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)

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