Chapter 220: Six Years? Half A Year!
Lin Ran wanted to return to China.
He didn’t want to stay in America at all.
He was already eager to return home.
But under the current situation, being in America, returning to China was very difficult.
After all, China had finally controlled the virus, but America started it again.
Secondly, what would he do after going back.
The reason Lin Ran still chose to first make a name in the mathematics community was because he had many achievements in this area that he could show off, which could quickly gain him fame.
Secondly, because doing aerospace in 2020 without fame or proof of himself, getting money from anywhere would be a problem.
Before going back to 1960, the idea of getting the first pot of gold from Bezos’s Blue Origin had been completely dismissed by Lin Ran.
Very simple, because helping Blue Origin would mean tying his own security to Bezos’s credit.
Once he revealed his desire to return to China, he dared to guarantee that Bezos would unhesitatingly sell him out.
Reach an agreement with him, using helping him clear his crimes as an excuse, making him work for him for a lifetime.
Lin Ran didn’t waste his years in 1960s America.
Having a gate certainly meant he could go back.
But using the gate to go back would be very troublesome to explain.
This was an era filled with cameras and full information flow; the more obvious his abnormal performance, the more comprehensive the investigation against him would be.
1960 spacetime couldn’t guess the gate doesn’t mean 2020 couldn’t.
So Lin Ran no longer planned to get money from Bezos.
On the contrary, he had a new target for getting the first pot of gold.
This was an idea gradually perfected over six years in the past 60 spacetime.
Information gap isn’t only from future to past; similarly, from past to present, there is also an information gap.
He was a professor who wielded great power in 1960, NASA’s top real-power figure, entering the White House and the Pentagon as if entering no man’s land.
The information gap from the past works greatly in the present too.
After Lin Ran finished speaking, Nilanjan was dumbfounded.
Because half a year was too short.
With current research work stalled, meetings stopped, exchanges only online, group meetings only online.
Students’ progress was completely unknown.
So in half a year, Lin Ran could solve the Twin Prime Conjecture.
Honestly, under the current situation, the verification cost for this time was almost zero for Nilanjan.
Because it was too short.
As a senior scholar in artificial intelligence, Nilanjan would actively or passively learn about some big news in the mathematics community.
Like the progress on the Twin Prime Conjecture a few years ago.
Nilanjan knew very well.
Because Zhang Yitang first gave an upper bound of 70 million, then the mathematics community started a project called Polymath8, reducing the gap upper bound from 70 million to 246.
This project named Polymath8 was initiated by Terence Tao, and it involved computer assistance.
They did it roughly like this.
Using online collaboration mode, discussing via blogs and wiki pages.
The project used a pipeline method, dividing tasks into different groups, including theoretical analysis and computational optimization.
Polymath8a mainly optimized Zhang Yitang’s allowable k-tuples, using GPY sieve method, Type I, Type II, Type III estimates, and numerical optimization.
Initial bound was 70 million, Scott Morrison used computer assistance to reduce the bound to 59,470,640, finally stabilizing at 4680.
It took 3 months, involving massive computational searches for allowable tuples; this part used computer assistance.
And James Maynard, the mathematician mentioned earlier who won the 2022 Fields Medal, proposed an improved GPY sieve method that could prove prime gaps no more than 600; his method was based on pure mathematical tools, core being analytic sieve theory, without extensive computation.
And reducing from 600 to 246 must rely on tool assistance; pure mathematical tools have not been achieved by any mathematician so far.
Nilanjan murmured: “Randolph, good, no problem, I believe you can do it.
So what do you want?”
If he brought out a Fields Medalist, even without any contribution, he could boast hard.
Not to mention mixing a professor position at Stony Brook University; with his qualifications and student’s resume, getting a professor at a US top fifty university wouldn’t be a problem.
Even at local New York City University, getting a professor position was no problem at all.
Moreover, if Lin Ran won the Fields, he would get Stony Brook University board special contribution award; everyone would have a bright future.
After getting the board contribution award, removing the assistant from assistant professor at Stony Brook wouldn’t be hard.
Indian descent instinct to occupy high ground, let Lin Ran play freely, waiting to fiercely boast his own merit when reporting to the leader.
Something like I knew at a glance that Randolph was a mathematics genius, so I gave him full freedom to perform; although I didn’t contribute in the mathematics field, I fully helped him in growth and life.
Something like I cleared obstacles for Randolph’s research and life, letting him work without distractions.
Without results yet, Nilanjan was already thinking about how to report.
Lin Ran said: “Nothing else, after I finish, I want to graduate; I want to get a PhD from Stony Brook University and then graduate and return to China.”
Getting a PhD degree would give him something when returning to China, and also so his mother wouldn’t be too disappointed.
Otherwise, Lin Ran really didn’t need a PhD to prove himself.
And honestly, if he could choose, Lin Ran still wanted to get a PhD from Göttingen, not Stony Brook University.
He had no strong feelings for it.
Nilanjan nodded: “No problem, but you still need a paper in artificial intelligence; you choose this yourself.
I’ll arrange this; if you really solve the Twin Prime Conjecture, I think the school side would also be happy to provide help.”
“How to evaluate Chinese student Randolph Lin?”
Lin Ran’s deeds were first replied to by Terence Tao on mathoverflow; people found it, then deleted the question.
Then mathematicians attending the zoom conference began spreading the news.
Everyone knew the Chinese descent mathematician named Randolph Lin was a PhD in artificial intelligence at Stony Brook University, who proposed an elegant cross-field combination method and solved the weak form of the Goldbach Conjecture.
The matter itself was full of drama.
Quanta Magazine published a feature article titled “Chinese Mathematician’s Goldbach Conjecture Plot.”
It wrote in the article:
“In the 20th century, Chinese mathematician Chen Jingrun made a milestone contribution to the Goldbach Conjecture. Chen Jingrun was born in Fujian Province, grew up in turbulent war years, entered Xiamen University Mathematics Department in 1949, mentored by famous mathematician Hua Luogeng. In a harsh environment, he focused on number theory research, publishing the famous Chen’s theorem in 1966, proving every sufficiently large even number can be expressed as the sum of a prime and a number with at most two prime factors, e.g., 100 = 23 + 7×11.
This result was a major progress on the strong Goldbach Conjecture, though not fully solving it, it inspired later researchers.
Chen Jingrun’s story was recorded in Xu Chi’s biography ‘Goldbach Conjecture,’ published in People’s Literature in 1978, becoming a classic chapter in Chinese mathematics history.
Fifty-four years later, Chinese mathematician Randolph Lin decided to re-examine the weak Goldbach Conjecture from a new perspective. Lin’s method was unique, combining algebraic geometry with number theory to construct an elegant proof based on elliptic curves.
Elliptic curves are core objects in algebraic geometry, usually defined by equations like y² = x³ + ax + b, with rich geometric and arithmetic structures.
Lin’s proof started from an intuitive observation: the sum of primes problem is essentially a Diophantine equation, and algebraic geometry excels at handling solutions to such equations.
The En he constructed was a carefully designed elliptic curve whose coefficients depend on n. By analyzing rational points on En, Lin established a mapping that turns these points into prime triples satisfying p1 + p2 + p3 = n.
In the introduction of Lin’s paper, he detailed how to construct this algebraic variety and used tools from algebraic geometry, like the Mordell-Weil group and height theory, to analyze its structure.
He proved that for every odd n > 5, En has at least one rational point, and this existence directly corresponds to the weak Goldbach Conjecture holding.
Lin’s method avoided the complex circle method and exponential sum estimates in Helffgott’s proof, providing a more direct path through geometric intuition and algebraic tools.
‘My goal is to find a more concise proof method,’ Lin said in a telephone interview, ‘Rational points on elliptic curves provide a natural language, allowing us to understand the sum of primes problem from a geometric angle. This method not only simplifies the proof but also reveals the potential structure of prime distribution.’
Helffgott’s proof relied on the circle method, a classic analytic number theory technique that estimates the number of prime sums by integrating on the unit circle. However, this method requires handling complex estimates for major and minor arcs and relies on computer verification for smaller n values. Lin’s proof is entirely based on pure mathematical tools, avoiding the need for analytic methods and computational verification.
‘Lin’s proof is a model of combining algebraic geometry and number theory,’ famous Chinese descent mathematician Terence Tao commented, ‘He transformed a problem traditionally dominated by analytic methods into a geometric one; this cross-field insight is exciting.’
Lin’s achievement is not only significant in the mathematics field but also carries the long tradition of Chinese mathematicians in number theory research.
From Chen Jingrun to Lin, Chinese number theorists have left a profound mark on the Goldbach Conjecture. Chen Jingrun persisted in research in harsh conditions, and his story inspired a generation. Lin, in the modern academic environment, carried forward this tradition. His proof is not only a tribute to Chen Jingrun’s work but also a new interpretation of mathematical beauty.
Lin’s paper has been submitted to New Progress in Mathematics, has passed peer review, and is about to be published.”
Just Lin Ran alone, the news wouldn’t spread back to China so fast.
But it couldn’t be helped that this was the Goldbach Conjecture.
It was the Goldbach Conjecture that enlightened countless Chinese people in mathematics and research.
After Xu Chi finished writing ‘Goldbach Conjecture,’ mathematical research units nationwide, from universities to Chinese Academy of Sciences Mathematics Institute, received countless self-recommendation letters claiming to have solved the Goldbach Conjecture.
Countless Chinese citizens insisted they solved 1+1 and wanted experts to see how to publish in academic journals.
Lin Ran himself had no fame, but the Goldbach Conjecture was too famous.
The day Quanta Magazine article was published, self-media moved it to Chinese Weibo, quickly sparking hot discussion.
From Weibo to Zhihu to Douyin, it was explosive news.
Anyone or dog could comment a few words.
After all, there was nothing to do at home.
With real-world activities almost stalled, virtual world activities would be unprecedentedly active.
“Thanks for invite, very impressive, AI PhD publishing in pure mathematics top journal, absolute big shot; to put it this way, there are only a handful of Chinese people who publish in top journals during PhD.
Know Chen Gao? From USTC Youth Class, also from Stony Brook University.
But different from Randolph, he was a pure mathematics PhD, following Professor Chen Xiuhong, solved Hawking’s 1977 gravitational instanton problem, then went to Princeton for postdoc in 2017; he hadn’t published any of the top four.
While Randolph, as a current PhD in artificial intelligence, directly starts with top four, top-tier big shot.
But I think saying Fields online is a bit too optimistic.
First, his work has some originality, involving interdisciplinary fields; recent Fields tend to go to mathematicians doing interdisciplinary problems.
But his work is something others already solved; he built on others.
Secondly, he has only one top four; other strong Fields competitors have way more top four than him.
Finally, he has no mentor; on his own, there aren’t that many problems to find; maybe publish one follow-up and hard to publish more.
If I were him, I’d immediately find a mentor; Stony Brook is a strong math school with plenty of Fields Medalists; quickly find a mentor, do more while young.
Fields Medal might have a slim chance.
But still too hard; Stony Brook in my impression isn’t strong in number theory, let alone combination of algebraic geometry and number theory; even with a mentor, probably can’t give much guidance.
I think better change schools, best to Princeton; with one top four in hand, transferring to Princeton is easy.”
High-praise answer on Zhihu as above.
All very pertinent suggestions.
(Mention, Chen Gao’s first top four published in 2021 in New Progress in Mathematics; current time node is March 2020)
What they didn’t know was that Lin Ran didn’t need masters to find problems for him at all, because he himself was a master, and a master among masters.
Pulling out the stuff in his head to show the world would scare them to death.
The general solution to N-S equations directly solved the Americans’ dilemma of no large wind tunnel.
“Thanks for invite, Randolph Lin’s Chinese name is Lin Ran, my high school classmate; this is Xu Xian, previously answered some questions on Zhihu, my homepage has resume too, current PhD in theoretical mathematics at Yenching University.
I’ll plant a flag here: Brother Ran is now 23, not yet 24; before 40, definitely gets Fields! If not, I’ll record a video on Bilibili standing on my head to wash hair, okay.
Anyone want to bet with me, leave message in comments; if Brother Ran wins, come record a video standing on head washing hair.
Say more: I’ve seen many big shots at Yenching, all kinds of gods emerging, but Brother Ran is absolutely the most impressive god I’ve seen; everyone wait and see.
This really isn’t excessive praise Brother Ran; Brother Ran doesn’t play social media; this is purely my own view; Brother Ran definitely gets it.”
Xu Xian’s Zhihu name is Mathematics Xu Xian, has five or six thousand fans on Zhihu, somewhat famous in this highly professional niche pervert field.
His answer’s approval count ranked second.
Comments section had all kinds:
“Nanda math PhD current student joins one; I bet he doesn’t get it.”
“Jiangda University math PhD also joins one; I don’t believe an AI PhD can get Fields, especially this suddenly emerging god; probably like Liu Lu, lifetime relying on a flash of inspiration solving one problem, then nothing.”
“No, Xu Xian, shouldn’t you advise Ran Shen to transfer schools as the top-liked answer says? How to get Fields without going to Princeton?
At least transfer major to math department? Otherwise, you an AI major PhD, Fields gives it to you, where does pure math put its face? Even if you can get it, Fields won’t give it to you.”
“Can you not stand on head washing hair? Can you come mix eat and drink? I’m Tsinghua old eighth already impatient.”
“Don’t want to bet then don’t talk nonsense; he’s only not yet 24 now, meaning final verification of this bet is at 2034 International Congress of Mathematicians; only if he hasn’t gotten it by then can it be concluded.
Too long, who can wait!”
Xu Xian as Lin Ran’s real-world friend, real person coming out to speak, sparked hot discussion among melon-eating masses.
Because the bet wasn’t big, standing on head washing hair many could do, and verification was many years later, tons of people left messages in comments to bet with him.
After Xu Xian saw, he forwarded the top-liked answer and his own consecutively to Lin Ran, and added:
“No, Brother Ran, do you want to consider this suggestion?
You go to Princeton now, just send one email, then administrative staff will connect with you; you can go in the second half of the year.
Mentors like Pierre, Langlands top cows not easy; they’re old and don’t personally mentor students much, but finding a professor in prime of life shouldn’t be problem.
Find a professor with similar research direction, collaborate on big achievements, Fields definitely promising.
You direct ascension, I don’t need to stand on head washing hair!”
Due to time difference, Lin Ran saw it the next morning.
He saw it and smiled faintly: Langlands? At 1962 Mathematician Conference this guy was only 26, still Princeton assistant, not even assistant professor, could only stand.
Pierre that Xu Xian mentioned wasn’t Jean-Pierre, but Pierre Deligne.
His mentor Grothendieck, I bantered with him too; even ideas Grothendieck didn’t want to think, he was willing to think for me.
Even starting from zero, no need to find juniors.
In Lin Ran’s eyes, these masters were really just juniors.
“No need
Wait and see
2034? Gets Fields in 2022.
You win for sure!”
Lin Ran just replied one sentence.
Then found Li Xiaoman’s WeChat; a faint smile appeared on his face, then a touch of sorrow, because he really didn’t know how to convince Li Xiaoman to drop studies and return to China with him.
And if not returning, when he becomes world-famous in China, their intersection would be Li Xiaoman’s biggest risk.
Lin Ran sighed long then sent a WeChat:
“Sister Xiao Man, on Polymarket about 2022 Fields Medal winner betting results, when Randolph Lin option appears, blindly bet on my option.”
Finally dialed Mikhail Lyubich’s phone:
“Hello Professor Lyubich, hi, this is Randolph, Randolph Lin.”
Mikhail Lyubich, Jewish descent, Stony Brook University Mathematics Department Head, top master in numerical calculation field.
But already sixty, academic life almost over.
“Randolph, very happy to receive your call; seeing Stony Brook have another outstanding student emerge is rare good news currently.” Mikhail Lyubich said: “I emailed you hoping you transfer to math department, to fully play your talent.
Your paper I couldn’t fully understand, sorry time limited, but I asked some colleagues who could.
They all gave extremely high evaluations.
Stony Brook always like this, from Shiing-Shen Chern, Chen Xiuhong, Chen Gao; okay, pity you not surnamed Chen.
If you were surnamed Chen too it would be perfect.
Anyway, every era at Stony Brook, excellent Chinese descent mathematicians are born.
In the 2020s, again Randolph, you such outstanding Chinese young mathematician.
Come to math department, let your talent fully bloom.”
After getting old, likes nagging on and on about all sorts of things.
Especially recently all at home, no group meetings, no young administrative secretary sweet-talking, staying home Mikhail Lyubich was about to go crazy.
Every time calling others, he always likes to talk a lot.
“Professor Lyubich, of course, I’m very willing that at final graduation, I simultaneously get math PhD from you, and AI PhD from AI Innovation Institute.
So I need you to provide a little small help.
I believe future Stony Brook math department will be immensely proud because of me.”
Mikhail Lyubich laughed: “Randolph, I admit you can become an excellent mathematician.
But to make Stony Brook math department immensely proud of you, you think you can become this era’s Grothendieck?
This century indeed hasn’t birthed a Grothendieck-like figure yet, but who can I don’t know; you, I think probably quite a ways off.
Randolph, distance between excellent and outstanding is large, and from outstanding to Grothendieck even larger.
Young people having ambition is good, but too much ambition often becomes a burden.
Even if you really can, do it first, talk after done.
I think if you want to become Grothendieck, probably start from Fields first.
He got Fields at 28; your time is running out.
Six years later, you must get Fields.”
“Six years? Half a year!”
Even just phone, even just voice, Mikhail Lyubich heard incomparable confidence.
