Chapter 198: Epic Of Modern Mathematics History
At this moment, no one cares whether the result is correct or not.
All the mathematicians who witnessed this miracle emotionally believe the answer is correct.
What everyone needs now is an emotional release.
Lin Ran led the way, and everyone was already exhausted just following along and going through these ideas once.
Everyone is a mathematician, not Superman.
The content over these six days is much more exhausting than fully focusing on an entire International Congress of Mathematicians.
After all, the International Congress of Mathematicians is just about understanding properties, learning what the most outstanding mathematicians have done in the past four years that is interesting, without needing to truly understand the achievements, more like a superficial acquaintance.
But this time, although Lin Ran’s content is a classic problem in the number theory field, the methods he used involve multiple fields.
What everyone has to do is not just understand, but a lot of thinking, demonstration, and confirming whether Lin Ran’s solution is correct.
For every mathematician present, this is not just Lin Ran’s mathematics marathon, but also their own mathematics marathon running along with him.
After Lin Ran finished speaking, no one wanted to ask questions; everyone was unanimously applauding.
As for whether the final step from 246 to 2 is correct, they want to verify it slowly over the next few days.
Being able to submit to a mathematics journal within this week would already be fine.
The students who had long prepared champagne rushed in from outside upon hearing the thunderous applause, spraying it wildly at everyone present.
Trying to turn this place into a sea of joy.
Of course, not everyone lost their calmness.
Döblin’s roar rang out first:
“Wait! Stop!
Play as you want, make noise as you want, I won’t stop you from spraying champagne.
But if anyone pollutes the blackboard, don’t blame me for being rude!”
Döblin is always thinking about these blackboards.
In his view, these will later be placed in the University of Göttingen’s school history museum for outsiders to visit, as witnesses to the Göttingen mathematics school’s resurgence of glory.
Gauss’s manuscripts are in Göttingen, Hilbert’s manuscripts are in Göttingen, and now Randolph’s manuscripts are also in Göttingen.
If they are destroyed by you students’ champagne, it would really make one want to kill.
Moreover, Göttingen is about to hold the Göttingen Mathematics Marathon, and if the blackboards are gone, it would mean half the gimmick is lost.
Döblin, who is single-mindedly determined to revive Göttingen, has a clear head and is not blinded by the joy of success.
You can celebrate however you want, but the prerequisite is that the witness of Lin Ran’s miracle—the blackboards full of formulas—must be preserved for me.
Only after the blackboards are moved away does today’s celebration officially begin.
The University of Göttingen is immersed in twilight, but the assembly hall is full of champagne.
After the champagne, various wines and snacks were brought in.
“Randolph, it’s too unbelievable, we witnessed another miracle in mathematics history.
Gauss solving how to construct a regular seventeen-sided polygon with ruler and compass overnight is a story we’ve heard, but you, solving the Twin Prime Conjecture in six days, is a miracle we witnessed together.” Pierre sighed, and looked at Seagull with envious eyes, “Seagull, you’re too lucky to have Randolph inherit your mantle.”
The mentor assigned Gauss homework, Gauss solved how to construct a regular seventeen-sided polygon with ruler and compass overnight, and when Gauss submitted the homework to the mentor, the mentor was extremely excited, saying it was a two-thousand-year unsolved problem; he had accidentally mixed the note with the problem into his notebook during recent research, not expecting Gauss to solve it.
The above is a rumor active on the Chinese Internet and even the global internet.
In fact, according to Gauss’s own letter to his friend Gerling, there is a clear record of how the idea for constructing the regular seventeen-sided polygon came about:
(Note: The above content has been verified by the author at the Göttingen Digitization Center, link to Gauss’s collected works volume 10 part 1: Nachtraege zur reinen Mathematik – GDZ – Gttinger Digitalisierungszentrum
Title page of Gauss’s collected works volume 10 part 1)
Seagull laughed: “Pierre, this is fate; fate made us master and apprentice.”
Lin Ran said: “Göttingen is my blessed land; every time I’m here, I feel my inspiration bursting, ideas flowing endlessly.”
Döblin nearby listened with brightening eyes, “Professor, Göttingen welcomes you anytime.”
Fox quickly added: “Professor, if you want, we can also replicate part of Göttingen’s architecture one-to-one for you at Columbia University.”
Göttingen has fame, has history; Columbia? Has money!
As a private university taking money from Rockefeller, Columbia is never short of money.
Rich enough to invite Eisenhower, replicating a Göttingen mathematics building is a piece of cake.
Seagull and Pierre exchanged a glance, their inner thoughts the same: America’s rich people.
The world’s current rich people are not Saudi or Qatar; the biggest rich people now are America.
Lin Ran stood in the corner of the assembly hall, the most eye-catching spot in the entire venue.
If you’re not a big shot, you wouldn’t even dare to come say hello.
Paul Erdős, the slim elderly man wearing thick-framed glasses, walked with light steps.
“Randolph, you’re truly amazing!” Erdős’s voice was high-pitched, full of passion, “I’ve chased the secrets of prime numbers my whole life, and today you showed me the dawn! Tell me quickly, how did you think of using multidimensional sieve methods? How was the weight function designed?”
Lin Ran nodded slightly, raised his glass in toast, and said: “Professor Erdős, my method is inspired by your and Selberg’s work. I extended the sieve method to high-dimensional space, controlling the error term by optimizing the weight function.”
Erdős patted his shoulder: “Fantastic! We must find time to talk properly. I have a new idea; perhaps we can apply your method to the Goldbach Conjecture, what do you think?”
Lin Ran said: “I look forward to collaborating with every mathematics master, but I have to return to America tomorrow; I hope we have a chance in the future to discuss the Goldbach Conjecture.”
Erdős then realized Lin Ran was a White House Senior Official besides being a mathematician: “Randolph, I’m certain of one thing: if you devoted all your energy to mathematics, you would surely become a master even greater than Gauss.
I see hope for mathematical unification in you.
Sigh, but the current situation is clear to us all; America can’t do without you, and if you weren’t there, the White House would be anxious about the space competition.
Randolph, as a senior, I remind you: power is often poison; while the White House gives you great power, it also deprives you of your freedom.”
Erdős didn’t persuade Lin Ran to leave; he just gave a reminder.
Lin Ran could feel the other’s good intentions: “I understand, I completely understand.”
Gauss Rao, active at the Swiss Federal Institute of Technology in Zurich, focusing on analytic number theory, has great overlap with Lin Ran’s research field, so as someone working in the same direction, he is Lin Ran’s natural admirer; he first congratulated then asked:
“Professor, your proof is impressive, but I have some doubts about the control of the error term. In high-dimensional space, how do you ensure the integral converges?”
Lin Ran calmly replied: “Professor Rao, your question is key. I introduced a new weight function and utilized the extension of the theorem we discussed on the first day to ensure the error term converges. You can see the detailed derivation on my blackboard; it’s fully recorded there.”
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 very much for your invitation; you let me witness a grand performance that will go down in mathematics history. I never imagined mathematics could be presented this way.”
On site, mathematicians gathered in twos and threes chatting idly.
Not everyone is convinced, and naturally some have doubts.
Like Kurt Maller, working at the Australian National University on transcendental number theory and Diophantine approximation, who wasn’t entirely convinced; he complained to Atiyah Selberg: “Atiyah, do you really believe Randolph solved the Twin Prime Conjecture in just six days?”
Atiyah is a pioneer in analytic number theory, famous for the elementary proof of the prime number theorem and the Selberg trace formula, winning the 1950 Fields Medal; he researches sieve methods and number theory.
Plus their good relationship, that’s why Kurt specifically came to ask Atiyah.
Atiyah read his meaning: “You mean Randolph solved the Twin Prime Conjecture long ago just to perform here?”
No one would say Lin Ran’s result is wrong; Kurt isn’t questioning the result, but the process and motive.
Kurt nodded: “Yes, Randolph’s proof of the Twin Prime Conjecture is impeccable; at least from my perspective, it’s a viable path, and the analysis he used in the process is equally ingenious.
But precisely because of this, to prove the Twin Prime Conjecture, he proved a full 31 lemmas in between, made major innovations to more than five tools, and created two tools himself, all in just six days.
Six days—what does that mean? For us to prove even just one lemma might stump us for a month, or even longer.
While doing it, we find the lemma a bit difficult, even needing lemmas for lemmas; once we finally prove the lemma, it’s enough for a paper.
In six days, he achieved results that might take me twenty years and I still might not accomplish.
Don’t you think this is too outrageous?
Can the gap between genius and genius really be this vast?
Do you know what I feel? I feel like we are laborers, and Randolph is Moses.
We have to painstakingly build bridges and roads to dig a passage to reach the other shore; what Randolph needs to do is just stretch out his staff toward the sea, and the sea automatically parts to reveal a path for him.
We live in the real world, Randolph lives in a myth story; we are fortunate to be invited by Randolph to witness together a moment comparable to Moses Parts the Sea, and we should feel happy about it.”
Atiyah saw the huge blow to Kurt; everyone had been running the mathematics marathon these days without good rest, but Kurt was mentally dazed.
As if struck to the soul by Randolph’s proof.
“em I don’t know, I can’t judge if it’s a performance or real.
But you need to think about one question.” Atiyah said slowly.
Kurt asked: “What question?”
Atiyah said: “That is, whether this was proven in advance or just now.
The result is here.
Randolph is 28 years old now, that can’t be wrong; even if his actual age is a bit older than claimed, let’s say he’s 30.
He is a mathematician who at 30 completed Fermat’s Last Theorem, Fermat’s Diophantine Conjecture, the Twin Prime Conjecture, and proposed the Randolph Program.
At just 30, he has accomplished so much, problems that ordinary mathematicians couldn’t solve in a lifetime.
Even more terrifying is that the tools inside were all made by him himself, the lemmas all proven by him himself; these tools can be used elsewhere.
Honestly, any random lemma inside is enough for a top paper.
In this proof of the Twin Prime Conjecture, at least four tools are worthy of a Fields Medal.
Do you know what this means? It means regardless of whether he created this miracle in these six days.
He is the god of the mathematics field in this era, a mathematician not inferior to Gauss, the new successor of the Göttingen school.
To say more, at the end of last year Randolph hosted the unprecedented manned moon landing project; from mid-November when the manned moon landing was completed to January 10 now, at most a month and a half for him to think about the Twin Prime Conjecture.
Is there a difference between 45 days and 6 days?
So, does it matter if it’s within six days?
What’s important is that from the University of Göttingen itself to the media to the mathematics community, all hope this story is true.
You even need to know, the White House hopes it’s true; if you nitpick whether it’s true, aren’t you opposing everyone?” Atiyah is very open-minded.
Because mathematical research is not a zero-sum game; it’s not that if you eat more cake, I eat less.
On the contrary, when masters produce achievements, there are plenty of fruits for everyone to pick.
In the process of masters producing achievements, the tools they casually create can make fruits that seemed hard to pick easy to pick.
This is good for everyone.
Unless your research topic happens to collide with a master’s.
If it collides, then indeed unfortunate.
But the problem is, masters generally don’t do simple topics; even if they think of some simple topics, they leave them for students to do.
This is like not hitting small monsters but leaving them for noobs.
Kurt then woke up; Lin Ran’s behavior hasn’t affected him at all, let alone proving the Twin Prime Conjecture; even proving Goldbach would just add another legendary color to him.
Even without the Twin Prime Conjecture, wouldn’t he be legendary? Why find trouble for himself; after figuring it out, Kurt said to Atiyah: “Thanks, I understand.”
“Randolph, you did it beautifully; my life has no regrets now.”
When the crowd dispersed, only Lin Ran and Seagull remained in the corner chatting slowly; the 69-year-old Seagull sighed.
“The greatest regret of my life is not being able to help Göttingen rise again, but after this, I can clearly see the scene of Göttingen’s resurgence.
I believe even without you, Göttingen can return to the position of mathematics center in the second half of this century.
For me to be one of the most famous mathematicians of the first half of the 20th century, and to cultivate the most important mathematician of this century in the second half, my life is fulfilled.”
Seagull is very gratified; after this, who dares say Randolph is not a Göttingen student? Who dares say Randolph has nothing to do with Göttingen?
After this, Lin Ran is a legend in mathematics history; and isn’t he himself?
From a mathematician’s perspective, Seagull is indeed fulfilled, with no regrets left.
Lin Ran smiled: “Professor, it was you who helped me first.”
Seagull knew what Lin Ran meant; he was also curious about Lin Ran’s real identity and origins, but he wouldn’t ask proactively; restraining curiosity is a basic skill for successful people.
Seagull said: “This can also be considered the telepathy between master and apprentice.”
Seagull then introduced to Lin Ran their ideas about the Göttingen Mathematics Marathon.
After listening, Lin Ran smiled: “I suggest Göttingen should cooperate with the Claridge Hotel.”
Lin Ran shared his idea of enlightenment in the prime number room at the Claridge Hotel: “I suggest adding this as the final prize.
Give the medal winners a chance to spend one night in the prime number room at the Claridge Hotel.”
Seagull laughed: “Good, I’ll arrange it right away.
I believe the hotel side will be happy to see their hotel gain such extraordinary significance.”
Precisely because Lin Ran proved the Twin Prime Conjecture on site at Göttingen, the Göttingen Mathematics Marathon was later also called the Randolph Prize.
Even in China, there is an unwritten rule that students who win the Randolph Prize will definitely find a faculty position back in China after doing two years of postdoctoral research at Göttingen upon PhD graduation.
This is also known as the ultimate competition in the mathematics field, a comprehensive test of brainpower, knowledge reserve, and endurance.
If you can exclusively win that year’s gold trophy, it’s equivalent to all global universities opening their doors to you.
In the future years, mathematicians who have exclusively won the gold Randolph trophy have over 60% probability of winning the Fields Medal before age 40.
And mathematicians who sequentially won IMO gold medals and the Randolph Prize have a 100% probability of eventually winning the Fields Medal.
Seagull asked: “So, Randolph, does staying in the prime number room at the Claridge Hotel really work?”
Whether curiosity needs restraint depends on the content; this kind of curiosity doesn’t need restraint at all.
Lin Ran smiled and said: “Professor, of course it works; am I not the best example?”
Seagull thought: “No, Randolph, it’s because of you that it works.”
Seagull then leaned to Lin Ran’s ear and whispered: “Randolph, in my heart, I consider this your PhD thesis defense at Göttingen.”
Lin Ran smiled and nodded: “So, Professor, did I pass my thesis defense?”
Seagull clinked glasses with him: “Perfect.”
In the NDR Hanover branch studio, the background wall hangs portraits of mathematics giants like Gauss and Hilbert, symbolizing Germany’s profound academic heritage.
Host Anna, dressed in a deep blue professional suit, sits poised at the anchor desk, her expression solemn yet excited.
Her partner, the second-rate mathematician Klaus invited from Berlin, with graying hair and gold-rimmed glasses, sits beside her, holding a stack of notes, preparing to interpret Professor Göttingen’s proof of the Twin Prime Conjecture, this historic event.
Only second-rate mathematicians could be invited; the first-rate ones are all at the Göttingen site.
Everyone needs a final result for Lin Ran’s proof; once there is a result, they sign as reviewers and send it to the mathematics journal.
They are all eager to sign their names behind the paper; who has time to come to Hanover for a TV program.
Therefore, only second-rate mathematicians could be invited.
Anna took a deep breath, smiled at the camera, and said: “Dear viewers, welcome to tonight’s special program.
Today, we bring you news shocking the global mathematics community: Randolph Lin, in just six days, on site at the University of Göttingen assembly hall, facing mathematicians from around the world, successfully proved the Twin Prime Conjecture that has troubled mathematicians for decades!
This is a historic moment, not only of profound significance to the mathematics community, but also making Göttingen once again the focus of the mathematics world.”
Klaus continued: “Yes, Anna. The Twin Prime Conjecture is an ancient problem in number theory, proposed since ancient Greek times, but never proven.
The modern Twin Prime Conjecture was proposed by Hilbert in 1900, also a number theory problem among Hilbert’s century questions.
The professor’s breakthrough not only fills a blank in mathematics history, but is also a great tribute to the Göttingen Mathematics Master, a landmark event in the revival of the Göttingen mathematics school.”
The screen switches to historical photos and videos of the University of Göttingen, accompanied by soft background music.
Anna’s voice sounds: “Since its founding in 1737, the University of Göttingen has always been a holy land for mathematical research. Here were born mathematics giants like Gauss, Riemann, and Hilbert; their achievements laid the foundation for modern mathematics. Today, the professor, under their glorious tradition, once again makes Göttingen the center of the mathematics world.”
The lens turns to Hilbert’s portrait; Klaus adds: “Hilbert is hailed as the ‘father of modern mathematics,’ proposing numerous ideas such as invariant theory, axiomatic geometry, Hilbert space, and more.
The Twin Prime Conjecture was proposed by the University of Göttingen’s Hilbert, and 65 years later proven at the University of Göttingen by the University of Göttingen’s Randolph; history forms a closed loop here, so profoundly significant.”
Compared to the previous days’ live broadcasts that no one watched, this popular science program saw a massive influx of viewers, quickly setting a new ratings high for the channel.
The footage shot before can now all be put to use, with BGM making it extraordinarily stirring.
The BGM initially assigned internally by NDR was “Forward! Forward! Sound the Trumpets Loud,” but this music was too politically incorrect; internal employees deleted it immediately after one watch.
Too politically incorrect, and the brainwashing effect too strong.
Anna and program director Helt sighed: “If the professor were Germanic, paired with ‘Forward! Forward! Sound the Trumpets Loud’.”
Anna said Germanic, not Germany; before she finished, Helt hurriedly covered her mouth: “This video is just for us to watch; if you air it, everyone from top to bottom will be done for.”
In the end, they used the apolitical “Carmina Burana,” here referring to the cantata composed by German composer Carl Orff in 1935-1936, not the medieval poetry collection.
When Lin Ran slowly ascended the podium, the hall’s lights focused on him, and the opening “O Fortuna” of Carmina Burana erupted.
The low orchestral and choir chants rose, the solemn melody as if the god of fate whispering.
It foreshadows the extraordinary significance of this moment: this is not just a speech, but a conquest of mathematical truth, a challenge to the limits of human wisdom.
The grandeur of the music and the historicity of the event blend seamlessly here; viewers in front of the TV feel as if in an epic prologue, holding their breath awaiting the hero’s feat.
Lin Ran turns to the blackboard, chalk flying in his hand. The rhythm of Carmina Burana becomes distinct and intense here, percussion like war drums echoing the chalk tapping the blackboard.
When Lin Ran puts down the chalk, turns to face the audience, and speaks eloquently, the melody of Carmina Burana becomes smoother and more direct.
Lin Ran finishes a segment of explanation, steps into the lounge, door gently closing. The dynamics of Carmina Burana soften accordingly, gentle strings and woodwinds bringing a moment of tranquility. This brief pause doesn’t weaken the epic atmosphere but adds tension and expectation.
Mathematicians gather at the blackboard, staring at those complex formulas; though the camera can’t capture their eyes, viewers guess they are full of contemplation.
The repetition of the music melody here is perfect, as if simulating their thought processes in their minds; viewers hold their breath, awaiting the hero’s return.
Time flows in cycles.
When he writes the final symbol on the blackboard, raises his head, extends both hands signaling the proof complete, Carmina Burana reaches its climax.
The choir’s chant erupts like a flood, orchestra and percussion resounding together, like thunderous might, symbolizing the final revelation of truth.
The mathematicians in the hall stand up one after another, applause surging like tides toward the podium, heart-shaking. The music’s solemn grandeur perfectly matches this moment’s sense of victory, as if the entire history of human wisdom reaches its peak here.
Lin Ran writes furiously on the blackboard, Lin Ran speaks eloquently, Ran enters the lounge and closes the door, mathematicians gather at the blackboard staring at the boardwork; the whole process cycles repeatedly.
Finally, Lin Ran extends both hands signaling completion, mathematicians applaud in unison, Lin Ran bows in thanks.
The entire process matched with Carmina Burana makes German viewers in front of the TV feel like watching a mathematics epic.
Current TV stations can’t statistically track viewership in real time.
But from the constantly incoming calls at the backend, the ratings effect is definitely explosive.
Station manager Karl, listening to Helt’s report, laughed: “See, this is the benefit of full live broadcast; the long wait before was all for this moment.
This edited video we can sell worldwide; it’s the witness to the professor’s miracle.
What we paid is just six days of ratings.
For viewers, they have now completely forgotten the boredom of those six days, only remembering the modern mathematics epic edited now.”
Gauss’s collected works volume 10 part 1 was also thrown into the group; interested ones can join the group to check.
