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/

By the way, how to solve the quadratic algorithm?

  

 By the way, how to solve the quadratic algorithm?

The most common mistake is just trying to combine the formula that is under the square root mark. The square root is marked in this text as the "sqrt". That is the C++ mark for square root. Forgetting the brackets is fatal in this kind of calculations. So solving this mystery formula happens like this:

x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x

That is how the numbers must be input in pocket calculators:

     -b + sqrt (b^2-4ac)=ANS and then ANS/2a

     -b - sqrt( b^2-4ac)=ANS and then ANS/2a

      -b + sqrt(b^2-4ac)

x=_________________   

2a

 Using pocket calculator:   

-b + sqrt (b^2-4ac)=ANS and then ANS/2a

or 

              

-b-sqrt(b^2-4ac)

_________________

              2a

Using a pocket calculator:

-b - sqrt (b^2-4ac)=ANS and then ANS/2a

The terms below the square root can mark like this:

-b + (sqrt b^2- sqrt(4ac) The calculation is:      -b+(sqrt b^2- sqrt(4ac)

     x=__________________________

2a

or

-b - (sqrt b^2- sqrt(4ac) The calculation is:           -b-(sqrt b^2- sqrt(4ac)

       x=________________________

2a

The sqrt is the square root. And don´t forget brackets.

x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x

And the most common mistake is that the person tries to calculate the calculations at both sides of the minus mark as the entirety. Or they simply forget to take the square root from both sides of the marks that are below the square root. 

So marking both of the parts under the square root mark by using their square root mark is making it simple to understand the idea of the quadratic algorithm. Combining those terms is not possible because there is a "minus" mark between them. Both of the numbers that are below the square root must calculate separately. 

https://thoughtsaboutsuperpositions.blogspot.com/

Simultaneously repeating things show that some things do not happen by accident.

Kimmo Huosionmaa

Probabilities and other things are the most interesting thing, what the mathematicians have ever created in their mind. Probability is the thing, what has caused grey hair for many military leaders and rulers around the world. What is the probability of the thing that meteorite will strike your house? This might be the very important thing for the insurance companies, that make the prices for their insurances.  If the meteorite would be destroyed some house, must the insurance company make the bills for that, and can they sell insurances, what covers the destructions of the meteorite? And will anybody buy those insurances, is the very good question, if those new insurances will come to the marketing.


The calculation about what is the probability that meteorite, what hits the house, if it hits to the Earth is quite simple. The area of the house would division with the area of the Earth, and as we will see, the probability that some particular house will be destroyed by the impact of the meteorite is quite small. But when the insurance companies or police want to find out, is something actually the cause of the probability, they collect the statistics, and that sometimes uncovers some things are made for the purpose. In the things what will happen in the long-period sequence, is sometimes visible that this kind of thing happens simultaneously. Let's take one fictional case, what provides that the archives and statistics show that this kind of things happens on purpose.


This is the key element why the statistics are collected. They will uncover if something is done by the purpose.  One thing is if the person who has been in some mental institute will get the letter from the steward's office, that this person has been noisy. What makes this letter very interesting, is that it comes when this person's family have been in the long holiday. Rest of this person's family had the way, that they would be a long period in the sunshine when they will celebrate their every ten years of the marriage.


And one day some person was realized, that those letters came all the time when this person's family have been at overseas. This kind of things shows, that somebody will make the wailings only when this person's family were on their holiday trip. When those reclamation letters were dropped from the mailbox only when the family of this person was far away, will the simultaneous action, what happens time and again, show the investigator, that there is something wrong in this fictional case.

When legends meet: Laplace and Napoleon

Pierre-Simon Laplace
(1749-1829)
Picture 1

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.



Sources:



Picture 1



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

Leaders of government needs crystal ball

Source of picture:
 https://richtopia.com/effective-leadership/throw-out-your-crystal-ball

Kimmo Huosionmaa

Everybody wants to see future. Leaders of government really need crystal ball to support their work, but there is some methods to forecast reactions of societies. There are two methods to forecast what will happen if we do something  mathematical and historical. They are not very trusty and some scientist think that some day we can build crystal ball what basis an electromagnetic black hole, what is created in NIF-type fusion test system. Last one is just reactor, where full geometrically made ball shape bite of metal or crystal will pumped with electrons or lasers, and then scientist could open wormhole to the future. That's possible in theory, but it needs other black hole in that target time, and those black holes oscillation must synchronize together. This way to see future through wormhole is theoretically possible, but making that machine is difficult because power what is needed is very huge.


When leaders of government makes their decisions you must realize that those people cant't see what really will happen in the future. They must just forecast what kind of influence is about those decisions what they make, but normally they can just imagine what could happen if they do something for laws or other things like international relationships. Of course there is tools what makes those forecasts easier, and one is mathematical method. There is formulas what are made for calculating massive gas masses movements, and those mathematical formulas are normally used by meteorologists when they want to forecast weather. Those formulas are useful to calculate people reactions for some decisions.


The idea of use of this kind of mathematical functions to forecast people reaction are basis on Science fiction book "The Foundation" what is written by novelist Isaac Asimov. In his book methodology was called "Psychohistory" The principle of use those meteorological or normal temperature pressure (NTP) formulas for sociological forecast is same as calculating  movements of massive gas masses. We can't calculate place of single atom, but we can forecast movements of giant gas mass, and calculating this kind of movement is easier for bigger masses of material than tiny mass.

Could NIF-reactor be tomorrows crystal ball?

That's because giant gas mass will not change direction of moving so easily than tiny mass of material elements. You see this in snow. Single snowflakes will move without sense but when we see snow falls we will know where it is going better when mass of moving snow is big, when even trees cant resist it power. And humans are like snow. We can stop one person of society, but problem is how we will find him. If all members of society will begin to move, we can forecast their actions, but they are harder to stop.


What is threat of society? Single group of people can't make our society unstable, but if many radical organisations are activating in same time, could result be devastating. That's why we have historical method to find out what our decisions can cause for society. It basis investigation of historical and political elements of crisis. In this method scientists will investigate history, and find similarities between historical decisions and decisions what leaders are making now. After that they investigate what influence that decision had to society.



After that they might want to inform leaders about dangers of some decisions. Methodology is not very sharp and it is not very trusty. But these unreliable methods are better than nothing. Of course scientist think that they can make tiny wormholes to see the future, and those wormholes are made with lasers or electric accelerators, what pump lots of energy to small target. Those systems might look like NIF, but I don't know is that technology tested in real life. And if they are right they could make small wormhole, what is smaller than atomic nucleus, and those wormholes could bring light from future like some light cable. And if everything goes right those scientist could theoretically make camera obscura what sees to future. But this is only theory.