117. Six on forty three
“Perhaps… … The proof of the Riemann hypothesis has been completed… are you?”
“I should have told you earlier… We haven’t finished the proof, but it seems that we have taken a new direction in the area that has been blocked.”
Professor Park nodded, and I continued.
“I’ve been stagnant in the realm of topology for the past four years. As you will know, topological mathematics is not the place to end the proof of the Riemann hypothesis.”
＜All non-explicit zeros of the Riemann zeta function lie on the critical line whose real part is 1/2 in the complex plane.>
This is the Riemann hypothesis, and the Riemann hypothesis is strictly a problem in the realm of complex analysis.
For reference, complex analysis is the study of properties such as continuity and differentiability of complex functions, and the Riemann zeta function is one of the complex functions that can confirm these mathematical properties in detail.
This means that the domain and range are clear, and the function value can be calculated directly.
On the other hand, in the case of topological mathematics, the definition of ‘topology’ starting from set theory itself is very abstract.
So, the object studied in topological mathematics is not captured with certainty like slippery soap.
Moreover, since topology does not deal with numbers, even the concept of ‘larger’ or ‘small’ is rarely used.
Four years ago, I transformed an infinite set of non-obvious zeros into a manifold in ten-dimensional space.
The characteristic as a ‘phase’ of the transformed 10-dimensional manifold does not help to prove the Riemann hypothesis.
That is, topological mathematics passes through the proof of the Riemann hypothesis. It acts as a kind of transfer station.
Professor Park opened his mouth to my explanation.
“It’s a transfer station role… So what are you going to do next?”
“I try to take this problem out of topology by using the M-theory.”
At my words, my sister-in-law said.
“M-Theory? it… You’re integrating string theory with theoretical physics, right? Hasn’t it been 5 years since the M-Theory came out?”
I nodded, and my sister continued.
“Up to the M-Theory! This is going to be fun.”
I smiled slightly and handed out the papers I had printed out in advance to Professor Park, the major’s sister, and Yeong-mi, one by one.
“I intend to use the content of this paper.”
It was a thesis that studied the hidden dimension, and it contained contents supporting the M-theory.
We live in a four-dimensional space-time, and only the space minus the dimension of time becomes three-dimensional.
However, according to the M-theory, our universe is actually an 11-dimensional world.
If we subtract the time dimension from the 11th dimension, we get 10 dimensions, and if we subtract the 3 dimensions we know, top and bottom, left and right, front and back, we have 7 dimensions.
That is, these 7 dimensions are hidden somewhere, and the most representative hypothesis to explain these hidden dimensions is the compactification hypothesis.
According to the compactification hypothesis, if a substance (for example, the circular string in superstring theory) was reduced to the level of the Planck length (1.6 x 10^-35 m), the basic unit of distance, it would explain the physical properties of this circular string. there is no way
Because it is smaller than the Planck length.
In other words, the existence of a string of this size means that a new dimension inevitably exists.
Let’s compare… 1 2 3 4 5, … … Suppose we have a world made up of positive integers like this.
The smallest number in this positive integer world is 1.
However, to explain the number 0.3 less than 1, it is the same principle as adding a new number system called rational numbers, that is, a new dimension.
In other words, the compactification hypothesis says that a new dimension is needed because of the Planck length, which fits without contradiction as a complete theory in physics, but is not applicable in the world of mathematics dealing with the concept of limit.
Another hypothesis that explains the hidden dimension in the M-theory is the brain universe hypothesis.
It is a kind of multiple cosmology that there is a universe with three-dimensional space in each brain. The most important characteristic of this hypothesis to me was the fact that it clearly explains why gravity is weak compared to strong, weak, and electromagnetic forces. .
There are four forces in our universe: strong, weak, electromagnetic, and gravity. Except for dual gravity, strong, weak, and electromagnetic forces do not exceed the brain range of our universe.
That is, they are trapped in a three-dimensional space.
However, since gravity extends beyond the three-dimensional space to other brains, the farther away, the faster the magnitude of the force weakens.
The thesis I prepared was the result of a study that explained the phenomenon of gravity spreading to other dimensions beyond three-dimensional space.
After confirming the formula in the thesis, the major sister opened her mouth.
“Hmm… So, are you saying that you want to use the phenomenon of gravity passing to another dimension in mathematics?”
I nodded and said.
“Right. But for us it doesn’t have to be gravity. All we need is a mathematical tool that scales some finite-sized object from three dimensions to more.”
I handed out two sheets of paper I had prepared.
“The whole formula development is really long, but I’ve shortened it as much as possible and summarized it on two A4 sheets of paper. The first expression shows an expression that extends from three-dimensional to five-dimensional space. It was finally derived from the paper you saw a while ago.”
Professor Park looked carefully at the formulas I prepared and said.
“By the way… If you look at the function expression you developed here… It seems to expand into 11 dimensions instead of 5 dimensions. right?”
“Yes, that’s right.”
Professor Park nodded at my answer, turned the paper to the next page, and began to check the formulas written there one by one.
After a while, the professor opened his mouth with a puzzled expression.
“I think I found the inverse function of the gravitational function that spreads out in 11 dimensions… Am I understanding correctly?”
“Yes, that’s right.”
“Inverse function? Hmm… Why is the inverse function? You mean reducing the dimension from 11th dimension to 4th dimension?”
Professor Parker is right.
Moving a 10-dimensional object into a 3-dimensional one.
Four years ago, I converted the set of non-obvious zeros of the Riemann zeta function into a 10-dimensional phase.
At my explanation, Professor Park put the paper down on the table, folded his arms, and made a serious expression.
It was a face that it was difficult to agree with what I said, but I could see why the professor was making that expression.
After thinking for a while, the professor slowly opened his mouth.
“If we reduce the dimension in this way, the number of cases would increase innumerable… . How are you going to solve that?”
This is the expected question.
For example, if (x, y. z) 3D information is reduced to (x, y) 2D.
We need to record the missing z-axis information, the only way is to create a new function using x and y.
Each time one dimension is reduced in this way.
We have to create a function that leaves information on the missing dimension, and we need to find a 7-dimensional information function to jump from 10 to 3 dimensions, and to jump over 7 dimensions.
To do this, you have to check the number of countless cases, which may be an impossible task forever.
But it wasn’t that there was no way out.
I opened my mouth carefully.
“The professor is right. It’s not easy. But there is one way I can think of.”
Professor Park and the major’s sister both looked surprised, and I continued speaking.
“Actually, for the last month or so, I’ve been working on finding a dimensional transformation function. I tried to convert about 300,000 non-name zero values.”
“In the military?”
I nodded my head at the major sister’s question, and she asked again.
“Five–! Do you think computers can be used in the military these days?”
“It’s not.”
“Then how did you calculate the value of the dimension transformation function? There must also be a series function calculation… .”
At my sister’s question, I smiled and said.
“I did it with my head.”
“Really?”
When I nodded, my sister shook her head and said.
“I always thought you were a monster… … . What the hell can’t you do?”
While I scratched the back of my head, Professor Park said in a urging voice.
“Jeong-ho, what the hell is your way of thinking?”
In response to the professor’s question, I pointed to the paper I had prepared and said.
“If you look at the first four terms of the equation of a function that transforms from ten to three dimensions, it will feel a little familiar.”
“The first four terms?”
There was a moment of silence in the laboratory, and it was Yeong-mi who broke the silence.
“Perhaps… Are you talking about the Navier-Stokes equation?”
“… !”
After checking the formula again, Professor Park said to me.
“It really is. Then this is… What do you mean?”
“I am not sure yet, but I tried to map the non-obvious zero values of the Riemann zeta function in three dimensions through a 10-dimensional phase, and it seems to be related to the flow of the fluid.”
For reference, the Navier-Stokes equation mentioned by Anglo-American is a differential equation that describes the motion of a fluid.
I was talking.
“In particular, as I just said, I tried to find the dimensional transformation function of about 300,000 non-name zeros, and I got some interesting results.”
While we were talking, I suddenly met the eyes of Youngmi sitting next to me, and the two eyes of Yeongmi who were looking at me were really shining brightly.
It means that I am very focused on my story, which means that Youngmi fully understands the story I am telling.
Professor Park urged me again.
“So what was the result?”
“We divided the function values into groups that were accurately predictable and those that were not.”
“A group that is difficult to predict accurately?”
“Yes, so, just in case, I used the vorticity equation as a dimension transformation function, and found that the function values match surprisingly well.”
“Vorticity equation?”
The vorticity equation is an equation that simulates a vortex flow occurring in a fluid, and the vorticity flow is one of the important characteristics of turbulent flow.
In other words, when calculating the value of the dimension transformation function, the group that is difficult to predict corresponds to turbulence in the fluid flow, and the group that can be accurately predicted corresponds to laminar flow.
read at noblemtl.com
Now, let’s do the final arrangement.
We found a mathematical way to explain the phenomenon of gravity spreading to other dimensions beyond three-dimensional space, and in a similar way, we derived a functional expression that expands the dimension from three dimensions to ten dimensions.
Then, using this function inversely, a method of mapping the non-obvious zero value through the 10-dimensional topological space and into the 3-dimensional space was completed.
As a result of this mapping, the Navier-Stokes equations describing the flow of the fluid emerged, and the non-obvious zero values were divided into two groups corresponding to turbulence and laminar flow.
Although it has not yet been definitively proven, it is hypothesized that the non-obvious zeros of the Riemann zeta function are information describing the motion of a fluid in a new dimension.
After my explanation, Professor Park tilted her head to look at the ceiling and took a deep breath.
After a while, when the professor tilted his head back and straightened his head, tears welled up in both of his eyes.
He seemed to know the meaning of the tears that Professor Park shed.
When I first found a clue that non-obvious zero values are related to the motion of a fluid… Because I did too… .
The professor looked at me and said.
“So what are your plans for the future?”
“Now we have two tasks left to complete the proof.”
Professor Park nodded, and I continued.
“One is to find a seven-dimensional information function, and the other is to reduce the dimensionality to three dimensions through a 10-dimensional topological space in a similar way through a critical line with a real part of 1/2 in the complex plane.”
At my words, Professor Park smiled and said,
“The second task wouldn’t be that difficult, would it?”
What you meant is that, since the critical line is an open straight line, it will be easier to transform it into topological space.
“Yes, yes, but there are still a few blockages, so I need to study a little more.”
“That means… You mean you’ve already done a lot?”
“yes… .”
In response to my answer, Professor Park took another deep breath and opened his mouth.
“Finally now… … The end of the proof is in sight.”
If the threshold line on the complex plane is transformed through the phase space, the transformed threshold line will be defined as a region having certain characteristics in the 3D space.
If this region contains the range of a seven-dimensional information function… The Riemann hypothesis that ＜all non-obvious zeros are located at the critical line> is proved.
As Professor Park said, the end of the proof is now looming.
Professor Park smiled at me, still with tears in her eyes, and the major sister gave me a thumbs up.
And Yeong-mi was looking at the vorticity equation used as a dimension transformation function with a dazzling gaze.