Quantum systems require a new way to think about math.

"IISc physicists discovered that Ramanujan’s classic π-formulas arise naturally in modern theories describing critical phenomena and black holes. The connection suggests his early mathematics may have foreshadowed key structures in today’s high-energy physics. Credit: Stock" (ScitechDaily, Ramanujan’s 100-Year-Old Pi Formula That Hides the Secrets of the Universe)

"A new study reveals that Srinivasa Ramanujan’s century-old formulas for calculating pi unexpectedly emerge within modern theories of critical phenomena, turbulence, and black holes."(ScitechDaily, Ramanujan’s 100-Year-Old Pi Formula That Hides the Secrets of the Universe)

100 years ago, Srinivasa Ramanujan introduced a Pi formula that hides a powerful argument. Pi is a mathematical constant, approximately equal to 3.14159, that is the ratio of a circle's circumference to its diameter. It appears in many formulae across mathematics and physics, and some of these formulae are commonly used. for defining π, to avoid relying on the definition. Of the length of a curve.” Wikipedia, Pi) We know that Pi has a certain value, and we can use that value in mathematical formulae. To use in calculations to determine the area of the circles. 

Pi is also needed. To calculate the volume of things like balls. The ball can be. Determined as a series of circles or rims. So, where is that information needed? What would you do with formulas that can calculate the distance from the ball surface to the layer? That information is useful in the calculations. That is used. For. Calculating the qubit interaction with the receiver. This information is urgent for quantum networking and quantum computing. 

The new quantum systems require new types of calculations. Or those calculations are not. A very new thing. The needed accuracy. The third-degree and higher polynomial functions are very high. The new mathematical formulas must be created. For the quantum systems that require new types of dimensions. And new variables. To make it possible. To simulate quantum systems. For making a complete simulation, the machine requires all information from the system. And the main problem with quantum systems is this. Everything happens in the 3D universe. 

"Choose a point on the circle (blue). You want to map it to a unique point on the straight yellow line. To do this, draw a dashed line between the green point at the top of the circle and your chosen blue point. Then map the blue point to whichever yellow point this dashed line passes through. You can do this for any given point on the circle. (The green point at the top of the circle gets mapped to a special yellow point at infinity.)" (QauntaMagazine, String Theory Inspires a Brilliant, Baffling New Math Proof)

"Unlike in the previous examples, your dashed line sometimes maps two different points on the elliptic curve (blue) to the same point on the yellow line below. You can’t find a map that avoids this, meaning that the elliptic curve has a more complicated set of solutions than the circle or sphere." (QauntaMagazine, String Theory Inspires a Brilliant, Baffling New Math Proof)

A second problem is this. Everything means something in those systems. Things like solar winds, changes in magnetic fields. And other kinds of things. It can have a big effect on systems. There, a superstring travels through a photon. And that turns a photon into a quantum router that shares photonic information into qubits.

Those calculations are needed for models that the systems use for quantum simulations. The millennium problem P=NP (P versus NP) means that checking calculations should be as fast as solving them. Error detection happens. By. Calculating all calculations backward. The problem is in extremely long calculations. If.  The machine uses. Even. Days to calculate some formula. Using backward calculation is a very long process. So if some stage needs more time to check, there should be a problem. But the fact is this. Nobody proved or disproved that problem universally. 

“The P versus NP problem is a major unsolved problem in theoretical computer science. Informally, it asks whether every problem whose solution can be quickly verified can also be quickly solved.”(Wikipedia, P versus NP problem). The idea is that these complex polynomials can be checked by calculating the time. If P=NP. 

Here, "quickly" means an algorithm exists that solves the task and runs in polynomial time (as opposed to, say, exponential time), meaning the task completion time is bounded above by a polynomial function on the size of the input to the algorithm. The general class of questions that some algorithms can answer in polynomial time is "P" or "class P". For some questions, there is no known way to find an answer quickly, but if provided with an answer, it can be verified quickly. The class of questions where an answer can be verified in polynomial time is "NP", standing for "nondeterministic polynomial time” (Wikipedia, P versus NP problem)

The new calculation models give new changes. To solve and check a complex polynomial problem. Things. Like, high-class polynomial functions are new tools. For quantum simulations. New. High-power computers can be used to calculate polynomial functions with new accuracy. This thing requires new accuracy for mathematical constants, like Pi. 

https://www.claymath.org/millennium/p-vs-np/

https://www.quantamagazine.org/string-theory-inspires-a-brilliant-baffling-new-math-proof-20251212/

https://en.wikipedia.org/wiki/P_versus_NP_problem

https://en.wikipedia.org/wiki/Srinivasa_Ramanujan

The LLM-style operating systems can make quantum computers more scalable.

New types of advances in quantum computer technology make those systems more scalable than ever before. The new operating systems can use the Large language model, LLM style portal that offers a better interface between binary computers and the quantum system. The LLM is always similar. It allows to use of multiple things to give commands to the system. The LLM can operate between humans or it can also operate in an interface between computers. The LLM can also make binary computers, and quantum computers understand each other better. 

The large language model, LLM is only one version of the command languages. Written for computers. In traditional programming and command languages like DOS language, C, C++, etc. the command syntax happens through certain formulas. The user must give those commands precisely the right way. The LLM gives freedom to the operators. The LLM allows to use of spoken language to give commands. The language model searches keywords from text. 

Then it translates those things to commands, that the sub-application requires. Those sub-applications can be the internet browser or some programming editors. 

The idea for those LLMs is taken from the Internet search field. It is much easier to write search words and go to the homepage. Clicking the link then write long addresses into the address bar. 

When a user gives the order to the computer. Using spoken language. The system transports data to a speech-to-text application and then it can transfer that data to the LLM user interface. That is the thing that makes the LLM so effective. The LLM translates those commands for the modules that search data from the networks. 

The new quantum computers that run the large language models, LLMs, can quite soon make the doctoral thesis. The system can search data from multiple sources and then fix the text into the form required for a doctoral thesis. 

Those LLMs require lots of data and complicated algorithms. Those things require lots of calculation power. The LLM and the quantum computers are the ultimate duo. Because quantum computers have that kind of calculation power. 

That is one thing that makes quantum computers more powerful than other systems. 

And the only thing that can beat quantum computers is the quantum neural network. Which is the network of quantum computers. That means quantum computers make old-fashioned data security useless. 

But otherwise thinking. That system can protect data more effectively than binary computers. There are multiple levels of data security. The system that runs complicated algorithms can confirm the computer that the person uses. 

But it can also recognize the user. And AI can see if there are other suspectingly acting persons. In the same space. Those things make AI an ultimate tool for data security. The AI can make a profile. If the writer is always the same person. And when the style is always different that makes suspicion that there are multiple makers in documents. 

The mathematical work that shakes the world.

"As a graduate student, Maryam Mirzakhani (center) transformed the field of hyperbolic geometry. But she died at age 40 before she could answer many of the questions that interested her. The mathematicians Laura Monk (left) and Nalini Anantharaman are now picking up her work where she left off."  (QuantaMagazine, Years After the Early Death of a Math Genius, Her Ideas Gain New Life)

Happy International Women's Day. Today, I will handle one work of a female mathematician who died too early. Have any of you ever heard the name  Maryam Mirzakhani? That mathematician died of cancer at the age of 40. The work of  Maryam Mirzakhani handled hyperbolic surfaces.  She was the first woman who win the Fields medal. The highest recognition in mathematics. 

"Her earliest work dealt with “hyperbolic” surfaces. On such a surface, parallel lines arc away from each other rather than staying the same distance apart, and at every point, the surface curves in two opposing directions like a saddle. Although we can picture the surface of a sphere or doughnut, hyperbolic surfaces have such strange geometric properties that they’re impossible to visualize. But they’re also important to understand because such surfaces are ubiquitous in mathematics and even string theory." (QuantaMagazine, Years After the Early Death of a Math Genius, Her Ideas Gain New Life) 

(QuantaMagazine, Years After the Early Death of a Math Genius, Her Ideas Gain New Life)

The ability to model those surfaces makes it possible to model the black holes. The black holes and wormholes can be a series of hyperbolic surfaces. Also, molecular, atomic, and subatomic bonds are the things that act like wormholes. There are many useful things in that kind of mathematical formula from information to engineering. 

Or, we can think that those things are hyperbolic curves that are rolled into the tunnel-shaped structures. The hyperbolic surfaces and their interconnections can also shape the connections between black holes. And maybe those things can help researchers to make the models of the entropy in the black holes. The geodesic that illuminates the surface is the thing that can used to model the time loops. The time loop is the thing that forms an energy wave that travels back in time. 

(QuantaMagazine, Years After the Early Death of a Math Genius, Her Ideas Gain New Life)

The reason why time travels in a certain direction is this. The past is in higher energy levels than in the future. That means information can travel to the past if the event's energy level is high enough. The time loop means that there is a thing that raises the energy level in the future higher than in the past. When information travels in a certain moment in time, outcoming effects will pump energy to them. 

Then that energy causes time dilation that pushes information back in time. The problem is that the entropy mixes that information to a way, that denies us to understand it. The thing is that. The size of the quantum system determines entropy. But another thing is that the limited systems have limited entropy. Theoretically is possible to see things that happened in the past or even in the future. 

But entropy causes a disorder in the information. That disorder makes information nonunderstandable by sorting it into a new order. The entropy is like whirls that disturb the information form. But if the entropy is limited that means it's possible to calculate those whirls backward. The system can put the pieces of information into the original form. That thing is possible only if the system calculator knows every movement and part of the system. 

This kind of work will make fundamental things in chemistry, information technology, and maybe many other types of engineering and scientific work. The ability to model surfaces and curves makes it possible to create models about Hall fields. And that helps the system control information in the quantum tunnels. 

https://www.quantamagazine.org/years-after-the-early-death-of-a-math-genius-her-ideas-gain-new-life-20250303/

https://en.wikipedia.org/wiki/Maryam_Mirzakhani

Can the three object problem be the key to the gravitation?

When we want to calculate the position of two objects. Those are orbiting each other that thing is really easy. But when we are involving the third object in this problem that thing makes everything so hard that even the best computers cannot calculate that thing. The fact is that the position of the three objects in the orbiting system should be easy to calculate. But the results of those calculations have no match with reality. 

The thing is that the gravitation waves are proven that gravitation is some kind of wave movement like light. That thing can help us to model the situation. That makes those calculations very hard. If we are thinking that between the objects is the channel where the power of quantum fields is lower than around the channel. And the pressure of outcoming radiation will push the particles together that thing can explain why the third object makes the system very hard to calculate. 

When the channel with lower energy quantum fields is forming between two objects. That makes them positioned in the same system. If we are using the regular terms. We can say that the pressure between those objects is lower than around them. 

Diagram 1

And the third object is pulling the third quantum field through that channel. That can cause the pushing effect of unpredictable things in the quantum fields. Between those three objects. In the diagram, there is the model of how the third object is affecting the gravitational channel or quantum channel between the objects. 

It pulls the gravitational waves or gravitational curves through that channel. And when the third part of the system is orbiting the entirety. When the position of the third object changes the form and direction of the energy curve are also changed. That means the entirety of the three object systems is incredibly hard to calculate. 

https://www.wired.com/2016/06/way-solve-three-body-problem/

Researchers use binary star systems or triple stars to confirm the calculations. 

 Above this text is an artist's impression of the binary-star system GG-Tauri A (https://www.universetoday.com/Double Disc Found Feeding Each Other In Binary Star System)

Four effects are affecting that system.

1) Pure gravitational effect

2)Centripetal force 

3)Electromagnetic interaction

4) Effect of other members of the system

When we are thinking about the objects of a three-member system the third part will not pull only gravitational fields through two main objects. It pulls also ions and other particles to those objects. Even if the effect of those particles is minimal. That effect can last even millions or billions of years. In the real universe, the electromagnetic effects are not stable. Many high-energy reactions happen suddenly. And that thing causes unpredicted changes in the radiation of the stars. 

When we are looking at the binary-star systems there are also the ion bridges between those stars. The third part is also affecting that bridge. And the electromagnetic radiation will also be affecting that bridge. The gas bridge between the stars is high energetic plasma. That plasma is acting as an antenna and all electromagnetic radiation effects that plasma. When the temperature of the plasma is increasing. That thing that causes the heat of plasma is also pushing those stars away as well as gravitation is pulling them together. 

Image) https://www.universetoday.com/115494/double-disc-found-feeding-each-other-in-binary-star-system/

https://thoughtsaboutsuperpositions.blogspot.com/

The key is: how to prove the solution?

Carl Friedrich Gauss (1777-1855)

Prime numbers from Gauss to Riemann. And from RSA encryption to quantum computers that can break any code in the world. 

Carl Friedrich Gauss (1777-1855)(1) was a mathematician who spent a couple of hours each day trying to create prime numbers. His student Bernhard Riemann  (1826-1866) (2) created his "Riemann hypothesis" (3) that is also known as Riemann's conjecture that used to create the series of prime numbers. The question is where Gauss and Riemann needed those prime numbers? 

Those two famous mathematicians were not the first persons who were try to create so many prime numbers as they could. There were many people like Stanislaw "Stan" Ulam (1909-1984) (4). That man is better known for his work with Edward Teller and the hydrogen bomb. Who tried to create the geometrical model of how the prime numbers divide into spiral structures. That model is called Ulam's spiral(5). 

Even if the answer for Riemann's conjecture is 1/2 there is the possibility to chain the algorithms. The thing is that in point 1/2 the Riemann's conjecture is giving non-trivial zeros. If there are points where the answer is not a prime number or the answers are turning easy to predict that is the end of the use of pure Riemann's conjecture in cryptography. But that conjecture can connect with other mathematical formulas. 

So when we are going to Riemann's conjecture that is giving prime numbers all the time that the formula is driven there is also the possibility that there are prime numbers also outside the series that the Riemann's conjecture is giving. When the series of the prime number ends is unknown. That thing is possible because when the numbers are turning bigger. And there might be some prime numbers between the answers generated by using Riemann's conjecture. 

The sequence between those solutions is turning longer. And that means there is the possibility. That Riemann's conjecture is leaving some prime numbers away from the series that the formula is giving. The thing that makes that formula so impressive, interesting and mysterious is, where Riemann or Gauss needed those numbers. The modern RSA encryption requires Riemann's conjecture. 

If Riemann's conjecture is used purely. That makes secrecy quite easy to break. Purely used conjecture is easy to break simply by using fast computers that are calculating prime numbers. And then the system can simply try every prime number to the captured message. That is called a brute force attack. But if Riemann's conjecture is connected with other mathematical algorithms and functions. That thing makes the algorithm safer and harder to break. 

(1) https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss

(2) https://en.wikipedia.org/wiki/Bernhard_Riemann

(3)https://en.wikipedia.org/wiki/Riemann_hypothesis

(4)https://en.wikipedia.org/wiki/Stanislaw_Ulam

(5) https://en.wikipedia.org/wiki/Ulam_spiral

Image: https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss

And finally, what people should do when they try to solve mathematical problems? 

The key element in mathematical problems is to show people how to get the answer? How to prove that some solution is right or some solution is wrong. Must be done by using a methodology that is accepted in mathematics. 

That thing means that only the answer is not enough. Proving the solution is the key. And the thing that is making that thing. Is that every stage of the calculation must write to the paper. The idea is that the inspector can retake those calculations. And the solution should be the original numbers. 

When some person is making those calculations. The thing is that every part of the formula must make exactly correctly. If something is left outside the mark the answer is always wrong. And the thing is that if the person makes a little bit too much work. 

That thing gives better or correct answers than just removing the "unnecessary parts". Like some "meanless" square root marks from the calculations. In formulas or algorithms is not unnecessary marks. 

And the thing is that proving the thing is the key element. If somebody presses some button unnecessarily that thing is not a mistake. The mistake is that if some mark is lost. And that thing causes horrible errors in the calculation. In mathematics is many things that are sure or they are not sure. But there are also unsolved answers. 

About the book "Hidden Figures" (Margot E. Shetterly)

https://gamesandtehories.blogspot.com/

Kimmo Huosionmaa

In 1960's NASA hired black American female teachers to make calculations for the Moon program, and those women were in the key role to making the moon flight possible, we must realize that this book is not telling the stories about the women who made an extremely important job for NASA. It tells the story that there are more men and women who are played in the key role in many fascinating and awesome missions on Earth. Those women were in the key role in ending the racial separation, and the advancing equality between genders. In the modern day, every position of the persons should depend on the personal skills, without the influence of gender or the color of the skin. 

The technical staff is not many times mentioned in the texts, what are told about space- and other programs. But when we are going to deep inside those missions, and the history of calculations, we are facing the thing, that in those times, there were no calculators, and the major question is that who makes those calculations, what is always needed for many technical missions. 

Many of those men and women, who made the atomic bomb possible in the "Project Manhattan" are ever mentioned in the stories about this weapon. And in the history of Cryptology, there are no mentions, how the formulas and calculations of the Enigma's positions were made. If some persons are saying that computers are making the calculations, that person forgets something. 

The calculation formulas are always made by the programmer or mathematician, and then everything would be perfect. But without those formulas, the computers are unavailable to make calculations. Even the computers have the most powerful processors in the world, they have no capacity for productive thinking, and they need a man to make those formulas for the calculations. 

There were many claiming that NASA used also autistic persons to make those formulas, what was very important for the Apollo program. If the main motor would not be started precisely right time, the spacecraft would be crushed to Moon or Earth, or it could fly pass the object. Those things were very important for Apollo mission successful passing. 

Apollo-astronauts made the awesome job, but there were many people, whose names were ever mentioned. Those persons worked for motors, airlocks, ventilates and electronics. Many people in the world have ever seen the names of those persons, whose successful work was addicted to those formulas. 

When legends meet: Laplace and Napoleon

http://crisisofdemocracticstates.blogspot.fi/p/when-legends-meet-laplace-and-napoleon.html

http://crisisofdemocracticstates.blogspot.fi/p/when-legends-meet-laplace-and-napoleon.html

The power of number Zero

http://crisisofdemocracticstates.blogspot.fi/p/the-power-of-number-zero.html

http://crisisofdemocracticstates.blogspot.fi/p/the-power-of-number-zero.html