"I got some inspiration from some of Hamilton's assumptions about your program of proving the geometry of a closed 3D manifold that I felt I could prove," says Lu Qiujian, "to build a key elliptic estimation and apply a coarse subdivision solution to prove your geometric guess"

Lu Qiujian looked at the expressions of the two professors opposite as he spoke, intending to decide whether to explain the content of his exposition more clearly according to their expressions.

The two professors gave two diametrically opposed expressions, Thurston listened with relish, but Professor Nan's face was full of confusion, and when he saw Lu Qiujian looking over, he waved his hand and said, "It's okay, don't worry about me, this is not my research field, I'll just listen to it, you focus on communicating with Professor Thurston!"

"Interesting idea!", said Professor Thurston, rubbing his chin, "using the previous collapse results on the lower bound of local curvature, an accurate proof of this guess!"

What Lucius wrote on the test paper was only a direction, and Professor Thurston had deduced from his few short sentences what he had to do, which saved him a lot of time, "It is so, using a monotony of the Ricci flow, which holds true in all dimensions and without the need for curvature assumptions"

So the two of them began to go back and forth, and Lu Qiujian found that Professor Thurston's way of studying mathematics was very intuitive, and his amazing visual ability often allowed him to "see" that a conclusion about a three-dimensional manifold was correct, even if he could not give a rigorous proof, if someone could complete the proof process, he would find that the answer he got was no different from Professor Thurston's prediction.

If you put it in a mathematician who is very strict with the process, he will find it very difficult to have a conversation with Thurston, but in Lu Qiujian's opinion, this kind of dialogue is more efficient and time-saving, which is like two Go masters playing against each other, mortals can see the situation after three moves, and Thurston can see seven moves away, Lu Qiujian can also do this, so ordinary people may have to play chess to the middle game, and these two people casually put dozens of chess pieces on the chessboard, and the result of this game was exposed in front of the two.

Thurston also felt that the conversation with Lu Qiujian was very appetizing, and those old-fashioned scholars who listened to his conjectures usually asked him to give the derivation process, which made him tired of these tedious work, and Lu Qiujian was able to quickly build a model of this guess in his mind after listening to his description, and then deduce more results, which made him feel that he was too late to see each other.

At first, Thurston could sit upright in a chair and chat with Lu Qiujian in a soothing rhythm, but later the more he talked, the more excited he became, sometimes waving his arms loudly to express his excitement, sometimes slapping the table vigorously to express doubt, and then laughing out loud and laughing at himself for having just found the wrong direction. Anna, who provoked the door, thought that there was a fight in the office, and came in several times in a row.

"Perfect chain!", when Lu Qiujian finished talking about the last derivation process, Thurston praised with both relief and regret, relieved that another boulder standing in front of the mathematician would be removed, and unfortunately it seemed that such a wonderful conversation had come to an end!

"Okay, it's time for us to go to dinner now, right?", Professor Nan, who was quietly listening to the exchange between them, flashed his watch, "It's nine o'clock in the evening, aren't you all hungry?"

“OK! Let's go!", Thurston smiled embarrassedly at Professor Nan, "I've got dinner in store to thank you for bringing me such a wonderful Christmas present!"

"No, I'd better do it!", Professor Nan shook his finger, "I argued with Dyson and Witten for a long time at noon, it seems that this time I am going to win this bet! The exam of the Physics School is over, and they don't have a chance to send these seven questions to students as exam papers!"

"Hahahaha!", it was rare to hear Professor Nan make a joke, and Thurston and Lu Qiujian laughed at the same time.

Putting on their coats, the three of them walked out of the office, and poor Anna was still guarding her desk outside the door, boredly browsing the advertisements for eBay's products.

"I'm sorry, Anna, I forgot to get you off work!", Professor Nan was a little embarrassed, why didn't she think about it after she had been in and out several times just now, "You can go back now, I will apply to the school for a promotion and a salary increase after Christmas, in recognition of your outstanding work in this section!"

If she hadn't made a low-level mistake, how could she have the opportunity to witness this great discovery that shook the entire world of mathematics! It seems that she is her lucky star! Professor Nan thought so.

Professor Nan drove them to a Chinese restaurant in a hidden corner, greeted the owner and waiter of the store familiarly, and looked at Lu Qiujian's curious appearance and explained, "From Chen Shiingshen, Yau Chengtong to me and Shi Yigong, and then to young people like you, Princeton has always been not short of Chinese, so it is still normal to have a few Chinese restaurants! The taste of this restaurant is very authentic, you can try it later!"

Without looking at the menu, Professor Nan reported a long list of dish names, and finally asked for a bottle of Moutai, which was called a celebration of Lu Qiujian.

When the wine and food came up, Professor Nan stubbornly blocked Lu Qiujian, poured a full glass of wine for him and Thurston with his own hands, and finally picked up the glass and said, "Come, the first cup of congratulations on the successful picking of another jewel in the crown of mathematics!"

The three of them drank it all, and Thurston smacked his tongue after drinking it, "Nan, this wine is too strong!"

"Haha, what is that!", Professor Nan laughed, refilling their glasses as he said, "When I was in Moscow, I drank a lot more vodka with Grisha than this!"

However, looking at Thurston's drugged expression, after the first three toasts, Professor Nan stopped pouring him liquor, and patiently asked about the follow-up work, "When are you going to finish your thesis?"

"Now the derivation chain has been almost completed, and it will probably take more than a month to complete, right?" Lu Qiujian replied, "As for the goal of submission, I have been publishing articles in the Annals of Mathematics before, and I chose them this time, what is your opinion?"

"No, no, no, it won't take a month at all!", without waiting for Professor Nan to speak, Thurston interjected, "I'll tell you a way to write a paper, you can do it, and you can get the paper out in half a month!"