Technology invades the modern world

Chapter 448 Divinity Has Never Disappeared

The entire meeting was arranged in a very relaxed manner.

Considering that Lin Ran would need to intersperse negotiations with the Chinese side along the way.

Four years ago, because the mathematicians' congress was held in Moscow, America sent only a small number of representatives, and China also sent only a small number of representatives.

Both countries sent a large number of mathematicians to participate in this congress of mathematicians held in France.

Among them, Chinese mathematicians were divided into two groups. One group was able to go to Area 51, led by people like Hua Luogeng and Su Buqing. The other group stayed in Yenching at the Institute of Mathematics of the Chinese Academy of Sciences, led by Wu Wenjun.

Wu Wenjun was a student of Chen Xingshen before 1949.

This classification is somewhat similar to the distinction between exoteric and esoteric Buddhism.

Almost all of Wu Wenjun and other mathematicians came this time.

This includes Jiang Lifu, the former director of the Institute of Mathematics, Academia Sinica.

Jiang Lifu was also Chen Xingshen's teacher, although not in the direct mentor-mentee relationship, but rather a teacher with whom he had taken classes and shared a close bond.

Jiang Lifu's son passed the exam to enter Area 51 before finishing university and became a member of the Hidden Sect, while Jiang Lifu himself continued to teach in Yanjing because of his identity.

Chinese mathematicians also took every opportunity to chat.

First, Chen Xingshen approached Lin Ran and exchanged a few pleasantries, explaining the problems he had been working on recently and expressing his hope to have the opportunity to collaborate with Lin Ran.

Then came Wu Wenjun, who expressed his gratitude and invited him to attend the bilateral mathematicians' conference held in China.

Lin Ran thought to himself, "I'm still too naive. If I could participate, wouldn't I come?"

Next was Jiang Lifu, who came to express his gratitude, but Lin Ran didn't know what he was thanking him for.

Upon closer listening, it was learned that Chen Xingshen had asked him to sign a copy of "New Advances in Mathematics," which was then sent across the ocean to Jiang Lifu, who used it to encourage his son, Jiang Boju.

As a father, Jiang Lifu thanked Lin Ran for giving his son spiritual encouragement.

This International Congress of Mathematicians is also a grand event for Chinese mathematicians.

Everyone can have ample opportunities for exchange at this grand event.

Many people, though living in different countries, have gained a new understanding of the concept of "cultural China" mentioned by Lin Ran when they communicate in Chinese.

In France, Americans and Chinese communicated about mathematics in Chinese, using similar allusions; the cultural ties had never been so clear.

On the third day of the conference, in the auditorium of the Nice conference center, Jean Lere, chairman of the organizing committee, stood on the stage and announced the next speaker: "Next, please welcome Professor Gian Carlo Rota from MIT, whose topic is 'Prospects for Array Theory'."

The name sounded familiar to Lin Ran.

Rota?

Is it the Rota conjecture?

Rota, an Italian-American mathematician, stepped onto the podium.

"Ladies and gentlemen," he began, "matroids as linearly independent abstractions have come from the work of Hasler Whitney, but today I would like to propose a bold conjecture, a unified framework for representation over finite fields."

In the audience, Lin Ran sat in the first row with his notebook open. He vaguely felt that the other person was talking about the Rota Conjecture.

Rota continued, “Consider a finite field F_q, where q is a prime power.”

A matroid M is said to be F_q-representable if it can be represented as a linear independent set in a vector space over F_q.

Whitney's theorem tells us that for the real or complex number field, a matroid can be represented by a finite number of forbidden subarrays.

But what about finite fields? I speculate that for every finite field F_q, there exist a finite number of forbidden elements such that a matroid is F_q-representable if and only if it does not contain these forbidden elements as submatroids.

The auditorium was filled with discussions among the mathematicians.

Rota drew examples with chalk: For GF(2), the forbidden parts are known to include uniform matroids and some binary affine geometry; for GF(3), the forbidden parts are more complex.

He explained, “This is similar to Kuratowski’s theorem in graph theory, but generalized to the matrix implementation of matroids.”

Proving this conjecture would unify the representation theory of matroids, providing finite barriers to determine whether a matroid can be embedded in a vector space of a finite field.

Once Rota got to this point, Lin Ran could confirm that this was Rota's conjecture.

The Rota Conjecture remained unresolved until 2025, the year he arrived.

When Rota finished her report and the Q&A session began, not many hands were raised, and in the first row, only Lin Ran raised his hand.

Lere immediately said, "Professor, please speak."

Lin Ran stood up and asked, "Professor Rota, your guess is fascinating."

I noticed that we might be able to partially verify this for the finite field of feature 2.

Suppose we consider binary quastic representations, which correspond to representations on GF(2).

The forbidden components are known to include the Fano plane, which is the dual of PG(2,2), and some non-Fano configurations.

However, if we restrict it to matroids with rank r ≤ 4, I believe we can prove the existence of finite forbidden parts.

May I come up and demonstrate?

Rota's eyes lit up: "Of course, please come up, Professor."

This is like you're nobody, and a big shot suddenly becomes interested in your report.

You were naturally overjoyed.

Luo Ta is no nobody, and Lin Ran is no ordinary genius either.

Lin Ran walked onto the stage, borrowed the blackboard, and began his explanation.

He first erased part of his notes and drew a rank 3 binary matroid representation: a 3xn GF(2) matrix with linearly independent column vectors.

"Let's start with the basics. The basis of a matroid M is the largest subset of its independent sets. For an M that is GF(2)-representable, the columns of its representation matrix satisfy the following: the linear dependence of any subset corresponds to the cycle of the matroid."

Everyone present realized that Lin Ran was about to begin her performance.

Lin Ran continued, “Assume that M avoids known forbidden pieces: 7-point matte, its dual, and 5-point 3-rank uniform matte.”

For r≤3, we classify them using Whitney’s broken matrix theory: all such M must be a graph matroid or its complement, or a subclass of the binary affine geometry AG(3,2).

Now, generalizing to r=4: consider the Tutte polynomial T(M;x,y), which is a bivariate polynomial that encodes the independent set and cycle of M.

T(M;1,1) gives the number of bases.

Lin Ran finished, wiping away the chalk dust: "This provides a partial proof for the low-rank case on GF(2)."

If extended to higher-order domains, the Schauder-Leray topology tool may be required.

Professor Rota, your conjecture is very interesting.

Under pressure, I can only provide a complete proof under specific circumstances.

Rota was completely absorbed in Lin Ran's answer, and the reaction from the audience was overwhelming.

From front to back, Grothendieck led the way in standing up and applauding.

Is this a repeat of the Göttingen miracle?

"Rota was completely stunned."

"I just want to ask, is the professor married? I'd like to marry my daughter to him! Or, if not, just raising a child with him would be fine too!"

A murmur arose from the audience. These were mathematicians who couldn't grasp Lin Ran's solution in a short time; those outside this field certainly wouldn't understand it so quickly.

The experts, on the other hand, were discussing Lin Ran's solution itself.

Lev Pontryagin whispered to the mathematician beside him, “The professor’s induction is so ingenious. He bridged representation theory and combinatorics with Tutte polynomials. It’s brilliant! It jumps directly from Whitney’s 2-isomorphisms to Tutte’s decompositions, filling the low-rank gap. Is this a flash of genius?”

Pontryagin was the first Soviet Russian mathematician to win the Fields Medal, which he received this year.

Grothendieck shook his head helplessly: "This guy, everyone says that mathematicians rely on a flash of genius, but I feel like his flashes of genius have never stopped."

Attending such an event for the first time, Jiang Lifu whispered to his student Chen Xingshen, "Xingshen, I'm not skeptical, I'm just a little curious, is the professor really that amazing?"

He lowered his voice further: "Could this be a staged event? Did the professor know the questions beforehand, come up with the answers, and then put on a show at this conference?"

Jiang Lifu even suspected that the answer wasn't what Lin Ran had thought of, but rather an operation by America to package a mathematical god.

Chen Xingshen smiled wryly and said, "I also hoped so, but unfortunately it wasn't."

The professor is truly amazing. I think his mathematical intuition is no less than Gauss's. If you had seen him prove the twin prime conjecture in Göttingen, you would know that what he said in the interview was true; mathematics is like breathing to him.

This is just another confirmation of his words.

When Lin Ran returned to his seat, applause rang out once again.

Jean Lere remarked, "Professor, your on-site proof has added a touch of legend to this Congress of Mathematicians, making it less unremarkable."

The following morning, newsstands in Nice were filled with headlines from local French newspapers and international media capturing this unexpected academic storm.

While the mathematics community may not attract as much public attention as the political arena, it still depends on who is involved and how dramatic the event itself is.

Lin Ran's breakthrough on stage quickly became a hot topic due to Lin Ran himself, as well as its dramatic nature and potential impact.

The headline in Le Monde reads: "Another teaching moment at the Nice conference: Breakthrough in matroid theory shakes the mathematics world."

America's New York Times headline read: "From Göttingen to Nice: The Professor's Divinity Has Never Disappeared."

America's favorite thing is to create gods.

As for Jean Lere's statement that this congress of mathematicians was unremarkable.

Is it unremarkable?
how is this possible.

This year's Congress of Mathematicians involved negotiations between China and America, so how could it be lackluster?

This negotiation alone is enough to make this year's Mathematicians' Congress legendary, isn't it?

As per Lin Ran's request, they were arranged to stay in villas near Nice, with Lin Ran and the Chinese representative each staying in one room.

However, the two villas are spaced a certain distance apart to ensure that both parties have sufficient privacy.

Lin Ran meant that this would be a long negotiation.

Negotiations began on the fourth day of the mathematicians' congress.

The three events are interwoven: negotiating, attending a mathematicians' congress, and preparing to return to the 2020 timeline as a cyber God in 1960.

Lin Ran stood up to greet him, and the representative from China waved for him to sit down.

"Professor, you're too kind. This isn't the first time we've met, but it's been quite a few years since we last met. That time was in Geneva, and now we're in Nice."

The night breeze in Nice is lovely, reminiscent of the sound of the Yangtze River.

I heard you were born in Berlin and went to America after the war. You may never have set foot on Chinese soil in your life, yet you have such a deep affection for Chinese culture. This suggests you come from a family with a rich scholarly tradition, not an ordinary one.

In that era, most of the people who could get to Berlin were not ordinary people.

At the very least, if someone could fill in the gaps in Berlin during World War I, they would be considered an elite soldier. To stay on, one would need to have some connections.

"Mathematicians getting involved in politics—the world never goes the way we expect."

Lin Ran felt like he could hear the subtext: Are you implying something about the Gao Bao Qi Ren, or about the raspberry pie I gave you?

Lin Ran was alone in his villa; security personnel were on duty outside.

Therefore, this conversation consisted only of him and the Chinese representative.

But that doesn't mean he can say whatever he wants.

Nobody knows if there are any security devices installed here.

Both sides are being very cautious.

"Yes, after World War II, people thought that peace was coming, but little did they know that what was coming was the Cold War."

The Cold War caused devastating losses to all countries.

No one knows whether peace or war will come first.

Will the Cold War continue indefinitely, or will it eventually escalate?

But we hope to make every effort to bring about peace.

The shadow of Soviet Russia loomed over the East.

The normalization of our relations should not be merely a geopolitical game, but rather a mutual learning between our two civilizations.

Consider this: if the harmonious principles of Chinese civilization and America's spirit of freedom could be integrated, it would bring true multipolar balance to the world.

Lin Ran quickly got to the point.

“In America, I have witnessed racial divisions, the struggles of immigrants, and fought for the rights and equality that Chinese people deserve!”
We Chinese people, struggling to survive in the cracks, have always cherished the dream of rejuvenation.

President Nixon's proposal was pragmatic, because he understood that a strong China was not a threat, but an anchor of stability.

If we can transcend ideology and jointly face global challenges—peace under the shadow of nuclear war and development amidst poverty—that will be a source of pride for all Chinese people.

In fact, Lin Ran was already hinting at it.

Nixon was able to accept a powerful China.

If it were another president, things might not be so simple.

"Professor, your love for your homeland moves me deeply."

We Chinese, no matter where we are, are all of the same lineage.

Negotiation is not a zero-sum game, but a search for common solutions.

The Cold War divided the world into two sides, and we need to mend it so that different camps can interact. China is willing to be a pioneer in this endeavor.

Tell Nixon: We are willing to talk, but only on the condition of respect—respect for our sovereignty and respect for Asian national self-determination.

If we can join hands in the future, it will not only end the tragedy of the Vietnam War, but also usher in a new era, an era in which the Chinese people can be proud.

This is certainly not something that can be discussed on the first try.

This is the main focus of the negotiations, which will last for a full month.

Negotiations can be conducted during the day, taking their time and allowing for plenty of discussion.

As for what happens late at night, Lin Ran will return to modern China to continue the final push for the lunar superconducting chip.

Incidentally, give Russia the N1 rocket as a selling point, and also develop a 5nm lithography machine to give the White House a little surprise.

(End of this chapter)