From failed candidate to chief scientist

Chapter 44 Discussion
Fu Mingli spoke sincerely, but Lin Mo, who was opposite him, completely ignored his words.

Fu Mingli couldn't help but feel slightly angry when he saw this, and couldn't help but speak again.

"You want to use complex analysis to prove Kratz's conjecture."

Hearing this, Lin Mo raised his head and glanced at Fu Mingli.

Seeing his words, Fu Mingli finally caught Lin Mo's attention, and unconsciously raised his head and continued.

"Complex analysis doesn't work."

Lin Mo looked up at Fu Mingli, waiting for his next words.

Lin Mo read a lot of information about Kratz's conjecture, including some assumptions and proofs made by many other people, and understood many previous experiences and ideas.

Through the thinking of the predecessors, Lin Mo felt that complex analysis is a good proof method.

For the study of certain number theory problems, the complex analytic method is an effective method, because the shortest path between two truths in the real number field is often through the complex number field.

So Lin Mo is starting from this aspect, but his research has encountered difficulties in the 3n+1 equivalent function equation summarized by predecessors.

Let g(z) be a transcendental integral function and z0 be a point in the complex plane. If the function sequence {gk(z)}∞k=1 exists, the subsequence will converge locally to ∞ or a certain value in a neighborhood of point z0. Analytical function, then z0 is called the normal point of g(z).Let the set of normal points of g(z) be Φ(g). Obviously, Φ(g) is an open subset of the complex plane.

If it can be proved that there is an integer function h(z), so that for the above g(z), every branch D of Φ(g) containing a certain positive integer, z0∈D exists, so that {gk(z0)}∞k =1 converges to 1, then it can be deduced that the 3n+1 conjecture is true.

But Lin Mo was stuck here and couldn't find this function h(z).

“你能想到的，你的前辈们早都想到了，之前还有人证明了满足g(z)=z/2+(1cosπz)(z+1/2)/2+1/π(1/2cosπz)sinπz+h(z)sin2πz的函数h（z），可是也就止步于此，再难有寸进。”

Lin Mo knew this, and he also conducted research on this basis, but he still had no clue.

"Do you know why this is? This is because simple complex analysis can no longer satisfy the establishment of proof conditions. 3n+1 is no longer simply a problem of number theory, but..."

"Ok?"

Lin Mo's pupils were slightly opened, slightly surprised, because just now, as Fu Mingli's words fell, a green bubble fell.

Lin Mo moved his body, as if attracted by Fu Mingli's words, moved towards Fu Mingli's direction, and inadvertently put the green bubble into his bag.

"Subject Bubble +2"

Lin Mo was quite surprised.

"In your opinion, how should this problem be solved?"

Lin Mo spoke at the right time and looked at Fu Mingli in anticipation.

"This is..."

"Current mathematics does not have a good method to solve this problem. A single mathematical method is not easy to use for this problem. Of course, you can consider combining other methods..."

Following Fu Mingli's words, another green bubble emerged.

"Subject Bubble +2"

Lin Mo was shocked, could this still produce bubbles continuously?
But the next moment, Lin Mo reacted and was ecstatic.

If you can say it, just say more!
"How should it be combined?"

"This one……"

Fu Mingli frowned. He had not thought about this question, but after all, he had a profound academic background, so he opened his mouth as if it was a conditioned reflex.

"That's a lot. Since complex analysis can't solve the problem, why not consider combining it with other things? For example, combining geometry..."

Um?Lin Mo frowned slightly, no subject bubbles?what is the reason?
Are there no bubbles anymore, or something else?Did Fu Mingli not mention that?Wrong direction?

"Combined geometry? I think it might not be possible to combine geometry. How about vector analysis?"

Lin Mo tried to guide the topic.

"Vector analysis..." Fu Mingli fell into thinking, then shook his head.

There were still no bubbles, Lin Mo was slightly disappointed.

"What about functional analysis?"

"Functional analysis is not impossible..."

There are no bubbles, so it still seems wrong.

Lin Mo simply listed the mathematical methods one by one.

"Chaos theory?"

"power system?"

"Graph Theory?"

"Measure theory?"

Still no bubbles.

"Topology?"

"Topology can be considered..."

Following Fu Mingli's words, Lin Mo's pupils dilated again, and a golden bubble popped out.

"Subject Bubble +3"

So the topology is correct?
Lin Mo became even more excited. He felt that he had caught something, but he didn't have time to think about it for a while.

Lin Mo got up and poured a glass of water for Fu Mingli, but there was no way, there was no tea in the office.

Fu Mingli was now a shining gold mountain in his eyes. In order to pull down a few more pieces of gold from the golden mountain, Lin Mo began to use all his strength to discuss with Fu Mingli.

Fu Mingli was asked by Lin Mo for advice, which made him active in thinking and full of inspiration, especially for many problems. Fu Mingli just put forward an idea, and Lin Mo could then extend his ideas without him having to go through many complex problems in detail. The obscure theorems and formulas made him very happy, and he even felt like he had regained the leaping thinking in his youth.

The two of them talked for an unknown amount of time, and even Zhang Qihua pushed the door in, but he couldn't disturb them.

Fu Mingli and Lin Mo were just discussing the 3n+1 issue, fascinated by the discussion.

Zhang Qihua listened for a while and could follow the two people's thoughts at first, but then he became increasingly incomprehensible.

Zhang Qihua couldn't hide the surprise on his face.

Fu Mingli knew that he was a professor of Tunghai University, an academician of the Academy of Sciences, a well-known figure in the field of mathematics, and it would not be an exaggeration to call him a dean in the academic world.

Needless to say, his academic level and theoretical depth are outstanding.

But what about Lin Mo?
Lin Mo is just his graduate student, who has not yet entered school, so theoretically speaking, Lin Mo only has undergraduate knowledge. Even if he has learned some graduate knowledge by himself, it is limited to this, and it is impossible. Comparable to Fu Mingli.

But now?
Lin Mo and Fu Mingli had a lively discussion with back and forth. Zhang Qihua didn't understand anything except that they were discussing the issue of 3n+1.

When did Lin Mo become so powerful?But thinking about it, I just gave Lin Mo a research project, and Lin Mo could directly publish a top-ranking paper. This seems... very reasonable...

Zhang Qihua shook his head, and in the end could only attribute it all to talent.

A genius is a genius. Zhang Qihua sighed silently in his heart, but then he became happy and proud again. Such a genius is actually his student?I, Zhang Qihua, am actually lucky enough to be such a talented teacher?

While Zhang Qihua felt lucky, he was also sincerely happy for Lin Mo.

Seeing the intense discussion between the two, Zhang Qihua did not disturb the two of them, walked into his office in the inner room, and thought about a problem again.

Why don't you agree to Fu Mingli and go to Tunghai University?

Dongshan University does not have an academic leader like Fu Mingli. If Lin Mo wants to continue to progress in the future, staying at Dongshan University will be a delay for him.

(End of this chapter)