Chapter 214: Goldbach Conjecture
Another New York Mathematicians’ Banquet.
This year, no matter how much Lin Ran declined, everyone insisted he come on stage to say a few words.
After all, this year’s Göttingen miracle in January wasn’t something everyone had the time and energy to travel thousands of miles to witness in person.
Whether they went to the scene, watched the live broadcast on television, or purchased the video tape from Science Press, everyone had seen Lin Ran’s heroic performance dazzling in Göttingen.
This time, no matter what, they wouldn’t let Lin Ran refuse.
No matter how much you say you want to give young people an opportunity, and that everyone’s attention is focused on you, that won’t work; you must speak this year, either opening or closing.
Harvey Cohen was extremely earnest when communicating with Lin Ran: “Professor, if you don’t speak, my promise is useless; the mathematicians present won’t agree.
They’re all waiting to hear your teaching.”
He had no choice but to listen. Leaving aside how effective the tools Lin Ran’s achievements in number theory this year provided to PhD students working in number theory—benefiting all mathematicians—just at last year’s International Congress of Mathematicians, the approach Lin Ran proposed to solve the Four Color Problem had already been solved by Columbia University mathematicians.
Is there a second big shot like Lin Ran, who can build wheels for everyone and casually give away his own ideas for solving problems?
If it were other mathematicians, even if they were so generous, they’d give at most a rough idea; how could they be like Lin Ran, handing you a complete approach?
The stingier ones treasure even a casual idea of their own, only sharing it when they really can’t refuse.
No comparison, no harm.
With so many comparative cases ahead, it’s enough to show Lin Ran’s generosity.
Personal fame is also an important factor.
Harvey Cohen continued: “Do you remember Chen? The student you had in Hong Kong.”
His own student, so definitely not Shiing-Shen Chern.
Lin Ran nodded: “Of course. I recommended him to you because he has great talent.”
Harvey Cohen smiled: “You’re right; he does have great talent. He made important achievements around the Goldbach Conjecture; it’s a major work.
Internally at New York City University, we’ve judged that this result is enough to advance the current work around the Goldbach Conjecture by a big step.”
Lin Ran understood; it should be the “1+2” of the Goldbach Conjecture that was proven. Calculating the timeline, it was about right.
In the original spacetime, Chen Jingrun’s achievement was published in 1966.
Lin Ran had read Chen Jingrun’s published paper. He came to New York at the end of 1960; calculating it, it was about five years of doctoral career, during which he published some mathematics papers.
Compared to sieve method specialization, the current Chen Jingrun clearly mastered more tools and was adept in the analytic number theory field.
“Good, so your meaning is that at the New York Mathematicians Conference, he’ll give an academic report around his own achievement, right?” Lin Ran asked.
Giving a report at the New York Mathematicians Conference was a burden for him, but for other mathematicians, it was absolutely an honor.
In terms of difficulty, it wasn’t much less than giving a report in the main hall of the International Congress of Mathematicians.
After all, the New York Mathematicians Conference was only one day, inviting at most three mathematicians to report; the International Congress of Mathematicians lasted at least seven days.
Harvey Cohen nodded: “Right, Chen’s report will be after yours.
My meaning is, Professor, you don’t necessarily have to open or close.
If you want to challenge human limits, and perform a complete on-site proof of the Goldbach Conjecture at this year’s New York Mathematicians Conference, I can also put your report time after Chen’s.”
Harvey Cohen blinked, his face full of expectation.
Lin Ran smiled wryly: “Professor Cohen, I’m human, not a god.
Proving the Goldbach Conjecture on site, with only one day, is impossible no matter what.”
Harvey Cohen said: “Professor, if it could really be proven, I think no matter who, they wouldn’t mind extending this year’s New York Mathematicians Conference to a week or even longer.
Of course, even longer, we wouldn’t mind waiting.
Our colleagues have enough patience to witness the miracle with their own eyes.
I’m just afraid the White House can’t wait and will send someone to New York to invite you back.”
After Harvey Cohen finished, he continued: “Professor, being too amazing isn’t good either; at your level, Professor, even if you want to return to campus and focus on academia, the White House won’t allow it.”
Lin Ran pondered after hearing this: “Actually, it’s not impossible.”
Harvey Cohen asked in slight surprise: “What is not impossible?”
Lin Ran said: “On-site proof of the Goldbach Conjecture.”
Harvey Cohen excitedly said: “Really?”
Lin Ran raised an eyebrow: “Let’s try.
It does have difficulty; I don’t dare guarantee what level I can achieve.”
Harvey Cohen quickly stood up: “Professor, I was just saying it tentatively, but I didn’t expect you to really agree.
Then I need to urgently contact more people and change the venue temporarily.
The original venue clearly isn’t enough to witness the miracle.
And extend the venue rental time.”
Harvey Cohen glanced at the time; there were only five days until the New York Mathematicians Conference: “Professor, how many days do you need?”
Lin Ran thought: “Three days. Don’t have too high expectations; I’m just doing a little work, setting an example for everyone.
In your promotion, don’t say I’m proving the Goldbach Conjecture; I’m just trying, giving everyone some ideas.
If you raise everyone’s expectations and I can’t do it, don’t blame me.”
Harvey Cohen smiled: “Professor, no one will blame you for not solving the Goldbach Conjecture.
On site with only three days, to prove the Goldbach Conjecture—though you’re Gauss reborn—it would be too difficult.”
Harvey Cohen thought to himself, Professor, if you can’t do it, everyone will breathe a sigh of relief; turns out the professor isn’t omnipotent.
The news that the professor would prove the Goldbach Conjecture on site spread throughout the mathematics community almost immediately.
The entire America mathematics community was boiling.
As for Harvey Cohen repeatedly emphasizing over telephone and fax: “No no no, it’s not on-site proof of the Goldbach Conjecture; how could it be on-site proof of the Goldbach Conjecture.
It’s just the professor talking about his understanding of the Goldbach Conjecture.
Maybe, I mean maybe, there might be some on-site derivation, that’s all.
I never said the professor would prove the Goldbach Conjecture at this year’s New York Mathematicians Conference!”
This is what Harvey Cohen told the conference organizing staff.
Big shots he personally invited; less important ones were handled by his PhD students or school administrative staff. Master’s? Master’s students weren’t qualified.
But when mathematicians called and chatted about this, it had completely changed.
“Heard about this New York Mathematicians Conference?”
“Of course! They say the professor will prove the Goldbach Conjecture on site!”
“Ah? I heard it’s just chatting about the path to fully proving the Goldbach Conjecture.”
“Anyway, I heard it’s on-site proof.”
“Why is what I heard different from what you heard?”
“Whatever it is, I’m definitely going to the site; I believe the professor won’t disappoint me.”
“The professor is too perverted; though in difficulty, the Goldbach Conjecture and Twin Prime Conjecture are similar, but they’re still different after all.”
“Yeah, even Gauss wasn’t this exaggerated!”
Not only that, New York media was much more developed than Göttingen.
Local New York media reported first, then national media rushed to report.
Lyndon Johnson himself needed some news to divert public attention from the Vietnam War.
The professor proving the Goldbach Conjecture was good news that could be reported continuously.
At Christmas, everyone forget about the Vietnam War and look at the professor in the distance.
The White House’s adding fuel to the fire gave the matter itself a boost.
“Göttingen Miracle to Reappear in New York, Professor Targets Goldbach Conjecture”
“Can the Professor Continuously Perform Miracles”
“The Professor Isn’t Gauss Incarnate; the Professor Is Mathematics Itself”
In the apartment by New York Central Park, Lin Ran stared dumbfounded at the newspapers on the dining table. I didn’t say that at all.
He called Harvey Cohen, complaints coming from the other end: “Professor, what I absolutely told them was that you’re just trying to talk about your views on the Goldbach Conjecture.
But they kept passing it along until it became on-site proof of the Goldbach Conjecture.
We can’t control the media even more.
We don’t want this situation either; we clarified with major newspapers, but they use words like ‘allegedly’ to mislead readers.
Giving readers an illusion.
Professor, really very sorry, but rest assured, even if you don’t prove the Goldbach Conjecture on site, it’s nothing.”
Harvey Cohen’s voice was utterly exhausted.
Lin Ran couldn’t pursue it further.
He believed the other hadn’t said it: “Then it seems I really need to prepare well.
There are still five days; I think it might not be too late.”
Harvey Cohen’s originally exhausted voice suddenly became energetic like he’d been injected with chicken blood: “Professor, are you really going to prove the Goldbach Conjecture on site?”
Lin Ran shook his head: “No, not on-site proof, but come up with a fairly complete approach in these few days.”
After hanging up, Lin Ran sighed deeply; it seemed he had to bring out the weak Goldbach Conjecture.
Jenny sitting across from Lin Ran asked: “Professor, so are you really going to prove the Goldbach Conjecture on site?”
She naturally knew what Lin Ran planned to do, and what he had to do after the newspapers hyped it up.
The New York Times clarification articles were personally written and published by her.
“Sigh, let’s try.”
Jenny smiled: “Then the prime number rooms these days for mathematicians coming to New York weren’t wasted.”
Lin Ran asked: “Prime number rooms?”
Jenny nodded: “Right, I heard that hotels around New York University, any room numbers that are prime numbers, have all been booked by mathematicians.
Especially Randolph numbers; not a single one left.”
The media called numbers that are prime themselves, with each digit also prime, and no repeated digits, Randolph numbers.
The specific determination would wait until the next International Congress of Mathematicians, to be confirmed at the conference.
Of course, that’s not all; later a mathematician proposed a number that is prime itself, each digit is prime, and any consecutive digit combinations are also prime; such numbers can be called complete Randolph numbers.
Such numbers are also called super primes.
It turned out such super primes don’t exist for four digits and above.
Defining it yourself, then proving a conjecture around it, can also get a paper published.
This is Lin Ran’s influence in the mathematics community.
Compared to the prince of mathematics Gauss, the mathematics community publicly acknowledged Lin Ran was already without any distance from the title of God of Mathematics.
The only reason he hadn’t been given that title yet was simply because it was too early.
Everyone wanted to wait for a more perfect time, like when the Randolph Program is outlined, at the Abel Prize awarding; that would be perfect.
Just like Grothendieck being crowned Pope of Mathematics after completing algebraic geometry.
Of course, at the media level, similar nicknames had already emerged, just not yet universally recognized.
“Originally I just wanted to casually say some things, but now it seems casually saying some things won’t do.
After reaching this position, everyone has put you on the spot.
Sigh, what is it to be out of control? This is being out of control.” Lin Ran sighed.
The New York Mathematicians Conference was held as scheduled.
Because Lin Ran and the Goldbach Conjecture had been hyped up.
For this conference, various media sent people; CBS and NBC each sent a full live broadcast team.
For live broadcast, they donated a large sum to New York City University and Columbia University.
Secondly, the organizer of the New York Mathematicians Conference was New York City University; this year, because Lin Ran was speaking on the Goldbach Conjecture, Columbia University insisted on adding their name. Also, the blackboard Lin Ran used on site must go to them.
After all, Lin Ran was still a Columbia University professor.
Finally, IBM offered five million US dollars in sky-high sponsorship for this New York Mathematicians Conference, with IBM logos everywhere on site.
Even at the entrance check-in, they placed IBM’s Deep Blue artificial intelligence for mathematicians to play chess against.
After seeing IBM’s Deep Blue, Lin Ran had a new idea, thinking he could try it next year or the year after.
Because Lin Ran was also speaking on the Goldbach Conjecture, Chen Jingrun gave the opening academic report, on his achievement of 1+2.
It had to be said, no matter when, this was a major achievement, worth applause and cheers from all mathematicians on site.
But because Lin Ran was after him, the applause seemed a bit perfunctory.
After Chen Jingrun came down, just seeing Lin Ran stand up, the applause didn’t stop; he couldn’t help sighing inwardly that compared to the professor, he was really far behind.
“Good, Chen just spoke very well.
Let’s applaud him. As a Chinese compatriot, I think this achievement deserves a Fields.”
Chen Jingrun was actually only 32 years old; even if he adjusted his age with Chen Dehui’s identity, at the 1968 International Congress of Mathematicians two years later, he still wouldn’t be forty.
After Lin Ran’s words, there was first polite applause, then hesitation.
Fields in 1964 and 1968 consecutively to Chinese people?
Even if Chen Jingrun’s achievement absolutely qualified for Fields, it would make many hesitate.
Considering it was Lin Ran saying it, it carried weight.
Mathematics is just mathematics, but mathematicians are far more than just mathematics.
Whether a mathematician gets Fields, your achievements matter, but who your mentor is, who your mentor’s mentor is, sometimes matters equally.
Though Lin Ran wasn’t mathematics-born, he was already trying to wield such influence.
I’ve publicly called out that Chen’s result deserves a Fields; shouldn’t the committee consider it?
At least be fair in the judging process?
Otherwise, if you give it to someone whose achievement is less than Chen Jingrun’s, I’ll publicly question and call out; can you withstand the public opinion pressure?
The experienced mathematicians present sighed inwardly.
Everyone knew Lin Ran would fight sooner or later; just didn’t expect it so soon, fighting for his Chinese descent compatriot.
A White House bureaucrat who climbed high, coming to the mathematics community is like dimensional reduction strike, Harvey Cohen thought.
Professor Fox thought, with Lin Ran here, the century-long Columbia School has no problem.
Lin Ran didn’t care what the audience below thought; he continued:
“I have a lot of pressure, because what I told Professor Cohen was to talk about my understanding of the Goldbach Conjecture, try to prove it a bit, give everyone some ideas.
Note, I said try a bit, but you guys hyped it into on-site proof.
That’s too much!
Directly putting pressure on me.”
Laughter erupted below the stage.
“Luckily, who am I? I’m the omnipotent professor.
So after pondering for a week, I think I can give everyone a proof of the weak Goldbach Conjecture.”
This time the audience really exclaimed.
“Oh!”
“Professor, start now!”
“Can’t wait!”
“Professor, you are God!”
Applause, screams, shouts mixed below; the venue holding five hundred people was exceptionally noisy.
This time even PhDs weren’t qualified to attend on site.
Lin Ran continued: “Good, because it’s a complete proof.
So no need for so many blackboards.
One blackboard is enough; I’ll write, you note it down, then I erase.”
Fox’s face darkened; the holy relic was gone just like that. Seagull sitting next to him was smug; it seemed the Göttingen blackboard was still unique.
Another dark face was IBM’s head.
At this rate, at most two days.
Five million US dollars only bought two days of advertising; a total blood loss.
Lin Ran smiled: “Good, let’s formally begin.
What we’re doing this time is the proof of the weak Goldbach Conjecture.
The Goldbach Conjecture has a strong form: every even number greater than 2 is the sum of two primes, and a weak form: every odd number greater than 5 is the sum of three primes.
What we’re doing today is the weak form.”
