wang Hao joked with a smile as he sat down.
Li Dong sat down as well and took out his textbook.
For the entire class, Professor Liu explained the direct sum decomposition of linear spaces and subspaces on the blackboard.
Sitting in the front row, Li Dong mentally admitted that Professor Liu was an excellent lecturer—his explanations were clear, logical, and made complex topics easy to understand.
But... there was just one small drawback.
He explained things in far too much detail.
’The essence of direct sum decomposition is really just an algebraic characterization of a projection operator.’
Li Dong complained silently in his head.
’If you just introduce the concept of an idempotent transformation—that is, define a linear transformation that satisfies P^2=P—and then understand it in conjunction with the complementarity of the image space and the kernel space, this proof based on basis extension becomes incredibly intuitive and concise.’
’Why bother breaking down and pulverizing an algebraic structure that you can see through with a single glance...?’
Wang Hao: ??? You tell me.
The end of class was approaching.
Professor Liu stopped and looked down at the crowd of students, their eyes shining brightly.
Everyone seemed to be following along with ease; many even wore expressions of confidence, as if to say, ’*Advanced Algebra* is no big deal.’
Professor Liu smiled faintly. This was normal. The freshmen were like this every year.
"It seems you’ve all absorbed today’s material quite well."
"In that case, let me give you a challenge problem, just as a spot check on what you’ve learned today."
"Let’s see if you’ve all truly understood direct sum decomposition."
As soon as he said this, the flock of first-year greenhorns below became eager to show off their skills in front of Professor Liu.
’Maybe I can make a good impression?’
If any sophomores or juniors had been there to see the freshmen’s expressions at that moment, they would have mocked them without mercy:
"Excited, are you? Think you’ve understood everything, no problem? Heh, we were just as naive back in our day. Just try not to cry in a little bit!"
Professor Liu turned around, picked up a piece of chalk, and with a series of SCRAPES, wrote a problem on the blackboard.
Let V be an n-dimensional linear space over a field F. Let V_1 and V_2 be two subspaces of V, such that dim(V_1) = dim(V_2).
Prove: There exists a subspace W of V such that V = V_1 ⊕ W = V_2 ⊕ W.