From Almighty Scholar to Chief Scientist

Chapter 284 A Lonely Artist?

The 45nm chip process technology of the X-lithography machine exchanged for 5 truth points, Lin Xiao thought before, should be the same 5nm process as those chip processes in the world today.

But in fact, the 5nm process he redeemed from the system is the real 5nm process.

At present, whether it is Samsung or TSMC, the so-called 5nm process of these companies has not actually reached 5nm. People think they are really that awesome.

Ordinary consumers don't know what the physical limit of chips is. If Samsung claims that it is 4nm, TSMC honestly says that it is 5nm. Even if Samsung's 4nm is not as good as TSMC's 5nm, it is hard to guarantee that some consumers will not think that it is [-]nm. Samsung's is even better.

This is why there are reports that TSMC is engaged in both 3nm and 2nm. Obviously, 3nm has reached the physical limit. Even at the 4nm level, some quantum tunneling effects will actually occur, which will affect the actual performance of the chip. Case.

Just like Intel’s CPU is still above 10nm process, because they know very well, no matter how awesome you are bragging about the single-digit nanometer process, in the end, everyone’s actual process is still not up to that level. It's just a matter of chip design capabilities.

What's more, Intel has always been the big brother in terms of CPU. Even though massage shops have suddenly become stronger in the past two years, the gap with Intel in the market is still relatively large, so Intel doesn't care about using the manufacturing process. It's marketing.

However, no matter what, these situations are all because their actual technology cannot reach the real so-called process, and the 5nm process technology that Lin Xiao has exchanged now is a very practical 5nm process, that is, the source of the transistor. The distance between the drains is 5nm, that is, the width of the gate is 5nm.

This is the chip manufacturing process under the most standard definition.

This also means that if they use this process to make chips, they will make the most advanced chips in the world!
They can squeeze more transistors per unit area, and this is almost a one-and-done process.

Because no matter how the production process of other foundries is updated in the future, they need to catch up with their 5nm process first, because theirs is the real 5nm.

Of course, why the 5nm given by the system is actually 5nm must have something to do with their X-lithography machine. After all, according to Lin Xiao’s design, the wavelength of the light source of their X-lithography machine was finally selected as The 3.56nm X-ray, compared with the 13.5nm wavelength of extreme ultraviolet light, obviously has the advantage of their smaller wavelength light source in the preparation of such micro-process chips.

"It's not in vain. I spent 45 truth points."

Lin Xiao felt emotional in his heart.

This is also considered normal, after all, with his current level of various subjects, it takes 45 truth points to solve the technology, it should have such an effect.

From this point of view, although spending [-] truth points did not explore the secrets of the system that may be involved, it is not a loss to be able to exchange for these two technologies.

Of course, the technology of packaging materials will be available soon. As for this production process, we still need to wait for the lithography machine to be manufactured in the future.

Thinking of this, Lin Xiao also let go of his mind, and put these two technologies to the side of his mind first. Anyway, they exist in the system, so he is not afraid to forget them.

Next, it's time to look at other important points.

That is, the few lines of formulas dug out of my mind.

Lin Xiao frowned,

Today, he spent three truth points, which also allowed him to memorize a total of seven mathematical formulas.

The first is the two lines of mathematical formulas when exchanging the double workbench technology.

Lin Xiao recalled these two lines of mathematical formulas in his mind, then picked up the draft paper and pen from the side, and began to write.

【ζ(1/2+it)=O(t^e)】

【ζ(1/2+it)/(t^e)=O（√plnp）】

After writing these two formulas, Lin Xiao frowned and began to think.

He has an impression of the first line.

"This seems to be... Riemann's conjecture? It seems to be a weakened form of Riemann's conjecture?"

Thinking of this, Lin Xiao was shocked.

Among the weak forms of Riemann's conjecture, there is a Lindelof conjecture.

Lindelof's conjecture is a conjecture about the growth rate of the ζ function on the critical line, which shows that given any e greater than 0, when t tends to infinity, ζ(1/2+it) is equal to O(t^ e), which is a relatively weak form of the Riemann conjecture, and it can eventually be deduced that "given any e greater than 0, for a sufficiently large n, Pn+1-Pn is less than Pn^e(1/ 2+e)".

However, Lin Xiao then turned his attention to the second row of formulas, and became suspicious again.

What does this mean?
√plnp?

Does it mean that the above formula can be deduced from the following equation after the form transformation?
But suddenly, a flash of inspiration flashed in his mind, and he remembered a weak form of Riemann's conjecture, that is, the large prime number gap conjecture, and this is a stronger conjecture than Lindelof's conjecture.

The conjecture believes that if the Riemann conjecture is true, the gap between the prime number p and the next prime number should be O(√plnp).

That is to say, this second formula is equivalent to linking the weak forms of the two Riemann conjectures together?
Lin Xiao's eyes flickered.

Obviously, this is a rather miraculous discovery.

No matter from the matter of Riemann's conjecture, or he actually discovered such a thing related to Riemann's conjecture from the seemingly endless sea of ​​formulas in his mind.

However, for the latter, he also knows that he can't explore anything, and to study this thing is just to increase his curiosity. As for the former, he also has nothing to say, after all, he has nothing to do with the Riemann conjecture itself. Research, so even if he knows that these two weak-form conjectures can be linked together, it will probably take him a lot of time to study.

And he doesn't have time to study Riemann's conjecture now. After all, he still has more than a month to submit a manuscript to the International Congress of Mathematicians. Get it out?
In any case, the Riemann conjecture is too difficult. If he really wants to study it, he might as well study the Hodge conjecture, which is also one of the seven major problems of the millennium. At least, he has more research on the Hodge conjecture. Some.

However, speaking of Hodge's conjecture...

Lin Xiao frowned, and wrote out the other five formulas.

These five formulas are all related to Hodge's conjecture!
Of course, it is no coincidence that all five are related to the Hodge conjecture.

Because Lin Xiao was already prepared for the next two times when he spent truth points, so he specially selected these formulas related to Hodge's conjecture to memorize.

He is ready to try to do research on Hodge's conjecture during the spare time of the X-ray project.

Don’t ask for a solution. After all, the difficulty of Hodge’s conjecture is not necessarily lower than that of Riemann’s conjecture. Even compared to the Riemann’s conjecture that has been studied by countless people, Hodge’s conjecture is like a hard nut to crack. , although there are many talents in algebraic geometry, not many people dare to challenge this thing with confidence.

Just like until now, the millennium problem has only been solved.

Of course, even if he doesn't seek to solve it, Lin Xiao will try his best to try, what if it is solved?

So, looking at these five formulas, Lin Xiao fell into thinking.

For Hodge's conjecture, his research is not insignificant.

After all, in order to prove Lin's conjecture, he almost read all the famous papers related to Hodge's conjecture. As for the degree of research, of course it is also very deep.

As for these five formulas, except for three of which are relatively easy to understand, the other two formulas gave him a strange feeling.

[︶: H^(p, q)(X)*H^p(X)→H^p+p(X)]

【Hdg*(X)=⊕kHdg^k(x)】

Looking at these two strange formulas, Lin Xiao fell into thinking.

"The meaning of these two formulas is that in a closed-chain group of cohomology class, Hodge class and algebra are homeomorphic on the complex projective algebraic variety of singular generation?"

"Well……"

Lin Xiao patted his head, and then continued to write the formula.

Undoubtedly, these two formulas seemed a bit strange to him, which caused him some thoughts.

Hodge guessed that this kind of mathematical problem dancing between geometry and algebra is very difficult. Even with Lin Xiao's current ability, it is not easy to solve it.

Of course, he obtained these five formulas through a bug in the card system, which at least gave him some clues.

And so, as time passed, his research eventually got stuck.

"This... if the Hodge conjecture is integrated over C, will the full Chow group have smooth projective varieties of finite rank?"

After thinking for a while, he turned on the computer and searched for a paper. He remembered that this was mentioned in a paper he had read before.

With his powerful memory, he quickly found the paper.

"This is the article, "On the Trajectory of the Hodges"...Huh? Is it Professor Deligne's?"

When Lin Xiao saw the author of this paper, Lin Xiao couldn't help being taken aback. This paper was exactly the paper of Pierre Deligne.

As a bigwig in the field of algebraic geometry, Deligne certainly has the courage to challenge Hodge's conjecture.

Of course, he didn't prove it anyway.

Soon, Lin Xiao also finished reading the paper.

After reading it, he couldn't help feeling: "Professor Deligne is indeed a master in the field of algebraic geometry. This paper was written more than [-] years ago, but the content in it is still so powerful."

"However, according to the content here, choose a Kahler structure on X, and then decompose H(X, C)...you can use the formal role of C* to exchange with the Laplacian operator, thereby inducing C *The role in space, if this step is to define H2P (X, Z) through the Poincaré duality theorem..."

Thinking of this, Lin Xiao's eyes gradually lit up.

It seems feasible to go in this direction?

"However, there are still some problems."

"Well, it's better to ask Professor Deligne directly."

As soon as he thought of it, Lin Xiao took out his mobile phone and called Professor Deligne who was far away on the other side of the Pacific Ocean.

Soon, the phone was connected.

Deligne's hearty laughter came from the other end of the phone.

"Hey, Professor Lin, how come you have time to call me today?"

Lin Xiao smiled and said, "Professor Deligne, long time no see."

"Yeah, it's been a long time, but this year's International Conference of Mathematicians, we should see each other again, right?"

"Of course." Lin Xiao smiled.

"That's good." Deligne said, "I'm just waiting for you to win a Fields Medal this year."

Lin Xiao laughed: "It's not decided yet, I can't say."

If you talk about looking forward to it, then he must be looking forward to it. After all, if he can't get it this time, he will have to wait another four years.

"Hehe, if you still can't get it, the International Mathematical Union will be ashamed. We old guys are already waiting to drink your champagne." Deligne smiled, and then said: "Okay, I believe you must have something to do with me, right? Tell me."

"There is indeed one thing about a mathematical problem."

"Oh? Lonely artist, you also need to come and ask me questions?"

"Lonely artist? What is that?" Lin Xiao was taken aback for a moment. When did he have such a title again?
"It's you!" Deligne said with a smile: "Look at the many problems you have solved, almost which problem was not researched by yourself? Like our mathematics world, more problems are completed in cooperation Yes, a person like you who researches alone, and who can always research something, is not a lonely artist?"

"That's it..." Lin Xiao touched his nose, or could he be called...the lonely brave man?
Well, don't be a kid anymore.

Skipping over this topic, he talked about the purpose of coming to Deligne this time, and after telling Deligne the paper and his thoughts, Deligne fell into deep thought.

"Well...you wait for me for a while, and define H2P(X, Z) through the Poincaré duality theorem..."

Hearing the sound of writing from Deligne, Lin Xiao didn't wait, and started to think about it.

When two people study a mathematical problem together, it means that two people share inspiration, and this is very meaningful for mathematicians.

Especially when two top mathematicians collaborate.

(End of this chapter)