Chapter 199: The Magnificent Challenge At The Limit Of Human Rationality
The German audiences in front of their televisions remained unsettled for a long time; what they felt was not just the end of a speech, but the curtain falling on an epic.
The “Song of the Nibelungs” and Lin Ran’s speech were not simply a matter of background and foreground; they were a symbiosis of soul and form.
The solemn grandeur of the music highlighted the milestone significance of the event, while the intense rhythm and dynamic fluctuations echoed the ups and downs of the speech’s rhythm.
The repetition of the melody and the profundity of the theme subtly alluded to the persistence and eternity of mathematical exploration.
The sense of epic that the German audiences felt stemmed not only from Lin Ran’s feat of proving the Twin Prime Conjecture, but also from how the “Song of the Nibelungs” elevated this feast of wisdom into a symphonic movement about destiny, challenge, and victory.
The audiences in front of their televisions, through the screen, seemed to transcend spacetime, resonating with the Göttingen School that had stood unshaken for centuries, feeling a true mathematical epic.
Over the subsequent five days, the mathematicians still in Göttingen conducted demonstrations on Lin Ran’s results.
“Randolph’s approach is very clear; from the first day, his approach was clear. He knew exactly which methods and lemmas he would use. I think his logic is smooth, and I didn’t find any obvious mistakes in his approach.”
“Exactly, I didn’t find any mistakes either.”
“I agree. Randolph’s attainments in number theory are evident. With Pierre and Seagull personally responsible for checking his approach, we are reviewing the lemmas and tools.”
“Don’t rush. The Twin Prime Conjecture has troubled the mathematics community for so many years; we have a responsibility to ensure it’s flawless. This is being responsible to Randolph and to ourselves.”
“I have a worry. Lemma 3 on blackboard 15 relies on an unproven assumption.”
“That’s a standard assumption in number theory, but you’re right—it’s not trivial.”
“No, Randolph demonstrated that assumption on blackboard 52, proving it as a lemma to the lemma.”
Fortunately, the blackboards were distinguished by day numbers, and the PhDs sorted them by day numbers.
Later in the special issue, they followed the on-site standards: in addition to page numbers, day numbers indicated which day’s achievements these were from Lin Ran.
Ultimately, mathematicians around the world who saw the special issue but couldn’t attend the event were all amazed: just one day produced so many achievements—is this even human?
Over the five days, the team meticulously analyzed every equation and every inference, sometimes engaging in heated debates, sometimes reaching consensus.
In the end, everyone made a preliminary judgment that there were no issues.
Almost all the top contemporary mathematicians present left their names in the reviewer section, sending it to Acta Mathematica published by the Royal Swedish Academy of Sciences.
Among the four major mathematics journals, the other three all have university affiliations to some extent.
For instance, the New Progress in Mathematics founded by Lin Ran in this era is backed by Columbia and even the entire New York mathematics community. The New Progress in Mathematics from the original spacetime was probably published by Springer, but the Springer edition of New Progress in Mathematics no longer exists now.
Annals of Mathematics is backed by the Princeton Institute for Advanced Study in Mathematics, and J. AMS is published by the America Mathematical Society.
It can’t be that a century problem solved by Europeans in Europe gets published in America.
What would that make Europe!
Lin Ran had originally handed over the paper publication package to Seagull.
Therefore, everyone unanimously decided to send it to Acta Mathematica, despite strong opposition from scholars at Columbia and Princeton.
After all, this is not America, but Göttingen.
On January 18, the atmosphere in the Acta Mathematica editorial office in Stockholm, Sweden, was tense. The winter afternoon was cold and gray, but the room was filled with a heated atmosphere.
Portrait paintings of great mathematicians hung on the walls, bookshelves were stacked with years of mathematics journals, and the room was filled with the traditional atmosphere of academia.
The long table was piled with manuscripts, letters, and a telephone that kept ringing from all over the world.
Internally in the editorial department, they saw it as the lifeline connecting to the global mathematics community.
At the center of the heated atmosphere was a manuscript that had arrived that day: “Proof of the Twin Prime Conjecture,” authored by Randolph Lin.
This famous number theory problem from the century question—”Do there exist infinitely many prime pairs differing by 2?”—had finally seen a breakthrough.
Over the past week, the professor’s proof process had spread globally through newspapers and television, adding new topics for Lin Ran, who was already highly topical due to aerospace.
In terms of later public opinion operations, Lin Ran had too much material, and all of it was killer material—the kind others couldn’t achieve.
So much so that the Soviet Union originally thought everyone would focus on Gagarin: Gagarin’s recovery, Gagarin’s moon landing experiences, Gagarin’s thoughts on the moon—thinking these would be global discussion focal points.
At least for the whole year of 1965, the global focal figure had to be Gagarin.
But in just the first month, the media had stopped covering Gagarin; everyone was discussing the professor, the significance of the professor’s long Mathematics Marathon in Göttingen, Göttingen’s mathematical inheritance, and just how difficult this event really was.
Even the Soviet Union proactively releasing news that Gagarin would go to Europe for a speech right after recovery couldn’t claim the front-page headline.
Back to the editorial office in Stockholm, Sweden,
The editor-in-chief of Acta Mathematica was 65-year-old Professor Carl Lindström, sitting at his desk with furrowed brows, studying Lin Ran’s paper.
As a veteran mathematician renowned for rigorousness, Lindström knew the importance of this moment; members of the editorial committee gathered in the meeting room, many just back from Göttingen.
This manuscript was exactly what they had brought back.
The review team consisted of Professor Henrik Nelson (analytic number theory expert) and Thomas Anderson (expert in algebra and analysis), both just back from Göttingen.
The two were summoned to evaluate Lin Ran’s achievement.
Professor Henrik Nelson spoke first: “Sorry, I think we have no qualification to evaluate the professor’s achievement.
Every name on this reviewer list is more accomplished than me.
They unanimously believe the professor’s achievement is worthy of publication; what we need to do is publish their opinions verbatim in our special issue.”
Carl Lindström nodded: “I understand what you mean. Seagull, Pierre, Harold, Atiyah, Andrei—these are the best mathematicians of our era.
Of course I respect them.
I also respect the professor; his attainments in number theory are beyond doubt, and the proof of Fermat’s Conjecture has become required reading for young scholars entering the number theory field.
But we need to have our own attitude; as a top journal, we can’t lack our own attitude entirely.
That’s why we called in the two of you who were judges at the Göttingen mathematical epic performance.
We need to add our opinion as the preface to this special issue.”
Thomas Anderson broke the silence: “The professor’s approach is extremely ingenious.”
His tone was firm: “He used a novel analytic method, with smooth logic; I didn’t find any obvious errors.”
Henrik leaned forward: “I agree. The professor’s attainments in number theory are evident; this is the breakthrough the mathematics community has waited decades for.”
An assistant rushed in, holding a stack of telegrams. “These just arrived, messages from mathematicians around the world. They’re following us—when will Randolph Lin’s proof be published?”
Lindström glanced at the telegrams, his expression softening slightly, and smiled: “It seems the whole world is holding its breath; we must make a decision quickly.”
He continued: “You two, we’re not reviewing the professor’s result—we don’t have that qualification. We’re writing a passage as a conclusion to the professor’s epic performance.”
“There’s only one issue: what if the professor’s proof turns out to be wrong?” Henrik reminded.
Lindström shook his head: “That’s not important. With so many mathematics masters endorsing it, even if it’s wrong, everyone’s reputation will be affected together.
Besides, even if it’s really wrong, give the professor time to revise—mathematics papers going back and forth for revisions is normal.
It’s just that in the past, the professor’s papers were said to be so perfect there was no room for revision, or even much room for improvement.
If there’s an issue this time, we can just have him revise it then.”
Ultimately, the editor’s conclusion was drafted by Lindström, revised by Anderson and Henrik, as follows:
“Randolph’s proof is a monument in the history of mathematics. With unparalleled wisdom and elegance, it solves the Twin Prime Conjecture, a century problem that has troubled the number theory field for sixty years.
This is not only the ultimate response to the question ‘Do there exist infinitely many prime pairs differing by 2?’, but also a magnificent challenge to the limits of human rationality.
Randolph’s work, with its profound insight and exquisite logic, showcases the infinite charm of mathematics, elevates Göttingen’s long mathematical tradition to new heights, and opens unprecedented directions for future research.
His proof process is like an epic performance, blending the rigorousness of analytic number theory with artistic creativity. Through novel analytic methods,
Randolph not only solved this classic conjecture but also provided the mathematics community with entirely new tools and perspectives. His achievement transcends mere mathematical derivation, becoming a lighthouse inspiring generation after generation of mathematicians to explore the unknown. Just as the Göttingen School symbolizes resilience and inheritance, Randolph’s work is both a tribute to the wisdom of predecessors and a call to scholars of the future.
As editors of Acta Mathematica, we are deeply honored to witness and present this historic moment.
We unanimously believe that Randolph’s proof not only deserves publication but should be showcased to the world with the utmost solemnity to highlight its significance.
This conclusion is our tribute to Randolph Lin’s outstanding achievement and our respect to all mathematicians pursuing truth.
May this achievement shine eternally like the stars, illuminating the endless journey of mathematical exploration.”
Begging for monthly tickets; this segment concludes smoothly!
