Technology invades the modern world

Chapter 199 A Magnificent Challenge to the Limits of Human Reason (3k)

German viewers watching on television were deeply moved, feeling not just that the speech had ended, but that an epic had come to a close.

The relationship between "Carmina Burana" and Lin Ran's speech is not simply one of background and subject; they are a symbiosis of soul and form.

The solemnity and grandeur of the music reflected the milestone significance of the event, while the strong rhythm and dynamic fluctuations echoed the rhythmic rise and fall of the speech.

The repetition of the melody and the profundity of the theme allude to the persistence and eternity of mathematical exploration.

The epic feeling that German audiences experienced stemmed not only from Lin Ran's feat of proving the twin prime conjecture, but also from how "Carmina Burana" elevated this intellectual feast into a symphony about destiny, challenge, and victory.

Viewers in front of their televisions felt as if they had traveled through time and space, resonating with the Göttingen School of Mathematics, which has stood the test of time for centuries, and experiencing a true mathematical epic.

Over the next five days, the mathematicians who remained in Göttingen continued to verify Lin Ran's results.

"Randolph's thinking was very clear. From day one, his thinking was very clear. He knew exactly which methods and lemmas he would use. I think his logic was smooth and I did not find any obvious errors in his thinking."

"That's right, I didn't find any errors either."

“I agree. Randolph’s expertise in number theory is evident. Pierre and Siegel were personally responsible for testing his ideas, while we were responsible for reviewing the lemmas and tools.”

"Don't rush. The twin prime conjecture has been troubling the mathematics community for so many years. We have a responsibility to ensure that nothing goes wrong. This is a responsibility to Randolph and also to ourselves."

“I have a concern. Lemma 3 on the 15th blackboard relies on an unproven assumption.”

"This is a standard assumption in number theory, but you're right, it's not trivial."

"No, Randolph demonstrated this hypothesis on the 52nd blackboard, as a proof of a lemma of lemmas."

Fortunately, the blackboards had the days marked on them to distinguish them, and the PhD students then sorted the blackboards according to the days.

Later, in the special issue, following the same standards as on-site, in addition to the page number, there was also the day number to indicate which day of Lin Ran's work it was.

Mathematicians around the world who saw this special issue but were unable to attend in person were amazed, wondering if it was even possible for humans to produce so many results in just one day.

Over five days, the team meticulously analyzed every equation and every corollary, sometimes engaging in heated debates and sometimes reaching a consensus.

Ultimately, everyone reached a preliminary conclusion that there were no problems.

Most of the leading contemporary mathematicians present signed their names in the reviewer section and sent the manuscript to Acta Mathematica, published by the Royal Swedish Academy of Sciences.

Of the four major mathematics journals, the other three all have some degree of connection to universities.

The New Advances in Mathematics, founded by Lin Ran in this era, is backed by Columbia University and the entire New York mathematics community. In the original timeline, the New Advances in Mathematics should have been published by Springer, but the Springer version of the New Advances in Mathematics no longer exists.

The Annals of Mathematics is backed by the Institute for Advanced Study in Mathematics at Princeton, and the J. AMS is sponsored by the America Mathematical Society.

It's impossible for Europeans to solve such age-old problems in Europe and then publish them in America.

What does that make Europe?

Lin Ran had already handed over the paper publication package to Siegel.

Therefore, everyone unanimously decided to send it to Acta Mathematica, even though scholars at Columbia and Princeton strongly opposed it.

After all, this isn't America, it's Göttingen.

On January 18th, the atmosphere was tense in the editorial office of Acta Mathematica in Stockholm, Sweden. The winter afternoon was cold and gloomy, but the room was filled with a warm and enthusiastic atmosphere.

The walls are adorned with portraits of great mathematicians, the bookshelves are piled high with mathematics journals from previous years, and the room is filled with the traditional atmosphere of academia.

The long table was piled high with manuscripts and letters from all over the world, and a constantly ringing telephone.

Within the editorial staff, they viewed this as a lifeline connecting them with the global mathematics community.

At the heart of the lively atmosphere was a manuscript that arrived that day: "A Proof of the Twin Prime Conjecture," by Randolph Lin.

The famous number theory question of this century, "Does there exist infinitely many pairs of prime numbers that differ by 2?", has finally seen a breakthrough.

Over the past week, the professor's proof process has been broadcast around the world through newspapers and television, adding new topics to Lin Ran's already controversial life due to his involvement in space exploration.

To use modern methods of media manipulation, Lin Ran was incredibly skilled, and all of his skills were ruthless—the kind that others couldn't do.

As a result, the Soviet Union originally thought that everyone should pay attention to Gagarin, Gagarin's recovery, Gagarin's experiences on the moon, and Gagarin's feelings on the moon, thinking that these could become the focus of global discussion.

Gagarin should have been the focus of global attention for at least the entire year of 1965. But after only one month, the media had already stopped paying attention to Gagarin; everyone was discussing the professor, the significance of his long mathematical marathon in Göttingen, the mathematical legacy of Göttingen, and just how difficult this project was.

Even the news that the Soviet Union was actively releasing information that Gagarin would travel to Europe to give a speech as soon as he recovered failed to make headlines.

Back in the editorial office in Stockholm, Sweden
Professor Karl Lindstrom, 65, the editor-in-chief of Acta Mathematica, sat at his desk, his brow furrowed, studying Lin Ran's paper.

As a seasoned mathematician known for his rigor, Lindstrom was well aware of the importance of this moment. The editorial committee members gathered in the meeting room, many of whom had just returned from Göttingen.

This manuscript was also brought back by them.

The review team consisted of Professor Henrik Nilsson (an expert in analytic number theory) and Thomas Anderson (an expert in algebra and analysis), both of whom had just returned from Göttingen.

The two were summoned to evaluate Lin Ran's results.

Professor Henrik Nelson spoke first: "I'm sorry, but I don't think we are qualified to comment on the professor's work."

Every single name on this reviewer's list is more accomplished than me.

They unanimously agreed that the professor's findings were worthy of publication, and all we had to do was publish their opinions verbatim in our special issue.

Karl Lindstrom nodded and said, “I understand what you mean. Siegel, Pierre, Harold, Atiyah, and Andrei are among the best mathematicians of our time.”

Of course I respect them.

I also respect the professor. His expertise in number theory is beyond doubt, and the proof of Fermat's Last Theorem has become essential reading for young scholars entering the field of number theory.

But we must have our own stance. As a top-tier journal, we cannot be without our own stance.

That's why we invited the two judges who participated in the Göttingen Mathematical Epic performance.

We must include our comments as the preface to this special issue.

Thomas Anderson broke the silence: "The professor's thinking is very ingenious."

He said firmly, "He used a novel analytical method, and the logic was smooth. I didn't find any obvious errors."

Henrik leaned forward: "I agree. The professor's expertise in number theory is evident; this is the breakthrough the mathematics community has been waiting for for decades."

An assistant rushed in, carrying a stack of telegrams. "These have just arrived, messages from mathematicians all over the world. They're watching to see when we'll be able to publish Randolph Lin's proof."

Lindstrom glanced at the telegram, his expression softening slightly, and smiled, "It seems the whole world is holding its breath; we must make a decision as soon as possible."

He continued, "Gentlemen, we are not here to review the professor's results; we are not qualified to do so. Rather, we are here to write a statement as a conclusion to the professor's epic performance."

“There’s only one problem: what if the professor’s proof is found to be wrong?” Henrik cautioned.

Lindstrom shook his head: "It doesn't matter. With so many mathematical masters endorsing him, even if he's wrong, everyone's reputation will be affected."

Furthermore, even if it is indeed wrong, give the professor time to revise it; it is common for mathematical papers to be revised repeatedly.

It's just because I'd heard in the past that the professor's papers were so perfect that there was no room for revision, not only no room for revision, but also very little room for improvement.

If there are any problems this time, we can just have him fix them later.

The final editorial conclusion, drafted by Lindstrom and revised by Anderson and Henrik, is as follows:
"Randolph's proof is a milestone in the history of mathematics. With unparalleled wisdom and elegance, it solved the twin prime conjecture, a century-old problem that had plagued the field of number theory for sixty years."

This is not only the ultimate response to the question of whether there are infinitely many pairs of prime numbers that differ by 2, but also a magnificent challenge to the limits of human rationality.

Randolph's work, with its profound insights and exquisite logic, demonstrates the infinite charm of mathematics, elevates Göttingen's long mathematical tradition to new heights, and opens up unprecedented directions for future research.

His proof was like an epic performance, blending the rigor of analytic number theory with artistic creativity. Through novel analytical methods,
Randolph not only solved this classic conjecture but also provided the mathematical community with entirely new tools and perspectives. His achievements transcended mere mathematical derivation, becoming a beacon inspiring generations of mathematicians to explore the unknown. Just as the Göttingen School symbolizes resilience and continuity, Randolph's work is both a tribute to the wisdom of his predecessors and a call to future scholars.

As editors of Acta Mathematica, we are honored to witness and present this historic moment.

We unanimously agree that Randolph's testimony not only deserves to be published, but should also be presented to the world with the utmost solemnity to demonstrate its significance.

This conclusion is our tribute to Randolph Lin's outstanding achievements and our respect for all mathematicians who pursue truth.

May this achievement, like the stars, endure forever, illuminating the endless journey of mathematical exploration.

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(End of this chapter)