How good is Professor Feng
What conjectures did he prove, what theoretical foundations did he lay down, what achievements did he make in the end, and how was he evaluated
Lin Zhaoxi wanted to know this very much.
In the next few days, Lin Zhaoxi still maintained the rhythm of attending classes during the day, training in the evening, writing programs at Chen Zhu’s house at night, and working as a supervisor for Lao Lin late at night.
In her spare time, she would start to search for terms that she had never heard of before based on "Feng Deming"'s personal academic achievements in Baidu Encyclopedia.
The metric space structure of a certain manifold, the scaling theory and its fractal geometry... After those terms, there are many difficult papers, which are completely like the content of another space.
However, the development of relevant academic forums seven years ago was far behind that of later times. In many cases, she could not find what a certain theory and a certain conjecture meant, and could only roughly understand the content of what branch they were.
So she didn't regard these things as serious work, but when she was tired, she would start to check casually, more like gossip, a kind of aimless academic gossip.
Professor Feng has made remarkable achievements and is highly respected. Whether it is an academic conference or a forum at Yongchuan University, the students all respect him sincerely.
The reputation is like a huge wave, sometimes breathless, it seems that even if she brings back all the unfinished content of Lao Lin to reality, compared with Professor Feng's achievements, it is like the light of fireflies and the bright moon.
Lin Zhaoxi can only comfort herself, and it doesn't matter, Lao Lin's target has never been him.
During these long days, Pei Zhi would occasionally accompany her at night. After three weeks, Lin Zhaoxi confirmed that this "occasionally" specifically refers to Wednesday night and Saturday.
On Wednesday they went to Chen Zhu's house to surf the Internet together, and Pei Zhi would also use the computer for a while. At ten o'clock in the evening, Pei Zhi would take her home and leave alone.
Saturday was Lao Lin's cram school. After Lin Zhaoxi taught the elementary school students the Olympiad class in the morning, he began to learn a little graph theory related content from the two of them.
However, in these seemingly dull days, but Lin Zhaoxi became increasingly anxious, Lao Lin's proof work has made real progress.
Although, the so-called progress means that Lin Zhaoxi finally waited until the draft that Lao Lin made a mistake.
It was a certain Saturday in early autumn, when she was standing in front of the podium, as usual, she quietly showed Lao Lin dozens of drafts, her mind was full of v(g) and v(h) and collective mathematical symbols.
On the blackboard is the model of the Seven Bridges that she just drew. The content of the epoch-making proof made by Euler hundreds of years ago can be told to elementary school students now.
"Actually, Mr. Euler's way of proving it was very simple. He turned the island into a vertex, and expressed the bridge connecting the land as a line. Then the map I drew will become a simpler pattern."
Lin Zhaoxi decently drew a shape similar to a cone.
"It seems to be much simpler."
"But is it really impossible to walk down in one go?"
The children's questions came to mind again.
Enlightenment is almost here, Lin Zhaoxi said: "Can you give it a try?"
"How to try?"
"Draw a picture, start from the starting point, pass through each bridge, and then return to the starting point, and see if you can find that road~" The chalk strokes on the vertices and lines.
"Or use mathematical methods to prove that it's impossible." The ambitious little boy interjected.
Lin Zhaoxi nodded.
Before she finished speaking, many students began to discuss on their own. Someone decided to try one by one, and someone wanted to find a simple, mathematical method, but Lin Zhaoxi didn't say anything.
She went down and turned around twice, answered a few questions, and was driven back to her place by the children.
She could only take out the draft that she had just "stolen" quietly, and read it casually.
The autumn wind blows, and some leaves fall outside the window, crisp and golden.
Lin Zhaoxi flipped through the drafts that she had already read in the morning. She always felt that the problems that Lao Lin had made mistakes should be in it, and she was very close, but she couldn't find them.
During this period, because a group of students who decided to divide the work and cooperate to count the total number of moves had a small-scale quarrel about how to work, Lin Zhaoxi ran down to give them an idea.
Just as he sat down and picked up his pen, he heard the "fat" boy shout again: "How do you prove that Euler is wrong?"
She took her eyes away from the draft in front of her and looked at the boy.
"How could Euler be wrong!" retorted another.
"I think there must be a possibility of a one-time pass!"
"Then you can look for it. If you find the one that says 'do not go back', you will find a counterexample. If you find a counterexample, you can prove that Euler is wrong." Another very organized little girl said.
The classroom was filled with these voices. It was noisy, but it made people feel extraordinarily peaceful. Lin Zhaoxi did not try to stop their argument.
She turned a page and saw several lines of proof.
The memories in my mind and the manuscript paper in front of me gradually overlapped, and the voices of the children in my ears fell silent.
— found a counterexample.
right here.
—
There was no time for get out of class to end, Lin Zhaoxi couldn't hold back the excitement in her heart, she grabbed the manuscript and rushed to Lao Lin's office.
She pushed open the door, slapped the paper on the table, and held the red pen that she had just corrected for the children. With the tip of the pen down, she circled a few lines of the proof completely, then pushed it in front of Lao Lin, and said: " There is a problem here!"
Lin Zhaoxi's heart was beating very fast. She stared at her father's briefly surprised face, then took half a step back: "I'm going back to class!"
She knew very well how exaggerated her actions were just now, and now she wanted to run away from the door. But before she reached the door, she was stopped.
"Wait." Old Lin paused, "Turn around, come here, and sit down."
Lin Zhaoxi pawed at the door, desperate in her heart, but had to turn around slowly.
Lao Lin, including Pei Zhidu in the office, had no time to talk to her at all, and their expressions were very consistent. After a brief astonishment, they showed contemplative expressions and carefully read the contents circled by her.
Lin Zhaoxi sat at the side respectfully, not daring to show his air.
At that time, Lao Lin realized that his proof was wrong because there was a problem with the assumption. After proving that an automorphism induced by mapping is g(p ), he directly identified s as its subset.
She was forcefully memorizing key symbols like c→c, aibj→b, and so on, without fully understanding why this assumption went wrong. And because the repeated proofs are full of these symbols, I didn't recognize this until the child said "counterexample".
Yes, the essence is still a counterexample. When mathematicians run into difficulty trying to prove a proposition, they start looking for counterexamples to prove it isn't true. But it is easy for them to forget it in their daily work.
The camphor tree outside Lao Lin’s office won’t turn yellow, and it’s still green in autumn. Lin Zhaoxi took a deep breath and heard him say, “You’re right, you’re wrong here.”
There was inevitably loss and regret in his expression, a little dignified, but relieved. To admit that he was wrong means that the wall is raised, all his previous efforts are in vain, all assumptions must be completely overturned, which seems extremely cruel to anyone who has worked hard for a long time.
Lin Zhaoxi pursed her lips, not knowing how to restore Lao Lin's confidence, and then discover the new algorithm based on this.
"How did you find out?" Lao Lin interrupted her thinking.
"Ah? The kid suddenly yelled 'counterexample' just now, and I was thinking, if you assume this way, did you not consider the empty set
She made a nonsense reason, the actual problem is not that simple, it is impossible for a high school student like her to discover it, and it has nothing to do with Kongji. But she still observed Lao Lin, hoping that her sudden reason could be fooled.
"It's a bit silly." Lao Lin concluded.
"!!!" Lin Zhaoxi felt guilty all of a sudden, she forcefully argued, "It's really like that."
"You should say: the God of Mathematics suddenly took care of me." Lao Lin said slowly.
"The God of Mathematics suddenly favored me?"
"Yeah." Lao Lin looked relaxed and flat, and looked at the piece she circled with a smile, "Suddenly he also favored me."