Chapter 165

The next day.

When Senior Brother Gao saw Gu Lu in the video again, he couldn't help but be shocked.

"Gu... Junior Brother Gu, are you okay?" Senior Brother Gao couldn't help but ask when he saw Gu Lu had two big dark circles under his eyes.

"Senior brother, I'm fine." Gu Lu waved his hand nonchalantly.

He just stayed up all night, it wasn't like Gu Lu had never done this before.

Two or three bottles of Shenbao will last you through.

"Is everything okay?" Senior Brother Gao was still a little worried.

Gu Lu waved his hands and smiled, "It's really okay!"

"Okay." Although Senior Brother Gao was worried about Gu Lu, he was thousands of miles away and couldn't do anything.

Senior Brother Gao raised his head and looked at Gu Lu, "In that case, let's discuss a new proof plan as planned."

"We worked on the previous proof plan for a week. But this time it may take longer to formulate the new plan. Let's try to use half a month to develop another proof plan."

Senior Brother Gao clenched his fists and was full of energy.

Gu Lu looked at Senior Brother Gao with calm eyes and said in a calm tone, "Senior Brother Gao, no need."

"Huh?" Senior Brother Gao was suddenly startled, and then he seemed to have thought of something, and said hurriedly, "Junior Brother Gu, you must not give up! Our current progress is much faster than expected, but now we have encountered a little problem.

It’s just a small difficulty. Once you give up, all your previous efforts will be in vain!”

Senior Brother Gao sounded anxious.

He thought that Gu Lu couldn't bear yesterday's blow, so he decided to give up the research on the second issue of the minimal model program!

The loss would be too great!

So Senior Brother Gao hurriedly dissuaded Gu Lu, hoping that he would change his mind.

Gu Lu had a smile on his face and looked at Senior Brother Gao who looked anxious, "Brother, I never said that I would give up research on the second issue of the Minimum Model Program."

"Well, then Junior Brother Gu...what do you mean?" Senior Brother Gao was a little confused.

"I have already made the second plan to prove the termination of the flip operation of high-dimensional algebraic varieties." Gu Lu's tone was very calm, as if he was describing an ordinary thing.

Silence, long silence...

Senior Brother Gao froze on the spot, his mouth remained open, and his expression did not move for dozens of seconds.

"Junior Brother Gu, are you saying that you have already made a new proof plan?" After a long time, Senior Brother Gao frowned and confirmed to Gu Lu.

Gu Lu nodded, "Yes, it's been done."

"But……"

But, it only lasts for one day!

Senior Brother Gao felt that his cognition was collapsing little by little.

Because Gu Lu's performance was increasingly beyond Senior Brother Gao's cognition.

Gu Lu's incredible performance last time was still vivid in his mind. This time, Gu Lu repeated the previous scene again.

The same person can complete a task in one day that is expected to take two people half a month.

Moreover, the difficulty of this mission is much higher than last time.

Last time, Gu Lu just simplified the steps by introducing the concept of abstract-k clusters to a set of formulas that originally required complex calculations to obtain the results.

But this time, Gu Lu started from scratch and formulated a completely new proof plan in a very short period of time.

Whether it is difficulty or complexity, the latter is higher than the former.

Actually, one thing that Senior Brother Gao doesn't know yet is.

When Gu Lu formulates a new plan, he not only needs to prove that the plan is feasible, but also needs that the proof steps of the new plan are simpler than the original plan.

Only in this way can Gu Lu guarantee that the second problem of the minimal model program will be solved before the end of the six-month mission.

After some operations on the computer, Gu Lu said to Senior Brother Gao, "Senior Brother Gao, I have sent you the new plan via email. Please check it and see if there are any problems."

Senior Brother Gao opened the file sent by Gu Lu in his mailbox and browsed it roughly.

Then, Senior Brother Gao showed a strange expression, "Junior Brother Gu, your proof plan..."

"It's strange, isn't it." Gu Lu added the second half of the sentence for Senior Brother Gao, smiling casually, "Actually, I felt the same way when I was formulating this plan."

"But the fact is, it's right!" Gu Lu raised the corners of his mouth and spoke confidently.

The new plan proposed by Gu Lu is both simple and complicated.

There are only five words at its core: mathematical induction!

No one is unfamiliar with mathematical induction.

As we all know, mathematical induction is a proof method that we are exposed to in high school. It can be said to be one of the most basic proof methods.

But Gu Lu’s solution is not the most common mathematical induction method we learn in high school.

But...an epic and difficult mathematical induction method!

In order to prove the main theorem that the flip operation of high-dimensional algebraic varieties terminates after a finite number of times, six seemingly unrelated auxiliary theorems need to be proved.

We name these six theorems respectively: a, b, c, d, e, f!

The proof of these six auxiliary theorems requires mathematical induction.

For example, theorem d of less than or equal to n-1 dimensions, theorem b of less than or equal to n dimensions, and theorem c of less than or equal to n dimensions can deduce theorem d of less than or equal to n dimensions.

Theorem a is less than or equal to n dimensions, theorem b is less than or equal to n dimensions, and theorem c is less than or equal to n dimensions.

Theorem c which is less than or equal to n dimensions, theorem d which is less than or equal to n dimensions, can deduce the theorem e which is less than or equal to n dimensions.

A total of six mutual inference expressions of mathematical induction are required.

For laymen, it must be confusing just to look at it, but for mathematicians, it is quite easy to understand.

That's why Senior Brother Gao showed such a weird expression.

Because in the ten years he has been working in the mathematics industry, to be honest, he has never seen a proof method like Gu Lu's that uses mathematical induction to interpolate theorems and then prove the main theorems.

Unheard, unseen.

It refreshed senior fellow mathematician Gao’s understanding of mathematics.

"Is this really feasible?" Senior Brother Gao still had a dubious attitude.

Because what Gu Lu presented to him was a brand new thing that had never appeared in the world of mathematics.

Gu Lu smiled and said, "Whether it's feasible or not, we'll know after some research."

New things always need someone to try them.

And Gu Lu and Senior Brother Gao will act as the pioneers this time, or in other words, the first to eat crabs.

…………

Half a month later.

Senior Brother Gao said excitedly, "Junior Brother Gu, we, we... succeeded?"

Gu Lu smiled and nodded, "It's not completely successful yet. We just completed the first two steps. But it illustrates one point, that is, our proof idea is correct! After that, we just need to follow the steps."

Senior Brother Gao nodded heavily, his face flushed, "To be honest, I didn't expect that we would go so smoothly this time. It's all thanks to Junior Brother Gu's new plan!"
Chapter completed!