63. Seven Seon
After saying goodbye to my mother, the major sister ran towards me.
“Wow—! Our Jungho! You have grown so much!”
our jung ho?
How old am I now… The moment I thought of that, both of my cheeks were already caught by the major older sister.
My sister pulled my cheeks back and forth and continued talking.
“Our cute Jung-ho is turning into an uncle with a bald beard! OMG—! I spent so much time in Texas!”
Ugh, the smell of alcohol.
I said clutching my nose.
“Ugh! How much alcohol did you drink yesterday?”
“Are you going to nag like this as soon as you meet your sister? If you keep nagging, I will bite you!”
Both eyes gleamed brightly on the tanned face of the older sister.
omg! no way… Wouldn’t it really break?
We sat around the table, and towards the end of the meal, my mother said to her sister.
“Major-san, did you really want to eat yeolmu-guksu that much? I could give you something tastier… .”
The older sister said as she emptied the noodle bowl.
“no. About a year ago, I really wanted to eat yeolmu-guksu. Mother, by the way, can I have one more bowl of noodles?”
The mother smiled and took her sister’s empty bowl and said:
“It was good that the noodles were cooked well.”
While the mother was preparing the noodles, the older sister took a glass bottle from her bag and said:
“Jungho, take this.”
It was the BBQ sauce I requested by email.
“Oh my! thanks.”
one two three four… .
A bottle of BBQ sauce kept coming out of my sister’s little bag.
“Sister, how many did you bring?”
At my question, my sister smiled and said,
“County Line, it was really good there. That’s why I bought it on purpose.”
There were 8 bottles of BBQ sauce that my sister brought.
“Sister, I didn’t know that I would buy so many.”
At my words, my sister smiled and said.
“It’s not anyone else, it’s our Jeong-ho request! I can buy even 100 of these BBQ sauces.”
“haha! Thank you very much.”
“Actually, I bought 10, and I left two at home for my grandmother to taste as well. It really suits the taste of Koreans.”
The County Line.
When I was living in America, my mother’s favorite restaurant was County Line.
At that time, my mother said American food was salty and greasy, and she rarely went to restaurants, except for County Line.
She said that the BBQ sauce sticks to her taste buds, and her mother always visited County Line once a month, and often said that she remembered County Line food even after returning to Korea.
It’s my mother’s birthday in January.
On my mother’s birthday this year, I plan to prepare a BBQ by myself.
what is this… It’s not a big brag, but I’m pretty good at cooking.
In the past life, whenever I ate the food I made, Yeongmi used to give a thumbs up saying it was really delicious.
After eating at our house,
The major sister and I put on our thick coats, and went out to Korea University.
Professor Park Soo-Soo’s lab, Korea University.
When the long goodbye between Professor Park and my sister was over, my sister smiled and said to me.
“Jeong-ho, do you have something ready?”
The older sister turned her head and covered her mouth with her hand and spoke to Professor Park in a low voice.
“It’s the secret weapon that Jeong-ho prepared.”
“ah… ! okay? haha!”
I opened the bag, took out four papers, and handed them one to Professor Park and to my sister.
It was a research plan I had prepared two days ago.
After checking the research plan, Professor Park opened her mouth with a surprised expression.
“Perhaps… You mean overturning the continuum hypothesis?”
Continuum hypothesis.
This is a very popular hypothesis in mathematical set theory.
In 2000, the Clay Mathematics Institute in the United States will announce the 7 Millennium Problems, and the first of the seven problems is the Riemann Hypothesis.
In other words, it is the Riemann Hypothesis that is the final king among the mathematical difficulties in 2000.
A similar thing happened 100 years ago, at the World Mathematical Congress in 1900.
German mathematician Hilbert published 23 mathematical problems, the first of which is the continuum hypothesis.
This means that 100 years ago, the king of mathematical difficulties was none other than the continuum hypothesis.
For reference, it is said that at that time, the Riemann hypothesis was ranked 8 out of Hilbert’s 23 problems.
The continuum hypothesis is a bit complicated to explain, but it is as simple as possible.
There are an infinite number of consecutive points between 0 and 1, which means there are an infinite number of consecutive real numbers between 0 and 1.
read at noblemtl.com
Next, 1, 2, 3, 4, … Think of a positive integer like this, a natural number.
read at noblemtl.com
Note that natural numbers are not continuous.
This is because real numbers such as 1.2, 1.3, and 1.4 exist between 1 and 2.
However, the number of natural numbers is also infinite.
So the number of subsets of the set of all natural numbers (exactly 2 multiplied by the number of natural numbers) is also infinite.
So we can think of two infinite numbers.
One is the number of real numbers between 0 and 1, and the other is the number of subsets of the set of natural numbers.
The famous continuum hypothesis is the proposition that there is no other infinite number between two infinite numbers.
Simply put, there is no infinity between infinity and infinity.
For reference, the fact that the continuum hypothesis cannot be proved has been proven.
Interpreted as a pun, it means that modern mathematical systems cannot tell whether the continuum hypothesis is true or false.
This is why Professor Park asked whether the continuum hypothesis is reversed, and I am going to approach the Riemann hypothesis assuming that the continuum hypothesis is true.
read at noblemtl.com
Now let’s go back to my original goal, the Riemann zeta function.
The Riemann zeta function has an infinite number of non-distinct zeros.
Let the set of these infinite non-name zeros be set A, and the set consisting of an infinite number of continuous real numbers between 0 and 1 is set B.
read at noblemtl.com
Note that the elements of set B do not have to be on the line segment between 0 and 1.
It may be an infinite number of points inside a two-dimensional rectangle or circle, it may be a point constituting a three-dimensional cube, and it is also possible to consist of points in a specific section of four or more dimensions.
The important thing here is that these points must form a continuous line or plane.
read at noblemtl.com
Now suppose that the continuum hypothesis is true.
Since there is no other infinity between infinity and infinity, every element of set A can have a one-to-one correspondence with the elements of set B.
In other words, it means transforming all non-obvious zeros of the Riemann zeta function into constituent elements forming a continuum, and more simply, bringing the Riemann hypothesis into the realm of topology.
After my long explanation, the major sister opened her mouth in an excited voice.
“So… By making the Riemann hypothesis a problem of topology, you are saying that you are going to put an end to it using topology.”
I nodded quietly.
“Wow! Is this really clever?”
In an instant, Professor Park Soo-Soo started laughing.
The professor’s low laughter grew louder and louder, and the professor, who had been laughing for a while, opened his mouth.
“This is not a novelty, is it not meant to overthrow modern set theory? Establish a new mathematical system to prove the Riemann hypothesis… ah ha ha! Just imagining this makes my heart explode. ha ha ha!”
“Are you re-establishing set theory?”
The major sister came out with a curious expression and looked at Professor Park in turn.
Professor Park stopped laughing and said to me.
“Jung-ho, can you explain to Dr. Yoon?”
Set theory in modern mathematics is called ZFC set theory. ZFC set theory is a discipline built on the basis of nine axioms.
To say that it is impossible to prove the continuum hypothesis in this stacked study means that the continuum hypothesis is mathematically independent of the nine axioms that are the basis of ZFC set theory.
Therefore, even if the continuum hypothesis is used as the tenth axiom of ZFC set theory, there is no mathematical contradiction at all.
In mathematics, an axiom is a self-evident truth that is unconditionally true.
So an axiom is a proposition that is always true without needing to prove it.
That is, I no longer have to assume that the continuum hypothesis is true in order to transform the Riemann hypothesis into a problem of topology.
The continuum hypothesis used as an axiom is already a self-evident truth.
The explanation has been long, but to put it simply, the reason why the Riemann hypothesis has not been proven so far means that there is a problem with the modern mathematical system.
The core content of my research proposal is to modify the modern mathematical system by accepting the continuum hypothesis, and thereby bring it one step closer to the proof of the Riemann hypothesis.
When I finished my explanation, the major nodded silently, and Professor Park pointed to my research plan and said:
“If you’ve thought about it this much, it seems like you’ve been preparing for quite a while, so why did you bring it only now?”
“I thought it would be difficult to proceed with this research without the help of the major sister.”
Professor Park of my horse and the major older sister both looked at me with a surprised expression.
After a while, my sister said to me with a curious expression.
“How can I help you?”
By affirming the continuum hypothesis, he succeeded in transforming the Riemann hypothesis into a problem in topology.
But that’s it.
read at noblemtl.com
Now, this game takes place in the realm of topology.
So far, I have found non-name zeros of about 5 million Riemann zeta functions.
read at noblemtl.com
Now we have to start moving the non-obvious zeros to the continuum of the realm of topology.
For example, if we move to a one-dimensional line segment between 0 and 1, we need to find the regularity of the 5 million non-obvious zeros that have been moved.
It is necessary to confirm the position of 5 million new points, find a significant regularity through statistical analysis, and express it as a generalized formula.
If the target is a one-dimensional line segment, the computation is not very complicated.
But my goal is not a one-dimensional continuum.
It is not a two-dimensional, three-dimensional, or four-dimensional continuum, but a continuum of ten dimensions.
For reference, in order to know the specific characteristics of the 10-dimensional continuum, it is necessary to study the string theory and M-theory since the 2000s.
But we can’t just wait for the results of these physics studies to come out, and we have some ideas in mind.
Anyway, aiming for a 10-dimensional continuum means that 10 coordinate values are given for each non-announced zero, and this must be repeated for millions of zeros.
To do this, an enormous amount of computation is required, and computation on this scale is impossible without a supercomputer.
Supercomputers first appeared in the early 1990s, and Texas State University is one of the leading universities in the development of supercomputers.
The Texas Advanced Computing Center (TAC) will soon be established on the North Pickle campus of Texas State University.
So, when he said he needed the major’s sister’s help, he meant that he needed the supercomputer now at Texas State University.
I continued the explanation.
“Besides, your major is topology, and your doctoral thesis was a study on continuous functions in a multidimensional space with more than three dimensions, right?”
My sister nodded, and I continued.
“So, I thought that if my sister’s research was expanded to 10 dimensions and combined with non-announced zero point data, she could play an important role in conducting this research.”
When my long explanation was over, the major sister seemed to be lost in thought and said nothing.
Silence passed like that, and at the end of the silence, my sister opened her mouth.
“Then there is one condition.”