A Problem to Set

Shen Qi provided Academician Pan's team with a brand-new quantum key distribution theory system. The foreseeable application scenarios include military, finance, communications, and the Internet. It will render malicious hackers futile, make the military's communication system more reliable, and make people's bank cards more secure.

The large-scale application of quantum cryptography relies on fundamental quantum physics. The complete replacement of CPUs by QPUs is not something that can be achieved overnight, but Academician Pan's team has at least clarified their future research direction. With the Mozi quantum satellite in the sky and a brand-new quantum key distribution system on the ground, they know very well what to do next.

The theoretical framework of the "Riemann Theorem Prime Number Carrier Quantum Key System" cannot be published publicly for the time being. Shen Qi quietly left the quantum Computer Science laboratory to do something that could be made public to the world.

Today is Sunday. Shen Qi spent the whole day in seclusion in his hotel room, shifting his focus from Riemann Theorem to Riemann manifold. He temporarily forgot about number theory and Quantum Physics, concentrating on studying algebraic Algebraic Geometry and topology.

"Riemann is truly an energetic man; you can see his name in every field." Based on a fundamental property of Riemann manifold, Shen Qi takes orthonormal bases in each of its tangent spaces to simplify local calculations.

The topology section of the Hodge conjecture is another major problem that Shen Qi needs to solve during his return to China. The whole world knows that he is trying to conquer the Hodge conjecture.

The following Monday, Shen Qi arrived at the Morning Star Mathematics Center: "Director Wu, brothers, how was your four-day holiday?"

"My wife and I climbed the Great Wall. This is the eighteenth time in my life I've been a hero." Director Wu sniffled; he caught a cold from the cold wind on his eighteenth Great Wall trip.

"I didn't go anywhere; I just stayed home taking care of my child," said a researcher surnamed Liang.

"I went to Dali, and there were plenty of beautiful girls from all over the country, but unfortunately I didn't get a single number," researcher Xiao Bian sighed regretfully.

"Looks like everyone had a great holiday," Shen Qi said with a smile.

Director Wu, who is in his fifties, has a child who is a junior in college, and he and his wife chose to go on a short trip to the suburbs.

Researcher Liang, in his thirties, recently became a father and chose to stay home to take care of his child.

Xiao Bian, 28 or 29 years old and currently single, chose to travel to Dali hoping for a romantic encounter.

Director Wu and his researchers generally marry and have children later in life; apart from the single ones, most of their leisure time is spent with their families.

A family-oriented man is trustworthy. Shen Qi learned that five of the other six men in the conference room were married, three of whom were Cancerians. They loved their wives and children, and were filial to their parents and in-laws.

"Where did Professor Shen go off to have some fun?" asked Xiao Bian, a single guy.

"Me? Just a four-day trip to the capital," Shen Qi, who is unmarried but not single, said, handing a USB drive to Xiao Bian: "I've written some notes on the topological method of the Hodge conjecture these past few days, and I hope to share them with everyone. Engineer Bian, could you please project it?"

Shen Qi's insights were projected onto the screen, and Director Wu's six-person team stared intently at the screen. The holiday was over, and they were back at work.

Shen Qi began to explain his insights, "The core logic we previously established was to derive the eight Standard Model based on Thurston's Geometrization Conjecture. Director Wu, in the past few months, you have completed the derivation of the three Standard Model: the standard sphere S, Euclidean space R, and hyperbolic space H^3. You encountered difficulties with the left-invariant Riemann metric on the universal cover of special linear groups."

"The derivation of the left-invariant Riemann metric on the universal cover of special linear groups, which is the most complex of the eight Standard Model, is a significant development. I've done a derivation; please see the screen." Shen Qi switched to the next page and said, "The transition mappings of complex manifolds are holomorphic. I've applied a new treatment to the Cauchy- Riemann equations and obtained an interesting result: Γ is a 1-dimensional complex manifold, and its geometric and topological properties are quite unique..."

Shen Qi spent the entire morning explaining the detailed process and final conclusions of his derivation of the most complex Standard Model.

Of Shen Qi's first explanation, only Director Wu understood it.

Within a week, Shen Qi explained the plan six times. Combining new inspirations, he revised it as he explained it, and finally finalized the plan on Saturday. All six members of Director Wu's team understood Shen Qi's thinking.

"So we have completed the derivation of four of the eight Standard Model. My suggestion is that everyone should follow the derivation logic of the Riemann metric Standard Model to solve the remaining four Standard Model," Shen Qi summarized and gave his advice.

"Received!" Director Wu's team has received Shen Qi's true teachings, and in the coming period, they will complete the subsequent work based on the deductive reasoning set by Shen Qi.

Academician Pan solved the quantum key problem, and Director Wu solved the topology problem. Shen Qi left everyone with the impression of being efficient, responsible, and a specialist in solving difficult problems.

Besides high-level academic research, Shen Qi is also very concerned about mathematics education for primary and secondary school students.

With Shen Qi's consent, the Chinese Mathematical Society, the organizer of the International Mathematical Olympiad, displayed an artistically edited photo of Shen Qi on its official website homepage.

This year's CMO competition is in full swing, with a record number of applicants.

Shen Qi was invited to the Chinese Mathematical Society to undertake an important task—setting the questions.

"Professor Shen, you've won the CMO championship and the IMO championship, both with perfect scores. It's perfect that you set the final question for this year's CMO national finals," said the head of the CMO organizing committee.

"No problem."

Shen Qi walked to the blackboard, picked up the chalk, and immediately wrote down a question:

Let n be a positive integer. Consider a set of (n+1)^3-1 points in a three-dimensional space, S = {(x, y, z)|x, y, z =0,1,2,..., n, x+y+z>0}. What is the minimum number of planes required whose union contains S but does not contain (0,0,0)?

Shen Qi patted the chalk dust off his hands. "Hmm, this is the question I set. It's a bit difficult, meeting the standard for the last question in the CMO national finals."

The other three people in the meeting room stared at the problem on the blackboard, deep in thought.

"The design of this question is very ingenious. It utilizes high school math knowledge, along with some not-too-difficult supplementary knowledge. High school students should be able to find the correct answer," Vice President Tan commented first.

Shen Qi's old friend, Cadre Liu, said, "Is that possible? I predict that the number of high school students in all of China who can find the correct answer is less than a handful."

Shen Qi suddenly remembered something. "Leaders, there's a mystery I haven't been able to solve. In the CMO national finals I participated in, how many contestants got full marks on the last question?"

Cadre Liu said, "Shen Qi, the last question in your year's national finals was incredibly difficult, truly insane. I remember it very clearly. I was grading the papers at the time. That question required the contestants to prove that the square root of 2 is an irrational number, but they were not allowed to use geometric construction methods. Out of all the contestants, only two successfully proved that the square root of 2 is an irrational number without using geometric construction methods, and one of them was you Shen Qi."

"That square root of 2 question was quite interesting. By the way, what's the other contestant doing right now?" Shen Qi asked with interest.

"He was selected for the Olympic Math national team and was admitted to the Mathematics Department of Shuimu University without taking the entrance exam. I'm not too sure where he went after that. I heard he went to the United States for further studies?" Cadre Liu said uncertainly.

"What's your name?" Shen Qi asked again.

Cadre Liu: "His name is Yu Lei. He was selected for the national team in the same batch as you, Shen Qi."

"It's him! Yu Lei!" Shen Qi was stunned for a moment, then burst into laughter. "Yu Lei is currently pursuing his PhD in the Princeton Mathematics Department, and I am his doctoral advisor."

"What a coincidence?" Both Cadre Liu and Vice President Tan were surprised and found it quite amusing.

Only two high school students proved the most difficult and challenging math olympiad problem back then, and now the two are teacher and student.

Finally Cadre Kong hadn't spoken until now, said, "Everyone, let's talk about the question Shen Qi posted on the blackboard. Old Tan, Old Liu, can you two find the answer to this question?"