Princeton-Style Tribute
If you randomly interview ten citizens on the streets of America and ask them, "Who is the greatest mathematician of our time?"
Nine out of ten citizens would answer, "John Nash."
Nash and his film "A Beautiful Mind" are so famous that there are very few film and television works related to mathematicians, so everyone remembers Nash.
Princeton considers Nash a valuable asset to the school, and the information bulletin board on the first floor of the Mathematics Department building is always adorned with posters of "A Beautiful Mind".
Nash made outstanding contributions to game theory, a consensus shared by all the professors present.
Professor Milnor made greater achievements in perfecting systems such as differential topology and K-theory, a consensus among the professors.
These leading mathematicians emphasize the establishment of systems, and they use only two professional standards to measure the level of mathematicians: system and innovation.
In today's Mathematics Community, true innovation is becoming increasingly difficult, and integrating systems has become a reliable path to enlightenment, offering hope at least in one's lifetime.
It's a rigorous and completely innovative system; whoever can create this will be utterly awed by the entire Mathematics Community.
Professor Milnor dedicated his life to system integration, and the triple crown of Math Prize is the best affirmation of his career.
"A toast to John Milnor." Director Feierman raised his coffee cup.
"John Milnor."
"John Milnor."
Everyone raised their glasses, chanting the name John Milnor.
That's how Americans are; when inspiration strikes and they feel a connection, they like to celebrate or pay tribute to something or someone—it comes from the heart, and their emotions are genuine.
Professor Milnor smiled slightly, accepted the salutes, and said, "I was born in New Jersey and have spent my entire life at Princeton. I think it's time for me to leave."
"No way, John?"
Where are you going?
The professors and doctoral students were surprised; why did the old man just leave like that?
Milno said, "I'm over eighty years old, it's time to take a break. I sold my house in the US, and luckily, I can buy a house three times the size in Oristano for the same price."
Oristano is a Xiao Cheng on the Italy island of Sardinia, a popular holiday destination.
"So John, you're going to Sardinia to enjoy life." Director Feierman understood; Professor Milnor was retiring after achieving his goals and preparing to leave the political arena.
"I'll send you postcards, Charles," Professor Milnor said casually.
Director Feierman put down his coffee cup, walked over to Professor Milnor, took a fine pen from his pocket, and solemnly placed it on the table in front of Professor Milnor.
"Serving the nation, serving every nation." Director Feierman extended his right hand in a handshake gesture, his expression respectful.
Professor Milnor did not get up; he smiled and nodded, then shook hands with Director Feierman while still seated.
The originally relaxed coffee time suddenly turned solemn.
Next, Edward Witten walked over to Professor Milnor, placed a pen on the table, and respectfully shook hands with him. "Serve the country, serve every country."
As if they had rehearsed beforehand, dozens of F, W, and A Prize winners, including Faltings, Lyndon Strauss, Okonkov, Hirst, and Lenci, were doing the same thing over and over again.
Each of the distinguished scholars presented Professor Milno with a pen, saying the same thing, "Serve the country, serve every country."
"Serve the nation, serve every nation" is Princeton's unofficial motto; you don't usually hear it, but you might hear it on special occasions.
Dozens of different kinds of pens were neatly arranged in a row in front of Professor Milnor.
In the United States, people of status and position will always carry a high-quality pen with them, ready to sign checks and documents at any time.
For mathematicians, the pen is their closest companion; these top professors all carry a pen with them.
These pens were all given to Professor Milnor in a customary ceremony.
Shen Qi was shocked. He knew that this scene was definitely not rehearsed beforehand; it was an impromptu event.
"The more pens you receive upon retirement, the greater your achievement; it's Princeton- style tribute. If you acknowledge someone's accomplishments, then give them a pen," Professor Muller said to Shen Qi, then stood up to present a pen to Professor Milnor.
Shen Qi stood up, took out his Montblanc pen, and thought, "He's a master artist, after all; he should carry a pen with him, shouldn't he?"
"Shen Qi, sit down." Professor Muller pressed Shen Qi back into his chair.
"I fully acknowledge Professor Milnor's outstanding achievements." Shen Qi was puzzled. Why couldn't he present a pen as a sign of respect?
"When you become a full professor at Princeton, you will be eligible to give pens as gifts. But not now." Professor Muller explained the rules to Shen Qi, then presented the pen to Professor Milnor.
With a pile of pens and profound respect, Professor Milnor left the café, and soon after, he too would leave his hometown of New Jersey to move to Europe.
Princeton- style farewell ceremonies are simple yet solemn, and are respected here for moral, intellectual, and academic contributions.
The old chieftain of Milnor has retired from his life of crime, but his legend lives on forever. He never wrote a complete proof on the blackboard, yet he won the highest mathematics awards.
"Establishing a system is the most important thing." Shen Qi drew inspiration from Milno's real-world case.
However, everyone knows that building a logically rigorous system is far more difficult than proving a theorem. Building a system is a massive undertaking that requires huge and continuous investment of human, material, and financial resources.
The only advantage of establishing a basic mathematical system is that it doesn't require an astronomical amount of money; the biggest investment should be in human resources.
"I'm short-handed and my abilities are limited, so I can't come up with a new theoretical system right now. I should focus on proving my theorems first. Once I've proven enough theorems, the system will naturally emerge."
That makes sense. Euclid proved 465 theorems in his lifetime, and the classic system of Euclidean geometry has been passed down for more than two thousand years.
Shen Qi continued his work on proving the "Muller -Shen Theorem" and, at the end of September, collaborated with Muller on a first draft.
"The exciting result is that we have completely proven assertions (1) and (2), more perfectly than I proved in 1982, without any flaws." Muller's excitement was followed by a thoughtful expression. "But the problem is that the proof of assertion (3) is disappointing, and perhaps we will not be able to complete the final proof for another month."
Shen Qi said, "Every ω* closed convex set of X* is an approximate compact Chebyshev set. Regarding this statement (3), I think our initial thinking was wrong. It is independent and should not be linked to statements (1) and (2). But this is not a bad thing. Perhaps it is something to be thankful for because we discovered it early."