Technology invades the modern world

Chapter 198: The Epic of Modern Mathematics (7k)

At this moment, no one cares whether the result is right or wrong.

All the mathematicians who witnessed this miracle were emotionally convinced that the answer was correct.

What people need right now is emotional release.

Lin Ran led the way, and everyone was already exhausted just following along with these ideas.

We are mathematicians, not superheroes.

The content covered in those six days was far more tiring than attending an entire International Congress of Mathematicians with complete focus.

After all, the International Congress of Mathematicians is just for getting an overview of the nature of things, to learn what interesting results the best mathematicians have achieved in the past four years. It doesn't require you to really understand what they have done; it's more like a superficial understanding.

This time, although Lin Ran's content is a classic problem in number theory, the methods he used involve multiple fields.

What we need to do is not just understand, but also think extensively, demonstrate, and determine whether Lin Ran's solution is correct.

For every mathematician present, this was not just Lin Ran's mathematical marathon, but a mathematical marathon they all ran together.

After Lin Ran finished speaking, no one wanted to ask any questions, and everyone applauded.

As for whether the final step from 246 to 2 is correct, they want to verify it slowly over the next few days.

It would be good enough if we could submit the paper to a mathematics journal within this week.

The students, who had already prepared champagne, rushed in from outside upon hearing the thunderous applause and unleashed a torrent of champagne at everyone present.

They're trying to turn this place into a sea of ​​joy.

Of course, not everyone lost their composure.

Doylein's roar rang out first:
"Wait! Stop!"

Play around as you please, I won't stop you from spraying champagne.

"Anyone who dirties the blackboard, don't blame me for being ruthless!"

Doylein always kept those blackboards in mind.

In his view, these should be displayed in the University of Göttingen's history museum for outsiders to visit, as a testament to the resurgence of the Göttingen school of mathematics.

Gauss's manuscript is in Göttingen, Hilbert's manuscript is in Göttingen, and now Randolph's manuscript is also in Göttingen.

If you students ruin it with your champagne, I'll feel like stabbing someone in the face.

Moreover, Göttingen is about to host the Göttingen Mathematics Marathon, and if the blackboard is gone, the hype will be halved.

Deulin, determined to revitalize Göttingen, was clear-headed and not blinded by the joy of success.

You can celebrate however you want, but the prerequisite is that the witness to Lin Ran's miracle—you have to keep the blackboard full of formulas.

The celebration officially began once the blackboard was removed.

The University of Göttingen was bathed in twilight, but the auditorium was filled with champagne.

After the champagne was finished, various other drinks and snacks were brought in.

"Randolph, this is incredible! We have witnessed yet another miracle in the history of mathematics."

"We've heard stories of Gauss solving the problem of constructing a regular heptadecagon in a single night with only a compass and straightedge, but you, solving the twin prime conjecture in six days, is a miracle we've all witnessed." Pierre exclaimed, glancing at Siegel with envy. "Siegel, you're incredibly lucky to have Randolph inherit your mantle."

The tutor assigned Gauss homework, and Gauss spent an entire night figuring out how to construct a regular heptadecagon using only a ruler and compass. When Gauss submitted the assignment to his tutor, the tutor was very excited, saying that this was a problem that had remained unsolved for two thousand years. He said that when he was studying it recently, he had accidentally mixed a piece of paper with the problem into his notebook, and he never expected that Gauss would solve it.

The above are rumors circulating on the Simplified Chinese internet and even the global internet.

In fact, Gauss himself wrote a letter to his friend Gerling in which he clearly recorded how the idea for constructing a regular heptadecagon came about:

(Note: The above content has been verified by the author at the Göttingen Digitalization Center. The link to Part 1 of Volume 10 of Gauss's works is: Nachtraege zur reinen Mathematik - GDZ - Gttinger Digitalisierungszentrum)
(Title page of Part 1, Volume 10 of Gauss's Works)

Siegel laughed and said, "Pierre, it's fate. Fate has made us master and apprentice."

Lin Ran said, "Göttingen is my lucky place. Every time I am here, I feel that my inspiration is bursting and my thoughts are endless."

Doilyn, who was standing next to him, lit up with excitement. "Professor, Göttingen welcomes you anytime."

Fox quickly added, "Professor, if you'd like, we can also replicate a portion of the building at Columbia University, just like we did here in Göttingen."

Göttingen is famous and has history, but what about Colombia? It's rich!
As a private university that received funding from Rockefeller, Columbia University has no shortage of money.

They're so rich they could bring Eisenhower here; replicating the Göttingen Mathematics Building would be a piece of cake.

Siegel and Pierre exchanged a glance, sharing the same thought: America's dog-owning tycoon.

The biggest dog-lover in the world right now isn't Saudi Arabia or Qatar; it's America.

Lin Ran stood in a corner of the Great Hall of the People, the most eye-catching spot in the entire venue.

If you're not a big shot, you'd be too embarrassed to even say hello.

Paul Erdős was a thin, elderly man with thick-rimmed glasses and a brisk pace.

"Randolph, you are truly amazing!" Erdős's voice was high and full of passion. "I have spent my whole life chasing the secret of prime numbers, and today you have shown me the light! Tell me quickly, how did you come up with the idea of ​​using a multidimensional sieve? And how was the weighting function designed?"

Lin Ran nodded slightly, raised his glass, and said, "Professor Erdős, my method is inspired by your and Selberg's work. I extended the sieve method to high-dimensional space and controlled the error term by optimizing the weight function."

Erdős patted him on the shoulder: “Great! We need to find time to talk about this. I have a new idea that might apply your method to Goldbach's Conjecture. What do you think?”

Lin Ran said, "I look forward to collaborating with every mathematical master, but I'm going back to America tomorrow. I hope to have the opportunity to discuss Goldbach's Conjecture with you in the future."

Erdős then realized that Lin Ran was not only a mathematician but also a high-ranking White House official: "Randolph, I'm pretty sure of one thing: if you put all your energy into mathematics, you will definitely become a master even more amazing than Gauss."

I see in you the hope for a unified mathematics.

Alas, we all know the current situation. America can't do without you. If you're not there, the White House will be terrified about the space race.

Randolph, as someone who's been through this before, let me remind you: power is often poison. While the White House has given you enormous power, it has also taken away your freedom.

Erdős didn't try to persuade Lin Ran to leave; he just offered a word of advice.

Lin Ran could sense the other person's good intentions: "I understand, I completely understand."

Gauss Rao, active at ETH Zurich, focuses on analytic number theory, which largely overlaps with Lin Ran's research area. Because of this overlap, Rao is a natural admirer of Lin Ran. He also congratulated Lin Ran first and then asked:

"Professor, your proof is impressive, but I have some questions about the control of the error term. How do you guarantee the convergence of the integral in high-dimensional spaces?"

Lin Ran calmly replied, "Professor Rao, your question is crucial. I have introduced a new weighting function and utilized an extension of the theorem we discussed on the first day to ensure the convergence of the error term. You can see the detailed derivation on my blackboard; it contains the complete documentation."

Gauss Rao nodded: "Professor, okay, I will definitely study your full paper carefully. I think it should be published in a mathematics journal this week."

Thank you so much for your invitation. You've allowed me to witness a grand spectacle that will forever be etched in the history of mathematics. I never imagined mathematics could be presented in this way before.

Mathematicians were also seen chatting in small groups at the scene.

Not everyone was convinced, and naturally some people had doubts.

Kurt Mahler, who works at the Australian National University on transcendental number theory and Diophantine approximation, was not so convinced. He complained to Atiyah Selberg, "Atiyah, do you really believe that Randolph solved the twin prime conjecture in just six days?"

Atiyah was a pioneer in analytic number theory, best known for his elementary proof of the factor theorem and the Selberg trace formula, and was awarded the Fields Medal in 1950. His research focused on sieves and number theory.

Given their good relationship, Kurt specifically came to ask Atiyah about it.

Atiyah read his meaning: "Are you saying that Randolph solved the twin prime conjecture a long time ago, just to put on a show here?"

No one would say that Lin Ran's result was wrong. Kurt wasn't questioning the result; he was questioning the process and the motives.

Kurt nodded: "Yes, Randolph's proof of the twin prime conjecture is impeccable, at least from my point of view, it is a viable path, and the analysis he used in the process is equally ingenious."

Even so, in order to prove the twin prime conjecture, he proved a total of 31 lemmas, made significant innovations to more than five tools, and created two tools on his own. The whole process only took six days.

Six days—what does that mean? Proving even just a lemma could take us a month, or even longer.

As I worked on it, I found that this lemma was a bit difficult, and even required a lemma of lemmas. After finally proving the lemma, it was enough to publish a paper.

He can achieve in six days what I might not be able to do in twenty years.

Don't you think this is outrageous?

Can the gap between geniuses really be this large?
Do you know how I feel? I feel like we're the laborers, and Randolph is Moses.

We need to work hard to build bridges and roads to dig a passage to reach the other side, but Randolph only needed to stretch out his cane to the sea, and the sea automatically split in two to create a path for him to pass through.

We live in the real world, while Randolph lives in a myth. We are all fortunate to have been invited by Randolph to witness a moment comparable to Moses parting the sea; we should be happy.

Atiyah could see how devastating the blow was to Kurt. Everyone had been running a math marathon these past few days and hadn't had a proper rest, but Kurt was completely disoriented.

It was as if Randolph's proof had struck their very soul.

"I don't know, I can't tell if it's an act or real."

"But you need to think about something," Atiya said slowly.

Kurt asked, "What's the problem?"

Atiyah said, "That is, whether it was proven beforehand or it is being proven now."

The results speak for themselves.

Randolph is 28 years old now, that can’t be wrong, even if he is actually a little older than he claims to be, let’s say he’s 30.

He was also a mathematician who, at the age of 30, completed Fermat's Last Theorem, Fermat's Diophantine Conjecture, the Twin Prime Conjecture, and proposed the Randolph Program.

He's only 30 years old and he's already solved so many problems that ordinary mathematicians can't solve in their entire lives.

What's even more terrifying is that he created all the tools inside, and he proved all the lemmas himself. These tools can be used in other areas.

Frankly speaking, any one of the lemmas in it is enough to publish a top-tier paper.

At least four of the tools used in this proof of the twin prime conjecture are worthy of a Fields Medal.

Do you know what this means? It means whether or not he created this miracle in those six days.

He is a god in the field of mathematics in this era, a mathematician no less than Gauss, and a new successor of the Göttingen school. Let me say a few more words. Randolph just led the completion of the unprecedented manned lunar landing project at the end of last year. From the completion of the manned lunar landing in mid-November to now, January 10th, he had at most a month and a half to think about the twin prime conjecture.

Is there a difference between 45 days and 6 days?
So does it matter whether it's within six days?

The important thing is that everyone from the University of Göttingen itself to the media and the mathematics community hopes this story is true.

"You should even know that the White House hopes this is true. If you're going to worry about whether it's true or not, aren't you going against everyone?" Atiyah was much more open-minded.

Because mathematical research is not a zero-sum game, there is no such thing as you eating more cake and me eating less.

On the contrary, the achievements of the masters have provided a wealth of benefits for everyone to reap.

In the process of creating their masterpieces, the tools that masters casually craft can make fruits that originally seemed difficult to pick easy to harvest.

This is a good thing for everyone.

Unless your research topic happens to overlap with that of a renowned scholar.

If there's a car accident, that would be truly unfortunate.

The problem is that masters generally don't tackle simple topics. Even if they come up with some simple topics, they will leave them for their students to work on.

This is the same principle as leaving the weaker monsters for the newbies.

Kurt then realized that Lin Ran's actions had no impact on him. Proving the twin prime conjecture, or even proving Goldbach's conjecture, would only add another legendary chapter to his life.

But even without the twin prime conjecture, isn't he still a legend? Why did he go looking for trouble? After figuring it out, Kurt said to Atiyah, "Thank you, I understand."

"Randolph, you did a fantastic job. I have no regrets in my life."

After the crowd dispersed, only Lin Ran and Siegel remained in the corner, chatting slowly. The 69-year-old Siegel sighed with emotion.

"My biggest regret in life is that I couldn't help Göttingen rise again, but after this, I can clearly see Göttingen's resurgence."

I believe that even without you, Göttingen can regain its position as the center of mathematics in the second half of this century.

"To have become one of the most famous mathematicians of the first half of the 20th century, and to have nurtured the most important mathematicians of the second half of the 20th century—my life is already complete."

Siegel was pleased. After this, who would dare say that Randolph wasn't Göttingen's student? And who would dare say that Randolph had nothing to do with Göttingen?

After this incident, Lin Ran became a legend in the history of mathematics, and so did he himself.

From a mathematician's perspective, Siegel had indeed achieved his goal and had no regrets.

Lin Ran smiled and said, "Professor, you helped me in the beginning."

Siegel knew what Lin Ran was referring to, and he was also curious about Lin Ran's true identity and background, but he wouldn't ask. Restraining one's curiosity is a basic skill for successful people.

Siegel said, "This can be considered a tacit understanding between us, teacher and student."

Siegel then introduced Lin Ran to their ideas about the Göttingen Mathematical Marathon.

After listening, Lin Ran smiled and said, "I suggest that Göttingen should cooperate with the Claridge Hotel."

Lin Ran shared his thoughts from his enlightenment session in the prime number room at the Clarity Hotel: "I suggest that this be added to the final prize."

The medal winners will have the opportunity to spend a night in one of the prime rooms at the Clarridge Hotel.

Siegel laughed: "Okay, I'll arrange it right away."

I believe the hotel would be very happy to see its hotel gain this extra significance.

It was because Lin Ran proved the twin prime conjecture in Göttingen that the Göttingen Mathematical Marathon was later known as the Randolph Prize.

There is even an unwritten rule in China that students who win the Randolph Prize, do two years of postdoctoral work in Göttingen after graduating with their doctorates, will definitely be able to find a teaching position in China upon returning.

This is also known as the ultimate competition in the field of mathematics, a comprehensive test of brainpower, knowledge reserves, and endurance.

If you can win the gold medal that year, it's like having universities all over the world open their doors to you.

In the future, there is a greater than 60% chance that a mathematician who has won the gold Randolph Medal will win the Fields Medal before the age of forty.

Mathematicians who have won both the IMO gold medal and the Randolph Prize have a 100% chance of winning the Fields Medal.

Siegel asked, "So, Randolph, is staying in the prime number rooms at the Clarridge Hotel really useful?"

Whether or not one needs to restrain their curiosity when reading content is a question that absolutely does not require restraint.

Lin Ran smiled and said, "Professor, of course it's useful. Aren't I the best example?"

Siegel thought for a moment and said, "No, Randolph, it's because of you that it works."

Siegel then leaned close to Lin Ran's ear and whispered, "Randolph, I'm treating this like your doctoral dissertation defense in Göttingen."

Lin Ran smiled and nodded: "So, Professor, did I pass my thesis defense?"

Siegel clinked glasses with him: "Perfect."

In the studio of NDR Hanover, portraits of mathematical giants such as Gauss and Hilbert hang on the background wall, symbolizing the profound academic heritage of Germany.

The host, Anna, dressed in a dark blue business suit, sat upright at the anchor desk, her expression solemn yet excited.

Her partner, a mediocre mathematician from Berlin named Klaus, with gray hair and gold-rimmed glasses, sat beside her, holding a stack of notes, ready to interpret the historic event of Professor Göttingen's proof of the twin prime conjecture.

They could only invite mediocre mathematicians; the mediocre mathematicians were all present in Göttingen.

Everyone needs to reach a final conclusion on Lin Ran's proof. After that, the reviewers should sign their names and the paper should be sent to a mathematics journal.

They were all so eager to sign their names on the back of their papers that they had no time to come all the way to Hanover to participate in a television program.

Therefore, they could only hire mediocre mathematicians.

Anna took a deep breath, smiled at the camera, and said, "Dear viewers, welcome to tonight's special program."

Today, we bring you news that has shaken the global mathematics community: Randolph Lin has successfully proven the twin prime conjecture, which has puzzled mathematicians for decades, in just six days, right in the auditorium of the University of Göttingen, in front of mathematicians from all over the world!
This is a historic moment, not only significant for the mathematics community, but also bringing Göttingen back into the spotlight.

Klaus added, “Yes, Anna. The twin prime conjecture is an ancient problem in number theory, proposed since ancient Greece, but it has never been proven.”

The twin prime conjecture in its modern sense was proposed by Hilbert in 1900, and it is also one of the number theory problems in Hilbert's "Questions of the Century".

The professor's breakthrough not only fills a gap in the history of mathematics but is also a great tribute to the mathematical masters of Göttingen, marking a significant event in the revival of the Göttingen school of mathematics.

The scene then switches to historical photos and videos of the University of Göttingen, accompanied by soft background music.

Anna's voice rang out: "Since its founding in 1737, the University of Göttingen has been a mecca for mathematical research. It is the birthplace of mathematical giants such as Gauss, Riemann, and Hilbert, whose achievements laid the foundation for modern mathematics. Today, under their illustrious tradition, the professor is once again making Göttingen the center of the mathematical world."

The camera pans to a portrait of Hilbert, and Klaus adds: "Hilbert is hailed as the 'father of modern mathematics,' and he put forward a great many ideas, such as the theory of invariants, axiomatic geometry, Hilbert space, and so on."

The twin prime conjecture was proposed by Hilbert of the University of Göttingen, and proved 65 years later by Randolph of the University of Göttingen. This historical closure at that moment makes it all the more significant.

Compared to the lack of viewers during the previous days' live broadcasts, this science popularization program attracted a large influx of viewers, quickly setting a new record for the channel's ratings.

The footage taken earlier can now be put to good use, and with the background music, it sounds especially stirring and inspiring.

The earliest background music NDR used was "Forward! Forward! Sound the clarion call," but unfortunately, the music was too politically incorrect, and their employees deleted it immediately after only watching it once.

It's so politically incorrect, and the brainwashing effect is too strong.

Anna and program director Hert remarked, "If the professor were Germanic, and it were accompanied by 'Forward! Forward! Sound the trumpet!'"

Anna said "German," not "Germany," and before she could finish, Hert quickly covered her mouth: "We can just watch this video. You still want to release it? If you do, everyone from top to bottom will be finished."

Finally, the piece was accompanied by the apolitical "Carmina Burana," which refers to the suite composed by the German composer Carl Orff in 1935-1936, not a collection of medieval poems.

As Lin Ran slowly walked onto the stage, the lights in the auditorium focused on him, and the opening lines of "Carmina Burana," "O Fate," resounded loudly.

The deep orchestral music and the chorus's arias rise up, the solemn melody like the whisper of fate.

This foreshadows the extraordinary significance of this moment: it is not just a speech, but a conquest of mathematical truth and a challenge to the limits of human wisdom.

The grandeur of the music and the historicity of the event blend seamlessly at this moment, making the audience in front of the television feel as if they are in the prelude to an epic, holding their breath in anticipation of the hero's feat.

Lin Ran turned to the blackboard, chalk flying in his hands. The rhythm of "Carmina Burana" became vivid and intense at this moment, the percussion like the beating of war drums echoing the rhythm of the chalk hitting the blackboard.

When Lin Ran put down the chalk, turned to face the audience, and began to speak eloquently, the melody of "Carmina Burana" became even smoother and more direct.

Lin Ran finished his explanation and entered the lounge, the door closing softly behind him. The dynamics of "Carmina Burana" subsided, replaced by a moment of tranquility brought by gentle strings and woodwinds. This brief pause did not diminish the epic's atmosphere; rather, it added to the tension and anticipation.

The mathematicians gathered in front of the blackboard, staring at the complex formulas. Although the cameras couldn't capture their eyes, the audience guessed they were deep in thought.

The repetition of the musical melody was perfectly timed, as if simulating the thought process in their minds. The audience held their breath, waiting for the heroes to return.

Time flows by in endless cycles.

When he wrote the last symbol on the blackboard, looked up, and stretched out his hands to indicate that he was done, "Carmina Burana" reached its climax.

The chorus's arias erupted like a torrent, while the orchestra and percussion resounded like thunder, symbolizing the ultimate revelation of truth.

The mathematicians in the auditorium rose to their feet in unison, and a thunderous applause surged toward the stage, deeply moving everyone present. The solemnity and grandeur of the music perfectly complemented the sense of victory at that moment, as if the entire history of human wisdom had reached its zenith.

Lin Ran wrote furiously on the blackboard, Lin Ran talked eloquently, Ran walked into the lounge and closed the door, the mathematicians gathered in front of the blackboard and stared at the writing, the whole process was repeated continuously.

Finally, Lin Ran extended both hands to indicate that the task was completed, and the mathematicians applauded in unison. Lin Ran bowed in gratitude.

The entire process, accompanied by "Carmina Burana," made German viewers in front of their televisions feel as if they were watching a mathematical epic.

Nowadays, television stations cannot track viewership ratings in real time.

However, judging from the constant stream of calls coming in from the backstage, the viewership is definitely booming.

As the station manager, Karl, listened to Hert's report, he smiled and said, "See, this is the benefit of live streaming. All the long wait beforehand was for this moment."

We can sell this edited video all over the world; it's proof of the professor's miracles.

All we paid was six days of viewership.

For the audience, they have now completely forgotten the six days of boredom, remembering only the modern mathematical epic that has now been edited together.

　I've also shared the first part of the tenth volume of Gauss's works in the group. If you're interested, you can join the group to take a look.

　　
　
(End of this chapter)