The mysterious genius Srinivasa Ramanujan.

Srinivasa Ramanujan (1887-1920). (Quanta Magazine, Math Is Still Catching Up to the Mysterious Genius of Srinivasa Ramanujan)

The number theory is thankful to Srinivasa Ramanujan (1887-1920). The thing that makes this person, who was born into a poor Indian family in colonial India was a self-educated person, who made a lot of things in mathematics. Those theories are still handy tools for many types of advanced calculations. There are many interesting details in the life of that young person, who passed away in 1920. Many people say that Srinivasa Ramanujan died too early. If that person could live a longer life, he might stand in the place of Albert Einstein. 

There were many interesting things in Ramanujan's early life. The thing is that Ramanujan failed twice in college. Because of his passion for mathematics. And that's why he flees from home. Maybe he was afraid that his parents were angry. Finally, he went to Trinity College Cambridge where he started to work with Hardy and Littlewood in 1914. 

Pages from Ramanujan’s lost notebook. (Quanta Magazine, Math Is Still Catching Up to the Mysterious Genius of Srinivasa Ramanujan)

"Ramanujan’s first letter to G.H. Hardy included formulas (5), (6) and (7), strange nested fractions that Hardy said “defeated me completely; I had never seen anything in the least like them before.” (Quanta Magazine, Math Is Still Catching Up to the Mysterious Genius of Srinivasa Ramanujan)

(Quanta Magazine, Math Is Still Catching Up to the Mysterious Genius of Srinivasa Ramanujan)

There are lots of theories that this man created. At a young age, this man was very poor and also he had very big health problems. In 1912 he sent letters to famous mathematicians and one of them, G.H Hardy the expert in number theory and analysis at the University of Cambridge. When Hardy got the letter from Srinivasa Ramanujan. That man said, that his greatest work for mathematics was that he found Ramanujan. Then Hardy called Ramanujan to England. There Ramanujan made some works for Cambridge. He lived in England from 1914 to 1919. Then he returned to India where he died in 1920. 

"Hardy and Ramanujan collaborated closely for years. They exchanged letters about mathematics until Ramanujan’s death." (Quanta Magazine, Math Is Still Catching Up to the Mysterious Genius of Srinivasa Ramanujan)

And then he went sick. After returning to India Ramanujan died. An interesting thing is that Ramanujan died almost similar way as his colleague Nils Henrik Abel (1802-1829), a Norwegian mathematician. He came to his university, did impressive work, and then got some illness and then that ultimate genius died at a young age, 32. 

Images: (Quanta Magazine, Math Is Still Catching Up to the Mysterious Genius of Srinivasa Ramanujan)

Ramanujan work. 

Still today Ramanujan's work is very highly respected. 

The main thing that Ramanujan did is this: he introduce a way to calculate fractional numbers. There are five ways to introduce number 4.  The number four can be shared in pieces like this (2+2), or, (2+1+1), or, (1+1+1+1), or, (1+1+2). And then it is easier to make things like division calculations. 4/8 can be introduced like this: (1+1+2)/(2+2+2+2). And we all know that 4/8=1/2. 

The interesting thing is that. Those numbers can also be decimal numbers, which means that we can introduce as an example number 1 in this mode. (0,25+0,25+0,25+0,25). Or we can introduce number four in this mode. (0,5+0,5+0,5+0,5+0,5+0,5+0,5+0,5). Or we can share 0,5 to two 0,25. That is one of the most interesting things in mathematics. There are many ways to benefit from that model. 

The Ramanujan theorems play a key role in singularity calculations. There the curves and lines connect a series of points. The introduction for that is in the Quanta magazine article. 

The thing is that Ramanujan's work could help Grigory Prelman in his work with the Poincaré theorem. 

https://www.quantamagazine.org/srinivasa-ramanujan-was-a-genius-math-is-still-catching-up-20241021/

https://en.wikipedia.org/wiki/G._H._Hardy

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

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

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

List of Ramanujan work. 

• Ramanujan's sum
• Landau–Ramanujan constant
• Mock theta functions
• Ramanujan conjecture
• Ramanujan prime
• Ramanujan–Soldner constant
• Ramanujan theta function
• Rogers–Ramanujan identities
• Ramanujan's master theorem
• Hardy–Ramanujan asymptotic formula
• Ramanujan–Sato series

Wikipedia, Srinivasa Ramanujan

All images: (Quanta Magazine, Math Is Still Catching Up to the Mysterious Genius of Srinivasa Ramanujan)

How fast is the growing speed of the Universe?

How fast is the growing speed of the Universe?

The shape of the universe.

What is the shape of the universe? (1) This is a very good question because that speed can explain, why we cannot see the location of the big bang. In somewhere past the cosmologists got a fascinating idea that galaxies would be in the layer of the ball, what is called as the universe, and then by searching the directions of the galaxies, the researchers could define the point, where the big bang happened, and then the telescopes would be turned to the "south pole" of the galaxy.

One of the things is that I'm talking here the direction of the galaxy, what is to the direction of the point, where the big bang happened as the "south pole", and in fact, the black holes might have polar like planets and stars. The idea was simply the position of the galaxy is telling, where the big bang was, and then the telescopes would easily find that point.

And then the astronomers were looking at the stars more and more effective telescopes, and they noticed that there were many galaxies in location, what supposed to be in the direction of the big bang. But as you see the scientists must sometimes adjust their theories, because observations are chancing our knowledge.

The idea of a two-dimensional ball-layer changed to the combination of the multiple models, and the thing, what kind of model of the universe is used depends on the scale. as you might know, the Universe is very big, and if we would look at things by using the very large scale model, we would think that the universe is the straight layer, and that model could be suitable in the local galaxy group.

But then the thing, what is called "U-shaped" or saddle from would turn to dominate, if the scale is smaller, and the observed area, of the universe, is getting bigger. Then the universe is turning to the ball, if the area, what observer sees is big enough. And here I must say, that the observer is always hypothetical. I have thought the universe as the 3D ball-layer, where the galaxies are in the different locations and positions, and the width of this layer is extremely large.

Why the expansion speed of the Universe is slower than it should (2)

By using the most modern telescopes, we can see the distances of billions of light-years. That means that we can see objects from that distance. The distance of a farthest known galaxy is 13 billion light-years and the size of the universe is 46 billion light-years. So we see things, what is happening in the 13 billion years ago.

But when we are thinking that we cannot see the big bang, there is one very interesting theory, and that thing is that the beginning of the existence of the expanding speed of the universe was near the speed of light. And then it started to slow. There should be something, that slows that speed, and that would mean that there is a massive black hole in the place, where the big bang has happened.

The real number of expanding the speed of expanding the universe is about 67 meters per second, and that means that there is something, that would break the expansion speed. That thing could be the mutual gravity of the galaxies, the dark material, and the last hypothesis is that in the center of the universe is the giant black hole, what is larger than any galaxy, and that thing would pull the galaxies to it. This thing makes science very nice before we can create and confirm the models of everything, we must realize, that everything is possible in the world, where black holes are dominating their environment, and massive eruptions are disturbing the harmony.
(1)
https://en.wikipedia.org/wiki/Shape_of_the_universe
(2)
https://www.avaruus.fi/uutiset/kosmologia-ja-teoreettinen-fysiikka/maailmankaikkeuden-laajenemisnopeus-ei-tasmaa-olemme-jattaneet-jotain-huomioimatta-kosmologisessa-mallissa.html

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

Image:

https://scx2.b-cdn.net/gfx/news/hires/2014/compactgalax.jpg

When coincidence destroys common

When coincidence destroys common

The location of the single gas atom is impossible to calculate because it is impossible to create the precise decimal number, which is marking the position and direction of vectors. That means we can put more and more numbers behind the dot, and this makes the calculating precise location of the particle in the 3D universe or space impossible. And here we can go to one of the most interesting things in the black holes and the mathematical formulas, that are using to create the most advanced simulations in theoretical calculation models.

The idea of the black holes is that they are the most dominating objects in the universe, and the particles are falling in that object without disturbing from the forces, what are caused by other objects. So if we would like to adjust those formulas, what is used for making predictions of the movements of atoms and molecules, but for that thing we should take the single, well distinct particle, where we can focus the system, and then we can compare the theoretical results, what the system would give to the results, what we can get from the real life.

This is one way to check those things. When we are creating the models, how the gas is acting in the universe, we must realize that those molecular clouds are the biggest objects in the universe, but the problem is that single molecules are extremely light.

So we can observe the entirety because the universe is so stable place, but the paradox is that it is full of radiation. Another thing in that in the case, where we would want to calculate the movements of the molecules, we can make the observations even hundreds of years, and then comes thing, what we can call as coincidence.

Coincidence can destroy every model in the world and this case, the explosion of supernova can turn the beautiful gas mass what we have observed even years in a couple of seconds, and in this case, the problem is that we cannot notice that kind of chances in the giant gas mass, what size is hundreds of light-years. When the electromagnetic shock-wave would hit to that nebula, it can turn it's the direction or cause the extremely big-size movements in the gas mass.

And this makes adjusting the calculations very difficult because we would want to find the stable gas mass, where are no pulsars or what is not influenced by the radiation, what comes out from impacting black holes and neutron stars. The thing is that we can say, that those phenomena are really interesting, and they give us very much information about the behavior of energy and other things like black holes.

But those coincidences are breaking the stability, what we are needing when we are adjusting calculations. If we want to make formulas and check how well they are fitting to the environment or real life, that means that this kind of testing needs extremely stable conditions.

When we are observing things like impacting black holes, there is a possibility, that this kind of phenomenon is really interesting, but they are not exactly very common cases in the universe. That kind of thing where we are observing billions and billions of particles, we are seeing those things like gamma-bursts all the time, but they are not very common cases.

People who are observing gamma-ray bursts are not making mathematical formulas is the common thing, what people are saying. The thing in the mathematical formulas is that people, who are working with those things are always needed or want the common cases and stable conditions. This means that things like intelligent life-forms and other things are not things, what those people want.

They are needing entirety without uncommon things, and that means they would want to observe the galaxy, where is no single star and every particle has the same size. And rather saying they would want to close that gas galaxy in the giant ball, where is not outer emission to that mass, what they want to use for checking their calculations. And here I must say one thing, we are always confused by coincidence.