Chapter 281 A lonely artist?
The 5nm chip process technology of this X-ray lithography machine redeemed by spending 45 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 a real 5nm process.
At present, whether it is Samsung or TSMC, the so-called 5nm process of these companies has not actually reached 5nm. It can be said that this is just a naming trick, which is also commonly known as marketing, leaving some unknown people in the outside world. People think they are really that awesome.
Ordinary consumers don’t know the physical limits of chips. If Samsung claims that it is 4nm, but TSMC honestly says that it is 5nm, even if Samsung’s 4nm is not as good as TSMC’s 5nm, there is no guarantee that some consumers will not think that it is. Samsung's is even better.
This is why there are now reports that TSMC is working on 3nm and 2nm. Obviously 3nm has reached the physical limit. Even at the 4nm level, some quantum tunneling effects have actually occurred, affecting the actual performance of the chip. Case.
Just like Intel's CPUs are still made of processes above 10nm, because they know very well that no matter how awesome you brag about the single-digit nanometer process, in the end our actual process is still not up to that level. In this case, everyone is nothing. It’s just about chip design capabilities.
What's more, Intel has always been in the position of the big brother in CPU. Even if the massage parlor has suddenly become more independent in the past two years, the gap with Intel in the market is still relatively large, so Intel does not care at all about the manufacturing process. Marketing comes to spread the word.
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 to The distance between the drains is 5nm, which means the width of the gate is 5nm.
This is the chip manufacturing process under the most standard definition.
This means that if this process is used to manufacture chips, they will create the most advanced chips in the world!
They can pack more transistors per unit area, and this is almost a one-and-done process.
Because no matter how the production processes of other foundries are updated in the future, they need to catch up with their 5nm process first, because theirs is a real 5nm.
Of course, why the 5nm given by the system is a real 5nm must have something to do with their X-ray lithography machine. After all, according to Lin Xiao’s design, the light source wavelength of their X-ray lithography machine was finally selected. Compared with the 13.5nm wavelength of extreme ultraviolet light, 3.56nm X-rays clearly have the advantage of their smaller wavelength light source in preparing chips with this fine process.
"It's not in vain that I spent 45 truth points."
Lin Xiao sighed inwardly.
This is considered normal. After all, with his current level of subjects, the technology that still costs 45 truth points to solve should have such an effect.
From this point of view, although the sixty truth points were spent without exploring the secrets of the system that may be involved, it is not a loss to be able to redeem these two technologies.
Of course, the technology of packaging materials will be available soon. As for the production process, we still need to wait until the photolithography machine is actually built.
Thinking of this, Lin Xiao also put aside his thoughts and put these two technologies aside in his mind. Anyway, they are in the system and he is not afraid of forgetting them.
Next, it’s time to look at another important point.
That is, those few lines of formulas dug out of my mind.
Lin Xiao's eyebrows raised.
Today he spent three truth points and memorized a total of seven mathematical formulas.
The first is the two lines of mathematical formulas used when exchanging the dual workbench technology.
Lin Xiao recalled these two lines of mathematical formulas in his mind, then picked up the scratch paper and pen from the side, and then 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 was impressed by the first line of formula.
"This seems to be... the Riemann Hypothesis? It seems to be a weakened form of the Riemann Hypothesis?"
Thinking of this, Lin Xiao was shocked.
One of the weak forms of the Riemann Hypothesis is the Lindelof Hypothesis.
Lindelof's conjecture is a conjecture about the growth rate of the ζ function on the critical line. It shows that given any e is 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 Hypothesis. It can ultimately 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 line of expressions, and doubts arose again.
What does this mean?
√plnp?
Does it mean that after the above equation is transformed into a formal form, the following equation can be derived?
But suddenly, an idea flashed in his mind, and he once again remembered a weak form of the Riemann Hypothesis, which was the large prime number gap conjecture, and this was a stronger conjecture than the Lindelof Hypothesis.
The conjecture holds that if the Riemann Hypothesis 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 connecting the two weak forms of the Riemann Hypothesis?
Lin Xiao's eyes flickered.
Obviously, this is a rather miraculous discovery.
Whether it was in terms of the Riemann Hypothesis, or he actually discovered such a thing related to the Riemann Hypothesis from the seemingly endless sea of formulas in his mind.
However, regarding the latter, he also knew that he could not explore anything. Studying this thing would only increase his curiosity. As for the former, he also had nothing to say. After all, he had nothing to say about the Riemann Hypothesis itself. Research, so even if he knows that these two weak-form conjectures can be connected, it will probably take him a lot of time to study.
And he doesn't have time to study the Riemann Hypothesis now. After all, he has more than a month to submit a manuscript to report to the International Congress of Mathematicians. There is no way he can solve the Riemann Hypothesis in more than a month. Get it out?
In any case, the Riemann Hypothesis is too difficult. If he really wants to study it, he might as well study the Hodge Hypothesis, which is also one of the seven major problems of the millennium. At least, he should be more involved in the Hodge Hypothesis. Some.
However, when it comes to the Hodge Conjecture...
Lin Xiao raised his eyebrows and wrote out another five formulas.
These five expressions are surprisingly related to Hodge's conjecture!
Of course, it is no coincidence that these five are all related to the Hodge conjecture.
Because Lin Xiao was already prepared for the next two times he spent truth points, so he specially selected these formulas related to Hodge's conjecture to memorize.
He was ready to try to do some research on Hodge's conjecture during his free time in the X-ray project.
Don’t seek to solve it. After all, the difficulty of Hodge’s conjecture is not necessarily lower than that of Riemann’s hypothesis. Even compared to the Riemann’s hypothesis, which has been studied by countless people, the problem of 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 confidently.
Just like so far, only one of the Millennium Problems has 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.
He has done a lot of research on the Hodge conjecture.
After all, in order to prove Lin's conjecture, he had read almost all the famous papers related to Hodge's conjecture. As for the extent of his research, it was of course very in-depth.
As for these five formulas, except for three of them which were relatively easy to understand, the other two 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 expressions, Lin Xiao fell into thinking.
"What do these two expressions mean? In a cohomology-like closed-chain group, on the singular generation complex projective algebraic variety, the Hodge class and the algebra are homeomorphic?"
"Well……"
Lin Xiao patted his head and continued to write the formula.
Undoubtedly, these two strange expressions in his eyes aroused some thoughts in him.
Hodge guessed that this kind of mathematical problem that dances between geometry and algebra is very difficult. Even with Lin Xiao's current ability, it is not easy to solve it.
Of course, he got these five formulas through a bug in the card system, which at least gave him a clue.
So, as time went by, his research finally got stuck.
"This...if you integrate the Hodge conjecture on C, will the entire Chow group have finite rank and smooth projective varieties?"
After thinking for a moment, he turned on his computer and looked for a paper. He remembered that this was mentioned in a paper he had read before.
With his strong memory, he quickly found the paper.
"This is this article, "On the Trajectories of Hodgkin Class"...huh? Is it actually the one written by Professor Deligne?"
When seeing the author of this paper, Lin Xiao couldn't help but be startled. This paper was none other than Pierre Deligne's.
As a big figure in the algebraic geometry world, 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 but sigh: "Professor Deligne is indeed a great figure in the field of algebraic geometry. This paper was written more than 20 years ago, but the content inside is still so powerful."
"However, according to the content here, choose a Kahler structure on *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.
Does it seem possible to go in this direction?
"However, there are still some problems."
"Well, it's better to ask Professor Deligne directly."
Just do it when you think of it, so Lin Xiao took out your mobile phone and called Professor Deligne on the other side of the Pacific Ocean.
Soon, the call came through.
Deligne's hearty laughter came from the other end of the phone.
"Hey, Professor Lin, why do 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 indeed, but we should be able to meet again at the International Congress of Mathematicians this year, 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 want to talk about looking forward to it, then he must be looking forward to it. After all, if you can't get it this time, you will have to wait for another four years.
"Haha, if you still can't get it, the International Mathematical Union will be embarrassed. 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? Let’s talk about it.”
"There is indeed one thing, about a mathematical problem."
"Oh? Do you, a lonely artist, also need to ask me questions?"
"A lonely artist? What is that?" Lin Xiao was stunned. When did he get such a title again?
"That's you!" Deligne said with a smile: "Look at the many problems you have solved, almost none of them were not solved by you alone? In our mathematical community, more problems are solved through cooperation. Yes, people like you who study alone and always come up with something are not considered lonely artists?"
"Is that so..." Lin Xiao touched his nose, or could he be called... a lonely hero?
Well, it’s better not to be a child.
Skipping this topic, he talked about the purpose of coming to Deligne this time. After informing Deligne of Deligne's paper and his thoughts, Deligne fell into deep thought.
"Well... just wait for me for a while and define H2P (X, Z) through the Poincaré duality theorem..."
Hearing the sound of writing coming from Deligne, Lin Xiao didn't wait and started thinking too.
When two people study a mathematical problem together, it means that they share inspiration, which is very meaningful to mathematicians.
Especially when two top mathematicians collaborate.
