Technology invades the modern world

Chapter 214 Goldbach's Conjecture
It's that time of year again for the New York Mathematicians' Dinner.

This year, no matter how much Lin Ran declined, everyone forced him to come on stage and say a few words.

After all, not everyone has the time and energy to travel thousands of miles to witness the Göttingen miracle in January this year.

Whether you went to the event in person, watched the live broadcast on TV, or bought the videotape from the Science Press, you have all witnessed Lin Ran's spectacular performance in Göttingen.

This time, he wouldn't let Lin Ran refuse no matter what.

No matter how much you say you want to give young people opportunities, and everyone's attention is focused on you, that won't work. You have to talk about it this year, either at the opening or as the closing act.

Harvey Cohen was very earnest when he communicated with Lin Ran: "Professor, if you don't tell me, my promise is useless. The mathematicians present will not agree."

They're just waiting to hear your teachings.

You can't ignore it. Let's not even talk about how effective the tools Lin Ran's achievements in number theory this year have provided for doctoral students in number theory, which is a benefit to all mathematicians. Just the idea of ​​solving the four-color problem proposed by Lin Ran at last year's International Congress of Mathematicians has already been solved by mathematicians at Columbia University.

Is there another expert like Lin Ran who can both help others reinvent the wheel and readily share his problem-solving strategies?

Other mathematicians, even if they were this generous, would at most give you a general idea; how could they possibly tell you the whole complete thought process like Lin Ran did?
Those who are a bit stingy will cherish even their own ideas, only sharing them when they absolutely have no other choice.

There is no harm without comparison.

With numerous comparative examples before him, Lin Ran's generosity is evident.

Personal fame is also an important factor.

Harvey Cohen continued, "Do you remember Chen? He was your student in Hong Kong."

If it was his own student, then it certainly wasn't Chen Xingshen.

Lin Ran nodded and said, "Of course, I recommend him to you. He is very talented."

Harvey Cohen laughed and said, "You're right, he is indeed very talented. He has made important achievements around Goldbach's conjecture, which is a great job."

Our internal assessment at the City University of New York is that this result is significant enough to advance current work on Goldbach's conjecture by a large margin.

Lin Ran understood; it must be that Goldbach's conjecture "1+2" ​​has been proven, and judging by the timeline, it should be around this point.

In the original timeline, Chen Jingrun's work was published in 1966.

Lin Ran had read Chen Jingrun's published papers. Chen came to New York at the end of 1960 and spent about five years in his doctoral studies, during which he published some mathematical papers.

Compared to his previous expertise in sieve methods, Chen Jingrun now clearly possesses more tools and is a master in the field of analytic number theory.

"That's right, so you mean he'll give an academic presentation on his findings at the New York Mathematicians' Congress, right?" Lin Ran asked.

Giving a presentation at the New York Mathematicians Congress was a burden for him, but an absolute honor for other mathematicians.

In terms of difficulty, it's not much different from giving a presentation at the main venue of the International Congress of Mathematicians.

After all, the New York Mathematicians Congress only lasts one day, and a maximum of three mathematicians can give presentations in a day. The International Congress of Mathematicians lasts at least seven days.

Harvey Cohen nodded and said, "That's right, Chen's report will follow yours."

What I mean is, professor, you don't necessarily have to be the opening or closing act.

If you want to push the limits of human capability and give us a live proof of Goldbach's Conjecture at this year's Congress of Mathematicians in New York, then I can schedule your presentation after Chen's.

Harvey Cohen blinked, his face full of anticipation.

Lin Ran smiled wryly and said, "Professor Cohen, I am a human being, not a god."

Proving Goldbach's conjecture on-site with only one day is simply impossible.

Harvey Cohen said, "Professor, if it can really be proven, then I think no one would mind if this year's New York Mathematicians Congress were extended to a week or even longer."

Of course it will take longer, but we can wait.

Our colleagues have enough patience to witness miracles firsthand.

I'm just afraid the White House won't be able to wait and will send someone to New York to bring you back.

After Harvey Cohen finished speaking, he continued, "Professor, being too amazing isn't good either. If you're amazing to the point that you want to go back to academia and focus on academics, the White House won't allow it."

After listening, Lin Ran seemed thoughtful: "Actually, it's not impossible."

Harvey Cohen asked with slight surprise, "What do you mean it's not okay?"

Lin Ran said, "This provides on-site proof of Goldbach's conjecture."

Harvey Cohen exclaimed excitedly, "Really?"

Lin Ran raised an eyebrow: "Give it a try."

It is indeed difficult, and I can't guarantee how well I can achieve it.

Harvey Cohen quickly stood up: "Professor, I was just saying this to you on a whim, but I didn't expect you to actually agree."

Then I need to urgently contact more people and temporarily change the venue.

The original venue was clearly no longer sufficient to witness a miracle.

Then the venue rental period will also need to be extended.

Harvey Cohen glanced at the time; there were only five days until the New York Mathematicians' Congress. "Professor, how many days do you need?"

Lin Ran thought for a moment and said, "Three days, don't have too high expectations. I'm just doing a little bit of work to set an example for everyone."

When you're promoting this, don't say that you're going to prove Goldbach's Conjecture; you're just trying it out to give people some ideas.

You've raised everyone's expectations; don't blame me if I can't deliver.

Harvey Cohen laughed and said, "Professor, no one will blame you for not being able to solve Goldbach's Conjecture."

"With only three days on-site, proving Goldbach's Conjecture is incredibly difficult, even if you were Gauss reincarnated."

Harvey Cohen thought to himself, "Professor, everyone will actually breathe a sigh of relief if you can't do it. It turns out that even professors aren't omnipotent."

The news that the professor was going to prove Goldbach's conjecture on the spot spread throughout the mathematics community almost immediately.

The entire American mathematical community was in an uproar.

As for Harvey Cohen's repeated emphasis in phone calls and faxes: "No, no, no, it's not a live proof of Goldbach's conjecture, how could it be a live proof of Goldbach's conjecture?"

The professor simply explained his understanding of Goldbach's Conjecture.

Perhaps, I mean perhaps, we might do a simulation on the spot, that's all.

I never said the professor would prove Goldbach's Conjecture at this year's New York Mathematicians' Congress!

This is what Harvey Cohen said to the conference organizers.

The bigwig himself came to invite them; less important ones were handled by his PhDs and school administrators. Master's degree holders? Master's degree holders weren't qualified.

But when the mathematicians talked about it on the phone, things had completely changed.

Have you heard about the New York Mathematicians' Congress?

"Of course, they said the professor would prove Goldbach's Conjecture on the spot!"

"Oh? All I heard was about the path to a complete proof of Goldbach's conjecture."

"Anyway, what I heard is that on-site proof is required."

Why is what I heard different from what you heard?

"No matter what it is, I will definitely go to the event. I believe the professor will not let me down."

"Professor, this is a bit too extreme. Although Goldbach's conjecture and the twin prime conjecture are similar in terms of difficulty, they are still different after all."

"Yeah, even Gauss wasn't this exaggerated, Professor!"

Moreover, New York's media is far more developed than Göttingen's.

Local New York media reported on it first, and then national media rushed to report on it.

Lyndon Johnson himself also needed some news to divert public attention away from the Vietnam War.

The professor's proof of Goldbach's conjecture is good news and deserves continued coverage.

On Christmas Day, let's forget about the Vietnam War and instead look at the professor in the distance.

The White House's involvement further fueled the fire.

"The Göttingen miracle is about to repeat itself in New York; the professor sets his sights on Goldbach's conjecture."

Can the professor pull off a series of miracles?

"The professor is not Gauss reincarnated; the professor is mathematics itself."

In his apartment near Central Park in New York, Lin Ran stared blankly at the newspaper on the dining table. "I don't think I ever said that," he thought.

He called Harvey Cohen, and a complaint came from the other end of the line: "Professor, I absolutely told them that you just have to try to explain your own views on Goldbach's Conjecture."

But as they kept spreading it, it turned into a live proof of Goldbach's conjecture.

We have even less control over the media.

We didn't want things to be like this. We've clarified things with the major newspapers, but they're still misleading readers by using words like "suspected."

This gives the reader a false impression. "Professor, I'm truly sorry, but don't worry, even if you can't prove Goldbach's Conjecture on the spot, it's alright."

Harvey Cohen's voice sounded incredibly tired.

Lin Ran didn't press the matter further.

He believed that the other party had not actually said that: "Then it seems I really need to prepare properly."

There are still five days left, I don't think it might be too late.

Harvey Cohen's previously weary voice suddenly became energetic, as if he'd been injected with adrenaline: "Professor, are you really going to prove Goldbach's Conjecture on the spot?"

Lin Ran shook his head and said, "No, it's not about proving it on the spot, but about coming up with a more complete idea over the past few days."

After hanging up the phone, Lin Ran sighed. It seemed he had no choice but to bring up the weak Goldbach conjecture.

Sitting across from Lin Ran, Jenny asked, "Professor, so are you really going to prove Goldbach's Conjecture on the spot?"

She was naturally aware of what Lin Ran was going to do, and what Lin Ran was going to do after the newspapers advertised the changes.

She personally wrote and published all the clarification articles in the New York Times.

"Sigh, I'll give it a try."

Jenny laughed and said, "Then the mathematicians who have been in New York these past few days haven't stayed in the prime number room for nothing."

Lin Ran asked, "Primary number rooms?"

Jenny nodded: "That's right. I heard that in the past few days, all the prime number room numbers in the hotels around the New York University area have been assigned by mathematicians."

Especially the Randolph numbers, which were completely gone.

The media describes a number as a prime number in which each of its constituent digits is also a prime number and these constituent digits are not repeated. This is called a Randolph number.

The specifics will be determined at the next International Congress of Mathematicians.

Of course, that's not all. Later, some mathematicians proposed that a number is a prime number, then each of its constituent digits is a prime number, and finally, any combination of its consecutive digits is also a prime number. Such a number can be called a complete Randolph number.

Such numbers are also called super prime numbers.

The results showed that such super prime numbers do not exist for numbers of four digits or more.

You can publish a paper by giving yourself a definition and then providing a proof based on that conjecture.

This is Lin Ran's influence in the mathematics community.

Compared to Gauss, the "Prince of Mathematics," the mathematics community generally agrees that Lin Ran is no less than a "God of Mathematics."

The reason he hasn't been given such a title yet is simply because it's too early.

People want to wait until a more perfect time, such as when the Randolph Program is completed and the Abel Prize is awarded, then that would be perfect.

Just like Grothendieck was crowned the Pope of Mathematics after completing algebraic geometry.

Of course, similar nicknames have already emerged in the media, but they are still some distance from being universally recognized.

"I originally just wanted to say something casually, but now it seems that saying something casually won't work."

Once you get to this position, everyone will lift you up.

"Sigh, what does it mean to be powerless? This is what it means to be powerless," Lin Ran sighed.

The New York Congress of Mathematicians was held as scheduled.

Because Lin Ran and Goldbach's Conjecture were widely publicized.

This year's New York Mathematicians Congress attracted representatives from various media outlets, including CBS and NBC, each sending a full live broadcast team.

To fund the live broadcast, they donated a large sum of money to the City University of New York and Columbia University.

Secondly, the New York Mathematicians Congress is hosted by the City University of New York, but this year, because Lin Ran was going to talk about Goldbach's Conjecture, Columbia University insisted on adding its name to the list. Also, the blackboard Lin Ran used at the event had to belong to them.

After all, Lin Ran is a professor at Columbia University.

Finally, IBM offered a staggering five million US dollars to sponsor the New York Mathematicians' Congress, and the IBM logo was visible everywhere at the event.

Even at the registration area at the entrance, IBM's Deep Blue AI was set up for mathematicians to play against.

After seeing IBM's Deep Blue, Lin Ran had a new idea and thought he could give it a try next year or the year after.

Because Lin Ran was also going to talk about Goldbach's Conjecture, Chen Jingrun gave the opening academic report, talking about his achievements on 1+2.

It must be said that this is a great achievement no matter when it is presented, and it deserves applause and cheers from all the mathematicians present.

However, because Lin Ran was behind him, the applause seemed somewhat perfunctory.

After Chen Jingrun came down, he saw that the applause never stopped as soon as Lin Ranguang got up. He couldn't help but sigh in his heart that he was far inferior to the professor.

"Okay, Chen's explanation was excellent."

Let's applaud him. As a fellow Chinese, I believe this achievement deserves a Fields Medal.

Chen Jingrun was actually only 32 years old at the time. Even though he raised his age by using the identity of Chen Dehui, he was still not 40 years old at the International Congress of Mathematicians in 1968.

After Lin Ran finished speaking, there was first polite applause, followed by hesitation.

Why were the Fields Medals awarded to Chinese people in both 1964 and 1968?

Even if Chen Jingrun's achievements are absolutely worthy of Fields, it would still make many people hesitate.

Considering that these words were spoken by Lin Ran, and therefore carry some weight.

Mathematics is just mathematics, but mathematicians are much more than just mathematicians.

Whether a mathematician can win the Fields Medal depends on their research achievements, but sometimes it's equally important who their mentor is, and who their mentor's mentor is.

Although Lin Ran is not a mathematics major, he is already trying to exert such influence.

I've publicly stated that Chen's result deserves a Fields Medal, shouldn't the committee consider it?
At least the judging process should be fair, right?

Otherwise, if the people you provide don't achieve the same results as Chen Jingrun, and I publicly question and challenge them, can you withstand the pressure of public opinion?
The experienced mathematicians present were already reflecting on their experiences.

Everyone knew that Lin Ran would fight for it sooner or later, but no one expected him to come so early, to fight for his fellow Chinese.

Harvey Cohen thought that it was like a game-changer for bureaucrats who could climb to high positions in the White House to come to the mathematics community.

Professor Fox thought to himself, with Lin Ran around, the Columbia School of Thought, which has stood for a century, is no problem.

Lin Ran didn't care what the audience thought, and he continued:

"I feel a lot of pressure because I told Professor Cohen that I would talk about my understanding of Goldbach's Conjecture, try to prove it, and give everyone some ideas."

Note that I said I would try it out, but you guys turned it into a publicity stunt and demanded on-site proof.

This is absolutely outrageous!
They put pressure on me directly.

There was laughter in the audience.

"Fortunately, I am who I am: the all-powerful professor."

So I racked my brains for a week, and I think I can probably give you a proof of the weak Goldbach conjecture.

This time, the audience gasped in surprise.

"Oh!"

"Professor, let's begin!"

"Can't wait!"

"Professor, you are God!"

The applause, screams, and shouts from the audience blended together, making the 500-seat venue exceptionally noisy.

This time, even PhDs weren't qualified to be present.

Lin Ran continued, "Okay, because it's already a complete proof."

Therefore, we don't need that many blackboards.

One blackboard is enough. I'll write it down, everyone will write it down, and then I'll erase it.

Fox's face darkened; the relic was gone just like that. Siegel, sitting next to him, was quite smug; it seemed the blackboard in Göttingen was truly unique.

The other person with a dark expression was the head of IBM.

Judging from this, it will only last two days at most.

Five million dollars only bought two days of advertising time; it's a huge loss.

Lin Ran smiled and said, "Alright, let's begin officially."

What we're going to do this time is prove the weak Goldbach conjecture.

Goldbach's conjecture is divided into a strong form, which states that every even number greater than 2 is the sum of two prime numbers, and a weak form, which states that every odd number greater than 5 is the sum of three prime numbers.

What we need to do today is focus on the weak form.

(End of this chapter)