Chapter 216: Who Is Randolph?
“With this, the weak form of the Goldbach Conjecture has been perfectly solved.”
The formulas on the blackboard were written and erased, erased and written again.
If printed as formulas, it would take a full 70 pages.
(Helffgott’s weak form Goldbach Conjecture proof paper published on Arxiv was revised through three versions, with the final version totaling 79 pages)
After Lin Ran finished speaking, he came to the front of the blackboard and bowed to the audience below.
Thunderous applause erupted from the audience below.
Whoever could achieve such an accomplishment deserves such applause.
What’s more, they had once again witnessed a miracle on site.
Because according to the public statements of Harvey Cohen and Lin Ran, five days ago Harvey Cohen had only just notified the other party, meaning the other party had spent only five days to produce a complete proof of the weak form of the Goldbach Conjecture.
This matter on anyone else would make people feel unbelievable.
But on Lin Ran, with the Göttingen miracle at the beginning of the year and the Goldbach Conjecture at the end, and considering Lin Ran’s identity as a Columbia University professor, it doesn’t seem so unbelievable that they all have the surname starting with “Go.”
Lin Ran was surrounded by the crowd.
“Randolph, I’ll have someone organize the paper here and publish it in an academic journal at the fastest speed. The Goldbach Conjecture is a major achievement; even if it’s just the weak form, this is a big deal in the mathematics community,” Fox said.
Fox comforted himself inwardly: no matter how much the Göttingen miracle happened in Göttingen, the author affiliation column of the paper would forever read Columbia University.
Seagull said: “Randolph, I agree with Fox. Additionally, when will you produce the strong form of the Goldbach Conjecture?
I believe everyone present is very curious about this.
If you only get inspiration in Göttingen, Göttingen welcomes you anytime.”
Harvey Cohen said: “Professor, look, I nagged you, and you solved the weak form of the Goldbach Conjecture.
If we nag you more, won’t you directly complete the strong form?
How about we make a pact here today: at the Mathematician Conference one year from now, you solve the strong form of the Goldbach Conjecture?
It would also count as finding some fun for you outside of your NASA work.”
Solving the strong form of the Goldbach Conjecture is fun—this could only be said about Lin Ran.
Even Lin Ran himself found it outrageous, as if the Goldbach Conjecture were like a sudoku game, something to casually calculate with a booklet in spare time.
“Let’s forget it; I feel the strong form is very difficult.
My intuition tells me there’s an obstacle requiring other tools to overcome blocking our path toward it.
Like how I needed content from algebraic geometry to find algebraic varieties to complete geometric modeling.
This also benefits from the past twenty-plus years of mathematicians like Grothendieck, Pierre, and Andrew consistently trying to fuse number theory and algebraic geometry.
That’s how I could think of such a method.
Therefore, I conjecture that to solve the strong form of the Goldbach Conjecture, relying solely on traditional number theory tools like the sieve method and circle method is definitely unrealistic.
Like Chen’s work, the techniques themselves are already perfected; wanting to improve them, no matter how you improve, it’s hard to approach the strong form of the Goldbach Conjecture.
I want either to wait for tools from other fields to borrow a framework-level breakthrough for a cross-field solution, or to wait for new tools to emerge in the number theory field.
In short, using existing tools, solving the strong form is almost impossible.”
Lin Ran patted Chen Jingrun’s shoulder: “Chen, maybe you’ll complete the proof of the strong form of the Goldbach Conjecture before I do.”
He looked at Chen Jingrun, who was much more vibrant than in his memory of the original spacetime, and felt deeply emotional inside.
In the original spacetime, even though Chen Jingrun produced world-class achievements and gained nationwide fame through Xu Chi’s report literature “Goldbach Conjecture,” achieving certain status in academia and politics.
But his personal life was obviously far from good, with the most important reason being his body: early pulmonary tuberculosis and later Parkinson’s, both greatly limiting this mathematics genius’s peak achievements to just “1+2.”
Chen Jingrun was a bit shy, smiled, and then said softly: “Professor, I will definitely work hard.”
This was the big moment of his life, originally supposed to be his spotlight, but because of Lin Ran’s appearance, the limelight was firmly drawn to Lin Ran; for others, like some mathematicians who care about fame and fortune, they might not say it but would inwardly feel resentment.
In the original spacetime, he lived in a 6-square-meter small room, Zhongguancun 88 Building single dormitory. Later, the Mathematics Institute adjusted a 16-square-meter south-facing room for him.
His first reaction was: “My current housing is already very good; everyone’s housing is very tight. I am only one person; this is plenty good!”
Chen Jingrun wouldn’t; he was originally of a temperament indifferent to fame and fortune. The changes in his life brought by Lin Ran had already given him more than enough.
He felt deeply grateful inside; he himself bore heavy responsibilities, and similarly, from his perspective, Lin Ran active in the White House bore far heavier responsibilities than him.
Just thinking about it made Chen Jingrun feel immense pressure; if it were him, he would have long buckled under the pressure.
In the New York twilight, in the New York City University mathematics department office, the professor wearing pajamas sitting under the moonlight—Chen Jingrun still often recalled it even now.
“Professor, our ad deal this time is a total loss,” After Lin Ran finished greeting the mathematicians, IBM’s CEO Thomas Watson said with a bitter smile.
This Mathematician Conference, besides the mathematicians and the television station live broadcast team, also included Thomas Watson and IBM executives.
Everyone originally thought to ride on Lin Ran’s popularity.
IBM sponsoring the professor’s on-site proof of the Goldbach Conjecture—what a huge gimmick.
Compared to the Twin Prime Conjecture, the Goldbach Conjecture has a longer history, higher legendary status, and the problem itself is easier to understand than the Twin Prime Conjecture, so its dissemination is broader.
Therefore, facing the astronomical five million US dollars called out by Harvey Cohen, IBM gritted its teeth and agreed.
Deep Blue Giant has that confidence.
Thinking it would be five days or even a week, able to hang on two of America’s three major television stations for a week.
Five million wouldn’t be a loss.
But unexpectedly, it was done in just one afternoon—one afternoon and it was over.
Five million can’t be said to be completely wasted, but it definitely didn’t serve any purpose.
Thomas Watson naturally didn’t dare blame Lin Ran; he could only complain to Lin Ran in a joking manner.
Lin Ran asked: “What’s wrong?”
Thomas Watson dejectedly told Lin Ran the specific details.
Trying to leave the impression on the other party that IBM suffered a loss because of him, so that in the future for similar good things like Deep Blue, he’d remember IBM.
After hearing it, Lin Ran laughed: “Here’s the deal: at next year’s New York Mathematicians’ Banquet, I have a top design; IBM handles contacting the television stations for full live broadcast. It will definitely be a much larger marketing event than this Goldbach Conjecture one.”
Not only Thomas Watson, but other mathematicians also became interested.
“Professor, can you reveal it in advance?” Thomas Watson asked.
Lin Ran nodded: “Of course. Here’s what I’m thinking: next year at the Christmas party, we’ll do a live broadcast.
I’ll play chess simultaneously against the top eight chess grandmasters in America; my goal is to beat them all.
Then I’ll play one game against Deep Blue.
That way, my name can top Deep Blue’s Technology Ark hit list.
Whenever Deep Blue can beat me, it will mean it has beaten humanity.”
Why eight? Because Lin Ran wanted to arrange a Bagua array on the ground at that time.
After Lin Ran finished speaking, gasps of surprise rang out around him.
Because everyone felt it was too hard to accomplish; just hearing it sounded difficult.
There is still a difference between mathematicians and professional chess players.
The Elo system was developed by Arpad Elo; America Chess Federation (USCF) began using this rating system in 1960.
That is to say, although there is no worldwide chess grandmaster ranking now, there is an America chess grandmaster ranking.
Thomas Watson’s eyes lit up: “Professor, it’s a deal.”
He could clearly see what a huge gimmick and advertising value this had.
Lin Ran was naturally very clear too; he said: “Watson, this is basically me helping IBM advertise.
Let’s do this: a little bet. If I don’t lose a single game, it’s ten million US dollars in advertising fees.
Plus Deep Blue, a total of 9 games; if I lose even one, I won’t take a penny from you.
What do you think?”
Lin Ran directly doubled it for him; ten million US dollars in this era, even just calculated by consumer price index alone, is equivalent to 82 million US dollars in later years.
If by gold price, it’s equivalent to 500 million US dollars in 2020.
These two figures: the former too little, the latter too much.
In any case, 10 million US dollars is a huge sum.
This amount of money, if Thomas Watson were just an ordinary manager, he might not even have authority to decide.
Thomas Watson is the son of IBM founder old Thomas.
But he hesitated not even half a second: “No problem, Professor, it’s a deal. Looking forward to your performance at next year’s Christmas party.”
Plenty of people want to give money to Lin Ran but can’t; IBM has this opportunity and won’t let it slip.
These top American tycoons are in no way inferior to Chinese businessmen in networking and operations.
Stepping back ten thousand steps, spending ten million as Deep Blue’s technical fee isn’t even a loss.
What’s more, in everyone’s view, Lin Ran can at least hold the NASA Director position for twenty years starting.
How long exactly depends entirely on his personal mood.
At the banquet that evening, during idle chat with Lin Ran, Jenny asked: “Professor, how confident are you in winning that ten million US dollars from Thomas?”
Lin Ran thought for a moment and said: “Saying 100% is a bit exaggerated, but at least 95%.
During the daytime academic report, what Professor Cohen said about treating the Goldbach Conjecture like a sudoku game in spare time—I felt was too exaggerated.
But playing chess against oneself in the brain during spare time can indeed be considered an entertainment method.”
Jenny rolled her eyes at Lin Ran: “Professor, what you’re saying is equally exaggerated; an entertainment method that can beat the top eight chess players in America.
When I was little, I dreamed of becoming America’s number one female chess grandmaster and winning the America championship, just like Nona Gaprindashvili.”
America began holding women’s chess competitions in 1938.
But Nona Gaprindashvili was a Soviet Union female player; she won consecutively in England, defeating numerous England grandmaster-level players, and took the Hastings International Chess Tournament championship.
Not sure why a Soviet Union female player went to England to play chess.
In any case, Nona became the first female chess grandmaster since the chess grandmaster title was established.
Lin Ran explained: “Jenny, you know, people are different.”
Jenny clinked glasses, drank the red wine in her cup in one go, then sighed: “Professor, you’re right.
I’m very curious: in your eyes, aren’t we all about the same as gorillas, even though the people sitting here are already the smartest batch in America or even globally.”
Lin Ran also drank it all; he was used to the feeling of alcohol appropriately stimulating his brain nerves, and sometimes he even felt it helped thinking: “No no no, people’s talents differ, just like I can never guess what’s in your mind.
I know some men are very good at guessing women’s psychological activities.”
The virus outbreak is spreading globally.
Though Kangaroo Country only has sporadic virus, schools have called for everyone to stay home for remote classes, no need to go to school.
This is good news for Terence Tao, meaning he has more time to browse MathOverflow and Arxiv.
MathOverflow is a professional forum in the field of mathematics; Terence Tao is active there year-round under his real name.
After GPT was released, he did a lot of interesting work with GPT and posted it on MathOverflow.
These interesting works are a bit distant from professional mathematics journals; mathematics journals struggle to fully express what he wants to say, and compared to general knowledge popularization, they have much higher value—at least ordinary people find it hard to understand the essence of his work.
So he posts these math works related to AI on MathOverflow.
This day, as usual, he stayed home, enjoying this long, special, global holiday.
In the study, the bookshelf was densely packed with mathematics books, from the classic “Introduction to Number Theory” to the latest research monographs, each like a witness to his academic career.
A whiteboard hung on the wall, covered with formulas and sketches. The computer screen’s glow illuminated his face,
Outside the window, the streets were empty, people walking dogs becoming rare.
You know, for foreigners, walking dogs is as instinctive as eating.
Terence Tao was long accustomed to browsing Arxiv daily for the latest academic dynamics; for him, this was also instinct.
But that doesn’t mean he’ll read every paper.
After all, massive papers are uploaded to Arxiv daily, but for him, most can be judged unworthy by just glancing at the title.
Titles that don’t attract him, directly skipped.
Occasionally, some titles make him pause and read the abstract.
But papers that truly make him read deeply are rare, probably less than one in a thousand.
His screening standards are extremely strict: the title must be novel enough, the abstract deep enough, otherwise directly passed.
The strictness rivals Qidian readers facing novels recommended by Qidian.
As usual, he opened Arxiv, scrolling the page. Titles slid by like running water, most ruthlessly ignored by him.
Suddenly, a title caught his eye: “Application of Algebraic Geometry Methods in the Proof of the Ternary Goldbach Conjecture.”
This title made him stop his fingers.
The weak Goldbach Conjecture, he was all too familiar with.
In 2013, Helffgott used the circle method and large sieve method to prove this conjecture, that every odd number greater than 5 can be expressed as the sum of three prime numbers.
Helffgott’s work combined classical number theory techniques and modern computational power; Terence Tao still remembered its proof vividly.
But this new paper claimed to use algebraic geometry methods to improve Helffgott’s proof, which surprised him greatly.
Algebraic geometry and number theory, though both important branches of mathematics, only started showing slight overlap in the past forty years.
But mostly still unrelated, especially in the prime number field.
Algebraic geometry focuses on geometric objects defined by polynomial equations, while number theory’s prime number subfield focuses on properties of integers.
How to apply algebraic geometry to an additive number theory problem like the Goldbach Conjecture—this was a puzzling question.
Doubt flashed in Terence Tao’s mind: is this possible?
But he had to admit this title was attention-grabbing enough.
Looking again at the author: Randolph Lin, Chinese? he thought.
Only one author name, which is normal.
Stony Brook University, isn’t that famous for differential geometry direction? When did they start doing number theory combined with algebraic geometry?
Terence Tao felt even greater doubt inside; as a famous web-surfing expert in the mathematics community, his social attributes maxed out, and quite a few State University of New York professors were his friends.
He’d never heard of any professor trying research in this direction.
With curiosity and a hint of doubt, he clicked the paper link and started reading the abstract.
The abstract mentioned that the author constructed a specific algebraic variety whose rational points correspond to representations of odd numbers as sums of three prime numbers. By studying the properties of this algebraic variety, the weak Goldbach Conjecture could be proved.
Terence Tao frowned; this idea sounded very novel, but was it really feasible?
He decided to read the introduction deeply.
In the introduction, the author detailed how they constructed this algebraic variety and used tools from algebraic geometry to analyze its structure.
The author claimed this method not only simplified Helfgott’s proof but also provided a new perspective for understanding prime distribution.
Terence Tao’s eyes lit up; this line of thinking reminded him of unexpected connections between different mathematics fields he’d encountered in his own research,
Such connections often bring unexpected achievements.
He conjectured that perhaps this paper was such an example.
He leaned back in his chair, staring at the computer screen.
If this method holds, it would be a major breakthrough, not just for number theory but with profound influence on the entire mathematics community.
He recalled similar situations in his own research, like introducing analytic methods into combinatorial mathematics or using probability theory to solve number theory problems.
These cross-field attempts often open new research doors.
He decided to download the full text, planning to study it carefully later.
But at that moment, his wife walked into the study and asked: “Terry, lunch is ready; what do you want to eat?”
Terence Tao looked up, smiled, and replied: “Oh, okay, I’ll come in a bit.”
His thoughts were still on that paper.
He spent the entire day, page by page, checking every theorem’s derivation.
The mathematical language in the proof was complex and exquisite, interweaving number theory’s prime distribution and algebraic geometry’s variety theory.
He often paused to consult related literature, ensuring he understood every step.
Late at night, Terence Tao closed his notebook, rubbed his temples; though he generally grasped the paper’s framework, some technical details still puzzled him.
Early next morning, Terence Tao organized a video conference, inviting a few colleagues and graduate students to share this paper.
He opened the screen on Zoom, displayed the paper’s abstract, tone slightly excited: “This paper claims to prove the weak Goldbach Conjecture using algebraic geometry; what do you think?”
The discussion quickly heated up.
One colleague questioned: “Can algebraic geometry handle additive problems of primes? This sounds a bit forced.”
Another graduate student, specializing in algebraic geometry, eyes lit up: “If they really constructed a suitable algebraic variety, it’s theoretically possible. I think this idea is very novel!”
He further explained the geometric meaning of points on the variety, helping Terence Tao understand the paper’s core idea more clearly.
However, another professor raised a concern: “Helffgott’s proof is already very complete; what substantial improvement does this new method bring? Isn’t it just a different form?”
Terence Tao nodded slightly, noting down these questions.
He knew academic breakthroughs often hide amid controversy.
He decided to continue deep research, personally verifying every derivation in the paper.
On the third day, Terence Tao came to the study early, brewed a cup of fresh coffee, and reopened the paper.
This time, he jumped straight to the core proof section, focusing on how the author linked odd numbers to the algebraic variety.
The paper mentioned a construction based on elliptic curves; by analyzing the curve’s rational points, the author established representations of prime sums.
He stared at the screen, a flash of insight suddenly striking his mind.
“I see!” he murmured to himself with a smile.
The author utilized the special properties of elliptic curves, transforming the prime sum problem into a geometric one, then solving it with algebraic geometry tools.
This method was not only elegant but likely to provide new perspectives for other number theory problems.
Terence Tao leaned back in his chair, closed his eyes, countless formulas and geometric figures emerging in his mind.
He felt a long-absent excitement.
This feeling was just like the heartbeat acceleration years ago when he conquered a certain difficult problem.
He knew if this proof holds, it would not only be an improvement on the weak Goldbach Conjecture but possibly a revolution in the intersection of number theory and algebraic geometry.
Terence Tao thought: must find this author and discuss this idea personally.
But who is Randolph Lin? How have I never heard of a mathematician of this level?
