Chapter 190: Professor Personally Serves As Host
“From launch to return, every step relies on mathematics. Trajectory mechanics, numerical integration, optimal control—these are especially important in the moon landing process. Let’s start from the most basic,”
Lin Ran walked to the blackboard, picked up the chalk, and drew an ellipse: “We start with Kepler’s laws. Planets and spacecraft orbit along elliptical paths, following the area law and the period law.”
He wrote down the mathematical expression for Kepler’s first law: r=\frac{p}{1+e\cosheta
“r is the radial distance, p is the semi-latus rectum, e is the eccentricity; this provides us with the analytical solution to the two-body problem.”
Lin Ran then added a circle, symbolizing the three-body system of Earth, Moon, and spacecraft: “But in reality, we face the restricted three-body problem.
The gravity of Earth and Moon act simultaneously on the spacecraft; no analytical solution exists.
We need numerical methods to approximate the trajectory.”
He wrote down the equations of motion.
I knew everyone in the audience had questions in their hearts: “The numerical solution to the three-body problem is a computationally intensive task.
In the actual moon landing process, computing a suitable result would be extremely difficult.
This involves optimizing numerical calculation methods.
To solve these equations, we used the fourth-order Runge-Kutta method, which strikes a balance between precision and efficiency.”
“We relied on IBM’s 7094 computer, which had limited performance.
Many times, computing a complete trajectory took hours; we had to optimize the code to reduce floating-point arithmetic.”
“Once, our simulation ran for three days. I found the step size was set too small, wasting time. After adjustment, the computation time was halved.”
Lin Ran erased the blackboard and rewrote: “Next is trajectory optimization. We need to minimize fuel consumption while ensuring the spacecraft arrives at the Moon at the right time.”
“Now we come to optimal control theory. In recent years, there have been many outstanding achievements around optimal control theory.
Let me talk about one related to aerospace. We define a cost function, which is the integral of fuel consumption, in the form:”
J =\int_0^T|u(t)|dt
“Where u(t) is the thrust control vector. We use the calculus of variations to solve it, obtaining the Euler-Lagrange equation.”
Lin Ran drew a simple example: “Similar to the brachistochrone problem, we seek the optimal path.”
Lin Ran continued: “But in actual missions, the equations are non-linear; we use numerical methods, such as the direct shooting method, to discretize the trajectory and transform it into a non-linear programming problem.”
From Kepler and the three-body problem, to numerical integration methods, to optimal control theory for fuel optimization, and finally error analysis and mid-course correction.
Lin Ran had essentially covered all the mathematical applications used in the entire moon landing process.
“Sorry, due to secrecy requirements, I can only explain much of the content very superficially and basically.
To put it bluntly, it’s just to give everyone an idea of the role applied mathematics played in the moon landing process.
Most people here do pure mathematics theoretical research; you can treat the applied mathematics problems used in the moon landing as diversions in your leisure time.
In the words of an ancient Chinese saying, this is just me throwing out a brick to attract jade.
In my view, mathematics is the cornerstone of all applications. Mathematics drives breakthroughs in human science, and I also thank everyone for your contributions to human technological progress.”
Lin Ran bowed in thanks, and the audience erupted in the most enthusiastic applause of the day.
Lin Ran returned to his seat in the audience, and Harvey Cohen, sitting beside him, turned and said: “Professor, that was excellent.”
In New York, at the New York Mathematicians Conference on his home turf, others had to be addressed with their names plus professor, but Lin Ran only needed professor.
Lin Ran asked: “What I said was too superficial, just like I said at the beginning—this is just an appetizer.”
Harvey Cohen shook his head: “No no no, it gave everyone here great inspiration.
While you were speaking on stage, I was chatting with Fox, saying that in the future, our math department’s students without talent should be made to do applied mathematics.”
Fox was the head of Columbia University Mathematics Department, and Harvey Cohen was the head of New York City University Mathematics Department.
Those doing applied mathematics might feel offended, Lin Ran thought.
Fox’s voice came from beside Harvey Cohen: “Professor, we previously thought you’d work at NASA for at most eight years; once Kennedy steps down, you’d leave Washington and return to New York academia.
I was already looking forward to handing over the math department director position to you early and enjoying retirement life.
You could stay in the Columbia University Mathematics Department director position for at least fifty years.
Surely recreating the Göttingen school in New York.
But year after year, Professor, you’ve become the NASA director.
Now I just want to ask: will you return to teach at Columbia University?”
Fox was somewhat in despair.
Year after year, you’ve actually become the big boss at NASA.
White House special assistant and NASA director are completely different concepts.
The former follows the president; the latter has a chance to stay in the position as a technocrat.
Moreover, with the moon landing successfully completed, Gagarin is undoubtedly a hero of all humanity, but Lin Ran’s prestige has also reached an unprecedented high.
Not to mention the Donkey Party—even if the US President switches to the Elephant Party, they won’t rashly replace Lin Ran.
Furthermore, power players in the Elephant Party like Nixon and Fred frequently claim in media interviews that they have close relations with the professor.
Clearly, Lin Ran’s NASA director position is impregnable.
“Professor, if you don’t return to full-time teaching at Columbia University in the next decade, I’ll consider finding someone else to succeed me.” Fox said helplessly.
Harvey Cohen exclaimed in a low voice: “Fox, aren’t you retiring in the next two years?”
Fox said: “If Randolph is willing to return to Columbia to take over, I can grit my teeth and endure another ten years.”
To hand over the math department director position to Lin Ran at the first opportunity, Fox was willing to delay his retirement.
Harvey Cohen initially thought this sacrifice was too great, but then felt that if it was for the professor, it wasn’t impossible.
Actually, positions like math department director aren’t that important in the American university system; many big shots don’t care.
Of course, some do care.
The reason Fox felt that sitting in the position waiting for Lin Ran to resign from NASA and take it over immediately was important was mainly to prevent other universities from poaching.
If other universities poached Lin Ran with such administrative positions, Columbia University would lose big.
From Lin Ran’s willingness to take the White House bureaucracy position, he inferred that he was influenced by Chinese traditional scholar-farmer-artisan-merchant thinking and cared about these things.
This was Fox’s thinking.
Lin Ran said: “Professor Fox, I don’t know; I don’t know how long I’ll stay at NASA.”
Fox heard in this a possible meaning of not coming back. “Alright, Professor, I’ll ask you once a year. If by the year I retire you haven’t given me a definite answer, I’ll retire according to the original plan.”
Lin Ran smiled: “No problem. I’m not that attached to the math department director position.
Rather than that, I’d rather directly become the president of Columbia University; I believe the board of trustees would be very willing.”
Fox was stunned, then said after a moment: “I think those old men would definitely be willing.”
Yeah, how did I forget this, Fox thought. Columbia University is a project directly supported by the Rockefeller Foundation.
David Rockefeller served as chairman of the Columbia University board of trustees.
With the professor’s relations with Rockefeller and Morgan, plus his own prestige, becoming president of Columbia University would be more than enough.
Fox felt his previous worries were completely unnecessary.
At the dinner banquet that evening, mathematicians came one after another to toast and congratulate Lin Ran.
The Mathematician Conference had turned into a Randolph fan meet-and-greet.
“Lin Sheng, as expected of the light of the Chinese people. This time, the face you’ve brought to the Chinese people is worth far more than a Nobel Prize.” Shiing-Shen Chern, as a Chinese person, chatted a few more sentences with Lin Ran in Chinese.
Lin Ran said: “The living environment for Chinese people in America is harsh. Besides academia, we should try to do something for our compatriots.
What I can do is only some help in terms of reputation. If there’s any donation targeting Chinese descent later, just let me know; I can also contribute modestly in terms of money.”
Shiing-Shen Chern smiled: “Good, I definitely won’t stand on ceremony. I’m planning to set up a scholarship targeting Chinese descent afterward; I plan to ask Tsung-Dao Lee and Yang Zhenning’s opinions.
If they are willing, the four of us can create a Light of the Chinese Scholarship, hoping that Chinese descent recipients of this scholarship can become future lights of the Chinese people.”
Shiing-Shen Chern was very enthusiastic; after all, if this was done, it would also boost his own status.
Mathematicians are no different from ordinary people in vying for fame and profit.
After the mathematicians’ banquet ended, news related to Lin Ran, as the center of attention, was quickly reported by the media.
“On December 24, 1964, Professor Randolph Lin gave a speech in Columbia University’s Havemeyer Hall, detailing to mathematics professors and PhD students the advanced mathematical methods used in the joint US-Soviet moon landing mission.
The professor is considered the key figure in this moon landing for his precise calculations that aided Soviet astronaut Yuri Gagarin in returning to Earth.
This lecture, with its accessible explanations and showcase of cutting-edge technology, left hundreds of attendees in awe.
This moon landing mission marks the first joint effort between the US and Soviet Union during the Cold War, a milestone in human space exploration. The professor’s calculations ensured the landing point error between the fuel tank and lunar module was within 1200 meters, a true engineering miracle.
In the hour-and-a-half lecture, the professor used clear logic and vivid examples to expound the core roles of trajectory mechanics, numerical integration, and optimal control theory in the mission. His remarks repeatedly elicited full-house applause, highlighting the decisive power of mathematics in space exploration.
Columbia University Mathematics Department Head Professor Fox praised: The professor’s speech not only revealed the mathematical mysteries behind the moon landing mission but also showcased the infinite potential of applied mathematics. His explanation was inspiring and opened new horizons for us.
Professor Fox stated that he plans to train more promising students to join the ranks of applied mathematics.
Math department PhD students excitedly said: ‘I never thought mathematics could so directly change history. This lecture has made me determined to devote myself to applied mathematics research.’ ‘The professor’s numerical analysis concepts are shocking; the computational precision NASA achieved is unimaginable.'”
When interviewed, the professor claimed the most grueling part was signing autographs for the attending guests, which was even harder than the moon landing mission itself.
At the end of the speech, the professor called: ‘Mathematics is the cornerstone of space exploration. It is through rigorous models and precise calculations that we sent humans to the Moon and brought them back safely. I hope young mathematicians draw inspiration from this and meet future challenges.’
These words elicited sustained applause, with the audience standing in tribute.”
Inside the University of Göttingen, Seagull was reading the news handed to him by Döblin:
“Well done, as expected of an outstanding graduate of our University of Göttingen!”
Seagull was very pleased; his student was renowned worldwide, and he felt honored too.
He was a mathematics master of the first half of the 20th century; his student was not only a mathematics master but also a White House senior official and a top aerospace engineer.
The student surpassing the master—what a perfect experience.
Apart from a small regret that he wasn’t in Göttingen, the greater Lin Ran’s achievements, the more Seagull felt he was getting the better end of the deal.
No matter where Lin Ran was, the connection between Göttingen and him was shallow, but his relationship with him was close.
Mentor and student—in the modern academic system, this was an undeniable relationship.
Even if only nominal.
But both he and Lin Ran acknowledged it; who dared deny it?
Not to mention academia—if he went to West Berlin now, which high official in the Berlin Senate would dare not give him face?
In London, Downing Street 10 would personally arrange for people to receive him.
Which other mathematics master had this treatment?
Did Pierre of Paris Normal School have it? Did Grothendieck of Princeton have it?
Only I, Seagull, have it. Why? Because of my student, of course.
So, Seagull had completely accepted the fact that he was Lin Ran’s mentor and was fully enjoying it.
Döblin naturally saw through Seagull’s complacent mindset: so what if I let him go.
He was somewhat helpless: “Professor Seagull, take another look.”
Seagull then noticed a detail in this New York Times report that he had missed: “You mean the twin prime conjecture?”
Döblin nodded: “Exactly.
This is the 8th of Hilbert’s 23 problems.
Göttingen people posed the question of the century; Göttingen people solved the question of the century—what great inheritance.
Yet now we can only watch this honor flow to Columbia.”
All because of the decline of the Göttingen school after World War II.
Among Hilbert’s 23 problems, problem 3 and problem 18a were solved by scholars from the University of Göttingen; problem 2 had significant contributions from University of Göttingen scholars.
But these all happened in the first half of the 20th century.
After World War II, no Göttingen school scholars appeared among the solvers of Hilbert’s problems.
So Döblin felt particularly regretful.
It was rare for one to emerge, one who could be called the Gauss reborn of the Göttingen school, yet he ended up elsewhere.
Döblin’s thinking was no different from the Chinese feeling about the imperial seal being lost abroad.
Döblin sighed, his face full of regret, making Seagull awkwardly change the subject:
“I have some tickets here. Ask if any professors want to go and distribute them to everyone?”
Döblin asked puzzled: “Tickets? What tickets?”
Seagull said: “December 31, London BBC Face to Face special program, an exclusive interview with Randolph Lin and Korolev.
It’s called the interview of the century.”
Seagull took out five tickets from the drawer, elegantly printed with the trajectories of the Moon and Earth, and outlines of Lin Ran and Korolev’s faces.
The tickets themselves gave an artistic feel.
Döblin nearly cursed: “Was zum Teufel!”
(“Was zum Teufel” in German means something like “what the hell”)
He snatched the tickets and admired them closely.
Seagull continued: “Randolph had BBC send them to me, saying to invite me and my family to watch the interview live.
I thought to distribute them to everyone.”
Döblin nodded: “Good, but there are too few—not enough to go around. Only four tickets, and our math department has more than four professors.”
Seagull nodded: “So we’ll do a lottery draw.”
Watching Döblin walk away, Seagull suddenly realized: “Wait, the four people you mentioned include yourself?
What about me?”
Five tickets, four taken to distribute—Seagull thought he was definitely going.
Döblin said: “Professor Seagull, you’re not short of tickets; just ask Randolph for another one.
If the two of us each take one, only three left for the professors—that’s too few.
One more is one more; Randolph surely won’t let you miss the live event.”
Seagull was momentarily speechless: “This works too?”
Shear a sheep hard?
Third floor meeting room of the London Broadcasting House.
Outside the window, winter’s thin fog enveloped Portland Square.
On the long table in the meeting room, The Times’ front-page headline boldly read: “Gagarin Returns from Moon Landing, US-Soviet Cooperation Shocks the World.”
The clock on the wall ticked, reminding that only three days remained until the December 31 “interview of the century.”
In the center of the meeting room, program producer Edward Thompson stood before the whiteboard, sleeves rolled up. His gaze swept over the seated team: host John Freeman, assistant producer Sarah Jenkins, technician Tom Harris, and news editor Mary Brown. Everyone’s face showed a mix of excitement and tension.
Everyone knew that BBC getting this opportunity was a once-in-a-lifetime chance.
The Kremlin wouldn’t dare let Korolev go to New York; the White House even less so let Lin Ran go to Moscow.
Thompson cleared his throat, his voice resounding: “Everyone, we’ve just received confirmation: NASA’s Dr. Randolph Lin and Soviet Sergei Korolev have confirmed participation in the New Year’s Eve special interview; their itineraries are set.
This is BBC’s milestone, a moment the world is watching.
It will be broadcast live on television, synced globally; we must ensure everything is flawless.”
Sarah Jenkins adjusted her glasses, her tone laced with irrepressible excitement: “Edward, you mean Korolev is really confirmed! Is this interview of the century really by BBC?”
Thompson nodded, a smile tugging at his lips: “Yes, Sarah.
The Soviet side has unusually agreed.”
After Lin Ran learned of it, he spoke with Downing Street 10 by telephone; a high official from Downing Street 10 personally notified him.
Lin Ran didn’t quite understand what the English people were so excited about. The Soviets agreeing—wasn’t this naked mockery? Thinking London was much safer for the Soviets and Korolev than New York—what kind of good evaluation was that?
Lin Ran truly couldn’t understand the English mindset.
John Freeman leaned back in his chair, fingers tapping the table lightly, weighing the program’s weight in his mind.
He had interviewed Carl Jung and Edith Sitwell, but this was different: the two aerospace giants from the US and Soviet on the same stage—any misstep could spark unnecessary waves.
He said softly: “This will be one of our trickiest programs. Question design must be precise: dig into technical details without touching political landmines.”
Mary Brown opened her notebook, tone calm: “The public wants to know how they cooperated—Cold War rivals joining hands for moon landing. But we must be careful not to let the program spiral out of control.”
Tom Harris scratched his head; the technician’s pragmatism made him focus on practical issues: “What about sound and translation? Does Korolev speak English? If real-time translation is needed, we must ensure microphones and headphones don’t glitch.”
Thompson responded: “The professor speaks Russian—oh my god, what a bizarre development: a Chinese man and a Slavic man doing a global live broadcast in Russian on BBC in London.
So we’ll definitely need to prepare real-time translation; coordinate with the professor in advance on whether he’ll speak English or Russian.
The microphones must not fail!”
Only at this moment did Thompson realize something was off.
BBC century interview airing Russian dialogue—what a magical development; was London turning into Moscow?
Freeman opened the outline, tone steady: “I want to start with technology, ask the professor how errors were controlled. Korolev can talk about lunar module design, like handling the Moon’s low gravity.”
Sarah interjected, eyes sparkling with curiosity: “Can we ask some human-interest questions? Like, what was the most tense moment of the mission? Their impressions of each other?
The technical questions you mentioned— the audience won’t be interested!”
Mary frowned: “Human interest is fine, but carefully. Asking about collaboration feelings might lead to politics. We must stay neutral.”
Thompson nodded: “Mary’s right. BBC’s stance is science and human achievement, not Cold War rivalry. I suggest asking their views on future space exploration, like more joint missions.”
Freeman added: “I can ask: ‘Does this cooperation pave the way for peace?’ But use open-ended questions, let them answer themselves, avoid accusations of bias.”
Sarah said softly: “The public definitely wants to know about peace possibilities. I’ve heard people in coffee shops saying this could be a Cold War turning point.”
Mary sneered: “Turning point? Don’t be too naive. Nikita and Johnson are still competing over nuclear bombs; this cooperation is just expediency.”
Thompson clapped the table: “Alright, stay on topic. We need to show the allure of science without turning the program into a diplomatic battlefield. John, set the question tone; Sarah, compile background information.”
Three days later, Lin Ran arrived at the BBC building a day early. The meeting room was filled with densely packed questions prepared for the Face to Face interview program.
In England, Lin Ran could still enjoy home-field advantage.
Though these questions were now in the hands of Korolev on the special plane.
The home-field advantage was what the English people thought was home-field advantage.
Lin Ran said to the program producer:
“I greatly admire Major Freeman, but for this interview program, I hope there is no host.”
Edward was shocked: “No host?”
Lin Ran nodded: “Exactly, no host.
Or more accurately, I am the host.
Doesn’t face-to-face mean one-on-one?
Major Freeman interviewing both me and Korolev at the same time—what kind of face-to-face is that?”
Edward was conflicted, specifically pondering how to refuse this White House senior official.
Before he could answer, Lin Ran said directly: “It’s settled. Rest assured, my one-on-one with Korolev will be far more exciting than with your hosting.”
Ten thousand words delivered—begging for a monthly ticket!
