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. 

https://thoughtandmachines.blogspot.com/

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

Pierre-Simon Laplace
(1749-1829)
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When the mathematician Pierre-Simon Laplace and Napoleon Bonaparte met the Emperor of France said, that there were no mentions of the god in Laplace’s papers. And the scientist answered that he didn’t need that calculation. I think that Napoleon was not interested in the god or mathematics when he met Laplace. The thing what interested this man, who became the figure of excellent tactician and military leader was something that was drawn in the papers of Laplace.



That thing was the points, what were drawn on those papers, and the way how Laplace could calculate them in the paper. If Simon Laplace could do the same thing for the artillery, French army will have the most lethal cannons on the battlefield. For many people, those points on the paper were nothing more than just the points. But as we must see, Napoleon saw those things by the different way, he saw a very effective way to use artillery.


Those calculations what made the finding of planet Neptune possible were known as the mechanics of heaven. The idea of the celestial mechanics was that Universum is a very stable place, where all particles move stable trajectories. This made possible that the movements of the particles can be calculated very sharply

The planets are found near the ballistical area of the sky, what is called as elliptical, and there is possible to calculate the point, where the planet will be fine with very good sharpness. Problem with the celestial mechanics is that will work only in the universe, there is no wind to disturb the planets, and if the conditions are the same kind in the Earth atmosphere than they are in the empty space, we could calculate every flight trajectory same way, what the astronomers used to calculate the points of Neptune.





 The thing is actually possible on the Earth if those calculations were involved more values, what will help in that calculation. First one is the side wind or the position where the wind comes, the second one is the temperature, the third one is the air pressure, fourth value is the humidity because the air what has particles will cause the changing of the ballistic situations. The sharpness of those calculations depends on how many vectors and values quantities could the mathematician involve the formula, what calculates the point, where the ballistic form ends, and those things were interested in Napoleon, who wanted to take the control all the Europe.



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https://en.wikipedia.org/wiki/Pierre-Simon_Laplace

The power of number Zero

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Kimmo Huosionmaa

”Count zero” is the book in the bookshops, but here I'm writing about why the number ”Zero” is so difficult thing in mathematics? The ”zero” means nothing or empty, and the symbol of that thing, what we normally can't understand, because there is no absolute emptiness anywhere in the universe. By the way there might be places where the distance of single atoms could be even kilometre size, and at that point the material will be so space, that even the interstellar ramjets will not work in those areas, and they might cause risks for of the future interstellar spaceflights, what will be after 3000 years from to today will be routine missions.


But when we will return to the zero, we will see that nothing can bypass the empty. There are many things in the number zero, and one of the unique thing about that number is if you want multiplicate any number by the zero, the result will be always zero. The other numbers will be annihilated if they will multiplicity with the zero. The zero is the thing that can also make the calculations impossible to solve, and this case is in the division, where is the number zero as a part of the calculation.


Number zero makes those calculations impossible to solve because those are the rules of the mathematics. And the all things about the mathematics are the rules, how to make some calculations. Those rules are very clear, and if somebody thinks that they are easy, will that person be wrong. In the real life, zero persons can share the cake by leaving this thing on the table. But in the world of the mathematics is very simple rules, that the division of zero is strictly prohibited. And those rules are very clear. Zero is also part of some other numbers, and its mission is to show that the number is ”full ten”.


That will make the calculations easier. If we will division 120 by the number 12 will the result be 10. or if we divide that number by 10 will the result be 12. But zero is very strange and complicated number because it is everything and nothing. Every number line has place for that number and it is bigger than many numbers. All negative numbers in that line are smaller than zero, and this is the reason, why half of the numbers of the world are smaller than number zero. So this means this number is quite big if we compare it with the number -10.


If some people have -10 euros in the bank account, would that person get the warning from the bank because the person didn't calculate the incomes and then the bank account was turned to -10, but there is one nasty thing. The empty bank account would not cause the telephone call from the bank. This case means that the person has calculated the money what was spent in the shops, but the account would not be sat at the minus level. But this is only the writing about the number zero, and the court of the strange number in the middle of the number line, what continues forever in the strange world of numbers.

Sources

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https://media-exp2.licdn.com/mpr/mpr/AAEAAQAAAAAAAAJtAAAAJGQxMzgwZjQ1LTZjMzEtNDI4Zi1iYzk1LWNlNzNmOTczYmQ1YQ.jpg