Chapter 111 - 108: Target: Math. Comp
Li Dong returned to dorm room 404 in Building 35.
He didn’t waste any time. He stuffed his mobile workstation into his backpack, grabbing the power adapter and a few sheets of A4 paper for scratch work.
Since he was about to officially start writing the English paper on the algorithm for the non-trivial zeros of the Riemann Zeta function, his dorm room was clearly not a suitable place.
He slung the backpack over his shoulder, left Building 35, and headed to the Yuanpei Study.
Compared to the Yan University Library, which was perennially packed with people, the Yuanpei Study was much quieter.
Moreover, the campus network signal was at full strength here, providing a direct connection to all the top-tier Chinese and foreign databases purchased by the Yan University Library, which made looking up research papers very convenient.
Li Dong walked a lap around the study and found a seat in a corner with its own power outlet.
He plugged in his computer and powered it on.
At first, Li Dong had indeed considered submitting his paper directly to one of the top four journals in the mathematics world, like *Annals of Mathematics*.
But he always felt that Qin Fei wasn’t very reliable, so he did some research himself and then decisively gave up on the idea.
What was the acceptance threshold for the four top journals in mathematics?
They required solutions to major, publicly recognized problems in the mathematical community.
For instance, directly proving the Riemann Hypothesis, or making a decisive breakthrough in a core branch of the Langlands Program.
And while what Li Dong currently held was a god-tier dimension reduction algorithm from Riemann’s Manuscript, it was still, in essence, a computational method.
It didn’t provide a fundamental logical proof for the Riemann Hypothesis.
’A journal in the field of pure mathematics definitely wouldn’t work. The focus doesn’t match, and the editor would just reject it during the initial review.’
Li Dong finally set his sights on a top-tier journal sponsored by the AMS.
*Mathematics of Computation*.
Or *Math. Comp.* for short.
This journal was also considered top-of-the-line in the fields of computational number theory and algorithmic mathematics!
Many of the blockbuster papers that broke world records for zero computation had been first published in this very journal.
Having decided on the journal he would submit to, Li Dong opened the TeXstudio editor...
Although he had already rehearsed Riemann’s dimension reduction algorithm in his mind until he knew it like the back of his hand, and had even perfectly implemented it in C++, writing an academic paper was, after all, not the same as writing code comments.
He needed to seamlessly merge the 19th-century mathematical thinking from the manuscript with the modern computer science terminology of the 21st century.
He had to look up recent top conference papers for all sorts of specialized English computer terms and standard expressions for algorithmic complexity, then confirm and revise them word by word.
[Title: A New Dimension Reduction Algorithm for Multipoint Evaluation of the Riemann Zeta Function on the Critical Line]
[Abstract: This paper presents a breakthrough optimization algorithm for computing the Riemann Zeta function.]
[Compared to the traditional Odlyzko-Schönhage (OS) algorithm, this algorithm introduces a dimension reduction strategy based on Chebyshev interpolation and non-linear FFT grid expansion, successfully compressing the time complexity further from the traditional O(t^(1/2))... In a single mobile workstation environment, it completed a full and efficient verification of a hundred-billion-scale of non-trivial zeros in just 48 hours...]
Li Dong tapped away at his keyboard...
In the core section of his paper, he cited several classic papers, which naturally included Xavier Gourdon’s famous 2004 paper that set the record with 10^13 zeros.
Of course, the purpose of citing it was to elegantly demonstrate a "dimension reduction strike" in the subsequent discussion.
[Although the OS algorithm and its subsequent variations significantly improved the evaluation efficiency of the Riemann-Siegel formula, when processing extremely high-tier intervals, they are still inevitably constrained by the exponential explosion of memory fragmentation.]
[The algorithmic model proposed in this paper, however, completely circumvents this computational bottleneck by restructuring the underlying mathematical logic...]
Time ticked by, second by second.
Students in the Yuanpei Study came and went in waves, but Li Dong remained perfectly still.
Just then, a male student in a plaid shirt walked past Li Dong’s seat.
He was a third-year student from Yuanpei College and had already secured a direct-entry Ph.D. spot in the pure mathematics track at the School of Mathematics.
He had come to the Yuanpei Study today to look up some papers on homological algebra.
As he passed Li Dong’s table, his eyes inadvertently glanced at Li Dong’s mobile workstation and the screen filled with English text and mathematical symbols.
’Whoa, look at this guy. Is he writing his graduation thesis?’
’No, that can’t be right. I’ve seen most of the upperclassmen who come here regularly. Is this a freshman?’
The senior muttered to himself, his pace slowing slightly.
’FFT multipoint evaluation? Algorithmic complexity analysis?’
The student had a rough idea of what was going on.
At Yan University’s School of Mathematics, there was an unspoken hierarchy between fields.
Those in pure mathematics, like Algebraic Geometry and topology, delved into the uncharted territory of fundamental theory.
But those in computational number theory not only had to master the hardcore theories of analytic number theory but also had to tackle the tough nut of large-scale numerical computation. It was a top-tier track at the intersection of pure math and computation, a field you couldn’t touch without real ability.
’Whoa, this underclassman is actually tackling Riemann ζ-function zero computation?’
However, when he clearly saw the name of the target journal Li Dong had noted in the document’s header—*Math. Comp.*—
He stopped in his tracks. He knew very well the weight that journal carried.
As the top-tier journal for computational number theory sponsored by the AMS, forget about a freshman; even a proper associate professor or a "Thousand Talents Program" young scholar from the Yan University School of Mathematics would struggle to publish a first-author paper in it.
They would have to go through long and painful rounds of major and minor revisions, with no guarantee of acceptance.
He remembered how he had once been arrogant, riding on his competition gold medals, until he’d toiled under his advisor for two years and been rejected by top-journal reviewers so many times he began to question his life. Only then did he truly understand just how high the bar for top journals was.
’This underclassman... he probably hasn’t been beaten down by academia yet, has he?’
After muttering to himself, the senior quietly lightened his steps and walked away, not wanting to disturb Li Dong.
When he returned to his dorm after finishing his research, he pushed open the door and couldn’t help but speak to his roommate, who was busy coding.
"Can you believe it? I was just at the Yuanpei Study and saw an underclassman writing a paper to submit to *Math. Comp.* The topic was a computational algorithm for the zeros of the Riemann ζ-function."
His roommate burst out laughing.
"What’s so surprising about that? Last time, I saw an underclassman trying to prove the Riemann Hypothesis..."
Li Dong, however, hadn’t noticed the senior who had walked past him at all.
After typing out a long string of boundary conditions for the error analysis, a thought suddenly struck him...
’This algorithm can break the hundred-billion level in just a few days running on my workstation alone...’
’So what if I deployed it on a real supercomputer cluster?’
Li Dong was itching with curiosity.
’Just how many zeros can this dimension reduction algorithm calculate? Could it break the historical limits of 10^14 or even 10^15 in one go?’
He desperately wanted to know what the true limit of this algorithm was!
Moreover, a question had been lingering in his subconscious.
’Gauss’s message said I needed to increase my authority level...’
’Can I really increase my authority level just by running this algorithm from Riemann’s Manuscript to a higher order of magnitude?’
Li Dong’s brows furrowed slightly.
’Somehow, I feel like it’s not that simple.’
Just as his mind was wandering.
"Excuse me, sorry to bother you."
A gentle voice sounded beside him.
Li Dong snapped back to reality and saw a senior wearing a red armband standing by his desk.
The daily management and closing procedures of the Yuanpei Study were handled by student assistants from the college on a rotating work-study basis.
"Hey, it’s already ten o’clock at night. The study is about to close."
The student monitor pointed to the clock on the wall, offering a kind reminder.
"If you need to pull an all-nighter on your paper, you can pack up your things and go to the 24-hour reading room at the Yan University Library. That area is open all night, and you can connect to the WiFi there too."
Li Dong was taken aback for a moment and glanced at the time in the bottom-right corner of his screen.
"22:05."
"HISS— It’s this late already?"
He felt as if he had only just sat down.
"Oh, sorry, man. I didn’t notice the time. I’ll pack up right away!"
Li Dong stretched his sore neck.
’Pull an all-nighter?’
’Forget it. The core framework and algorithmic proof of the paper are basically done. The rest, like formatting and polishing, can wait until tomorrow.’
"Thanks, man. I’m not going to pull an all-nighter. I’m heading back to my dorm."