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Chapter 121: Chapter 118: A Complete Subversion of the Underlying Algorithm

The latest issue of Mathematics of Computation.

As the undisputed top-tier journal in the global computational mathematics community, every new issue drew intense attention from countless top universities and research institutions.

This time, however, the eyes of mathematicians and computer science titans worldwide were glued to the issue’s Featured Article.

Not only was this paper the headline feature, but the editor-in-chief had also dedicated a significant portion of his editorial to a special commentary on it.

An Efficient Parallel Algorithm for the Batch and Rapid Evaluation of the Riemann Zeta Function on the Critical Line

Author: Dong Li

In the paper’s supplementary materials section, there was an accompanying link to a concurrently updated arXiv preprint.

The link led to a detailed supercomputer verification report.

The report showed that Brown University’s Department of Applied Mathematics had utilized the top cluster nodes of its Supercomputing Center. After running at full capacity under high pressure for three full days, they used the new algorithm from the paper to successfully verify 60 trillion non-trivial zeros of the Riemann Zeta function. Without exception, all the zeros fell on the critical line!

In the issue’s editorial, the editor-in-chief of Math. Comp., Brown University Chair Professor Su Qiwang, wrote an authoritative and weighty commentary on the paper:

”This is by no means just a leap in the number of calculated zeros; it is a complete and utter disruption of the underlying algorithm!”

”The novel integral representation logic and memory reuse mechanism demonstrated by this algorithm have implications that are by no means limited to the field of number theory.”

”In the future, it is certain to have a profound impact on high-dimensional, large-scale linear algebra operations, the solving of numerical partial differential equations, and even the fundamental architecture of modern cryptography.”

—Su Qiwang

Once the journal was published, the entire world of computational mathematics and high-performance computing (HPC) erupted.

Initially, many of the top experts in the field who saw the paper thought it was a fantasy.

If you told them it was just some deep code optimization based on the original Odlyzko-Schönhage algorithm that pushed the computational scale a bit higher, they might have grudgingly accepted it.

After all, computer hardware iterates every year, and computing power is always increasing.

But this paper proposed a completely new algorithm, one with a framework entirely different from anything before it!

It completely shattered the bottleneck of the classic algorithm that had been in use for nearly 40 years. While maintaining optimal asymptotic complexity, it compressed the constant factor of the core computation by more than two orders of magnitude, thoroughly solving the memory wall problem and parallel scaling bottlenecks of traditional algorithms!

How was that possible?

But the official endorsement from a top-tier journal and the personal commentary from Professor Su Qiwang made it impossible for anyone to ignore this paper’s existence.

Thus, top universities and national laboratories around the globe began frantically applying for time on the computing nodes of their supercomputing centers.

They wanted to personally verify if this algorithm was truly as miraculous as it claimed.

They only needed to complete a test within a sub-interval to verify the algorithm’s true efficiency and correctness.

What followed was like a relay race of celebration across the global high-performance computing community.

Major laboratories began posting mind-numbing real-world test data on academic forums and Twitter:

[14:00]: Fudan University Supercomputing Center: Successfully deployed the underlying C++ code. A single node running at full load for one hour broke the 120 billion non-trivial zero verification mark. Memory scheduling smoothness far exceeds existing classic models. Single-node efficiency perfectly matches the performance data given in the paper!

[16:30]: MIT CSAIL Lab: Multi-node concurrent test complete. A 1024-node cluster easily surpassed the 2 trillion mark in 2.5 hours. The algorithm’s parallel scaling efficiency is far superior to traditional algorithms, with a multi-node speedup ratio that is nearly linear!

[21:00]: European Max Planck Institute’s Center for Computational Mathematics: Under sustained high-pressure operation, the data curve perfectly matches the predicted trajectory from the arXiv preprint. The algorithm’s efficiency breakthrough is completely confirmed!

Everyone in the field knew that, extrapolating from this real-world efficiency, if a top-tier exascale supercomputer were deployed and given a few months of full-load runtime, this algorithm could complete a full verification of zeros on the order of 10^16—a scale that no one had dared to even imagine before.

The entire academic world was stunned into silence by this algorithm.

A freshman from Huaxia Yan University, using a completely new mathematical logic, had just wiped the floor with every computational mathematician on the planet.

The academic community was in an absolute frenzy, especially the mathematics circle within the country, which was swept up in an unprecedented celebration.

Academic group chats at major universities were buzzing with heated discussions. Amid the shock, everyone unanimously reached the same conclusion.

This year’s Salem Prize definitely wouldn’t be vacant!

Because this undergraduate from Yan University, who had appeared out of nowhere, had already locked it down!

The Salem Prize is an international award in mathematics given to young mathematicians who have made outstanding contributions to the field of analysis and related areas.

It has also long been recognized by insiders as ”the strongest indicator for the Fields Medal”!

Looking at the list of past Salem Prize winners—Charles Fefferman, Jean Bourgain, Terence Tao...—nearly every single one of these geniuses who had their names on that list went on to bag the highest honor in mathematics, the Fields Medal!

And now, a freshman from Huaxia already had one foot in this hall of gods.

Of course, there was also a group of people who sneered at this historic academic breakthrough.

They had their own ”academic arrogance.”

”Pfft, what’s the use of calculating non-trivial zeros? That stuff is so low-brow, a complete waste of computing power!”

”Exactly! Can calculating some stupid zeros change the world?”

”Professor Yi in our group is using the Yi Jing Trigrams to deduce Pi! Once we calculate Pi to its final digit, we can prove that our world is actually a giant virtual projection program!”

”The academic world today is just majoring in the minors! I already proved the Riemann Hypothesis last month using a combination of Yin-Yang and the Five Elements with quantum entanglement. I’ve already sent my eight-page paper to the Swedish Committee, and these guys are still calculating zeros. It’s ridiculous!”

The Swedish Committee is the body responsible for reviewing the Nobel Prize. The Nobel Prize... for the Riemann Hypothesis...

Mathematics and the Nobel Prize?

What a niche combination...

In the eyes of this crowd of crank scientists, Li Dong’s top-tier journal paper wasn’t even as valuable as the ”perpetual motion machine blueprints” they’d derived in their dreams last night.

...

Unlike the clamor outside, inside an office in the Yan University Science Teaching Building...

Professor Zhang sat at his desk, pen in hand, answering questions for the two freshmen in front of him.

”You see, the core of singular homology lies in using a singular chain complex that satisfies ∂∂=0 to create a functorial, solid link between the elusive homotopy invariance of a topological space and the computable, rigorously derivable algebraic structures in the category of Abel groups...”

Professor Zhang went through the derivation step-by-step on a piece of scratch paper, explaining the logic behind it as he went.

Chen Nan and Liu Qiang listened, nodding repeatedly, their eyes shining with the light of curiosity.

Seeing their enthusiasm, Professor Zhang felt a sense of gratification.

’Not bad. These two kids have a solid foundation, a strong desire to learn, and quick minds.’

’When they’re juniors, I have to recruit them into my research group for graduate studies, no matter what.’

Just as Professor Zhang was happily planning the future for these two ”promising seedlings” in his mind...

BUZZ BUZZ BUZZ.

His phone on the desk suddenly started vibrating.

Professor Zhang glanced at the caller ID. It was Professor Wang, a colleague from the same school who specialized in computational mathematics.

He gave Chen Nan and Liu Qiang an apologetic smile and answered the call.

”Hello, Old Wang, what’s up?”

”Math. Comp.?”

”A new algorithm? A headline feature in the editorial? Professor Su Qiwang from Brown University personally endorsed it?”

As Professor Zhang listened, his brow furrowed deeper and his voice grew louder unconsciously.

”Wait a minute... Who did you say the author of this paper is?”

”An undergraduate? A freshman from our university?! From Yuanpei College?”

”Named Li Dong?”

He didn’t know who Li Dong was, but the fact that he was a freshman from his own university was enough to shock him.

Holding his phone, Professor Zhang turned his head to look at Chen Nan and Liu Qiang, who were standing in front of his desk.

A second ago, in his eyes, these two boys were promising academic seedlings glowing with golden light, the future hope of the School of Mathematics.

But now...

Professor Zhang looked at the two of them again.

’It’s like... they’ve suddenly lost their appeal.’

Meanwhile, Chen Nan and Liu Qiang, standing before the desk, were completely dumbfounded.

Although they couldn’t hear what was being said on the other end of the line, they had heard every word from Professor Zhang perfectly clearly!

”Math. Comp.?”

”Yuanpei College?”

”Li Dong?”

The two stared at each other, suddenly remembering how Li Dong had told them in the dorm yesterday that his paper had been published...

”HOLY SHIT!”

’Brother Dong, when you said your paper was published, you didn’t say it was in a top international journal!’

The world seemed to go dark before their eyes. In that instant, their Dao hearts shattered, joining Wang Hao’s in pieces.

...

And at this very moment, the instigator of the colossal wave crashing over the global academic community—Li Dong.

He was currently staring, wide-eyed, at another man.

The two just stared intently at each other, neither one speaking first to break the goddamn silence.