The mathematical genius Srinivasa Ramanujan, the man who knows to count endlessly


Another evidence shows that "genius is destiny". But in the short life of 32 years, Ramanujan has left a huge mathematical legacy for humanity.

If you don't really believe Srinivasa Ramanujan's genius math brain, scroll down to read two examples and two short stories to understand why he is the "endless count".

In the movie Good Will Hunting, Will guy in the film has a definition of "genius" as follows: an outstanding individual can see things ordinary people can never imagine. Like genius composers, they look down at the piano keys, they will see every note and type according to their instincts. Like a great physicist, they look at the relationship between things and deduce the doctrine that mankind could prove hundreds of years later.

And like when a genius mathematician looks at a thick page of formulas, they figure out all the relationships of those equations, see the numbers, the calculations that take years of research, I can understand it. There is such a person, Srinivasa Ramanujan, the great Indian mathematician.

Srinivasa Ramanujan, great Indian mathematician.

He himself had never learned pure mathematics - the mathematics focused on abstract concepts, different from the ones used in navigation, astronomy, physics, economics, engineering - but There are countless contributions in mathematical analysis, number theory, endless series, ... and even, solving problems that are deemed impossible to find results.

He was born in 1887 and died at a very young age. Ramanujan was only 32 years old, but in his short lifetime he created 3,900 mathematical results himself, most of which are equations and homogeneous - true equations for all variables. Even while living the final moments of his life at home, he sent a letter to Professor G. H. Hardy at Cambridge University, saying that he was still continuing to devote himself to mathematics.

In the photo below, Ramanujan stands in the middle, Professor G. H. Hardy stands at the far right.

The genius potential is awakened by a book
One would think a genius like him would come from a family with a tradition of mathematical research. But they were wrong: Ramanujan was born and raised in his grandfather's home in Kumbakonam, with his father working as a clothing store, his mother being a housewife and sometimes the main vocalist of a local temple. His family has two more children, but neither child survives to the age of 1.

Relocating to a new school shortly after Ramanujan's grandfather died, he had to follow his family home to Madras. He disliked his new school and frequently dropped out. Despite the family's efforts to get him to school, he quit for a short 6 months and returned to Kumbakonam, attending his former place of Kangayan. 10-year-old Ramanujan passed the entrance exam of English, arithmetic, geometry and Tamil with the highest score in the county. Ramanujan first came into contact with regular mathematics when he was at Level 2.

At only 11 years old, he surpassed two students living in the same house with math knowledge. Shortly after, he borrowed a book on advanced trigonometry. At the age of 13, he studied and mastered trigonometry, discovering his own mathematical theorems. He displayed outstanding talent in the field of geometry and endless series of numbers.

In 1903, at the age of 16, Ramanujan borrowed a copy of the Summary of Preliminary Results of Pure Mathematics and Applied Mathematics, containing 5,000 different theorems. He avidly studied the book and according to the scientists who had contacted him, this book was the push to push Ramanujan to a genius level. He developed and researched his own mathematical projects, individuals of the same age as Ramanujan "rarely understood him".

He received a scholarship but because nothing more than mathematics attracted the attention of this rare genius, he soon lost the scholarship. In August 1905, Ramanujan ran away from home, then attended a school in Madras. Still "horse familiar with the old way", he devoted all his love to mathematics and ignored all other subjects.

He failed the exam, left university but continued to study mathematics himself. At the moment, Ramanujan is living in extreme poverty, almost constantly starving.

Because very few individuals understood Ramanujan's genius mindset, not many could follow and support him. Luckily, when he was 23, the founder of the Indian Mathematics Community Ramaswamy Aiyer discovered the Ramanujan gem, meeting with countless other famous professors to bring a young individual to the university. study as a genius research scholar.

Very few individuals understand Ramanujan's genius mindset, not many keep up and support him

The genius steps chasing mathematical career
Ramanujan contacted the world famous G. H. Hardy, a professor of mathematics working at Cambridge. The first letter Mr. Hardy received was the historical marker of mathematics: it contained 120 theorems, which were all theorized by Ramanujan (though there was no specific argument for all theorems). Many theorems are completely beyond the knowledge of Professor Hardy and colleagues. Although they thought that some of the results were wrong, they still wanted to meet their creator. The decision to believe in Ramanujan and support this genius was right.

There were many obstacles from both the family and from the top English math professors who did not trust a young genius from India, but in May 1914 Ramanujan also arrived in England. From that moment on, the mathematical genius from India reached the peak of his career, when he was working with the world's leading academic minds, writing millennia-long studies.

"Ordinary people" we can not understand Ramanujan's mind so best, his sublime intelligence will be best presented by two short stories.

Mahalanobis, a senior at Cambridge, frequents the Ramanujan house and, one day, is invited to lunch by a mathematical genius. While waiting for Ramanujan to cook, Mahalanobis sat down to solve a problem of finding a pair of house numbers published in the newspaper. After a few minutes of applying the type test, Mahalanobis found the result of the pair 3 and 1 and happily told Ramanujan.


18 Alahiri Street, Erode, where the mathematical genius Ramanujan was born.

The Indian genius heard the problem, even while cooking with the pan, immediately deducing the result for the above problem using an infinite number equation. Any pair of results obtained from the sequence that Ramanujan calculates are suitable for the difficult problem.

He could immediately find an endless sequence of results for a problem, only to hear it once.

When Hardy visited Ramanujan was ill. The two were seated in a taxi number 1729. Hardy thought that number was bad and said that he hoped it would not bring bad luck to the two of them. Ramanujan dismissed: "It is a very interesting number; it is the smallest number that can be written as the sum of two cubes two pairs of positive natural numbers, presented in two different forms."

Seeing the number 1729, he immediately saw two additions, 13 + 123 and 93 + 103. Later people called such numbers "taxi numbers - taxicab numbers".


The taxi numbers we have found.

Faith in the gods and difficulties in working with a genius
Ramanujan has been studying in Cambridge for almost 5 years, with two other math professors Hardy and John Edensor Littlewood - both comparing Indian genius with bright stars who have made great discoveries in history. math industry. However, Hardy and Remanujan's personalities, beliefs and methods of work are contradictory, making collaboration not easy at all.

For decades before the time they met, mathematics always needed strong evidence to prove it. While Hardy is a man of evidence and strict laws, Ramanujan has a strong belief in his intuition and his wisdom. Hardy tries to lead Ramanujan into his way of thinking and obviously, both are uncomfortable with the way the other person works.

Ramanujan believes that the genius mathematical achievements he has come from are the Goddess Namagiri. According to him, she would appear in an illusion before his eyes, writing down mathematical formulas for himself to prove. He related one of these events:

"When I slept, I experienced an extraordinary experience. There was a bloody red veil. I stood there observing it. Then suddenly a hand appeared to write on the curtain. I concentrated intensely on the what's going on. The hand writing the numbers. They get into my memory. When I wake up, I'll write them down on paper. "

it was Goddess Namagiri who contributed to bring Ramanujan to England

It was also the goddess Namagiri who contributed to bringing Ramanujan to England, when she dreamed to the mother of the mathematical genius, forbid the Indian woman "from preventing her children from reaching the fulfillment of life's wishes. ".

Life is full of illness, another proof for "genius is destiny"
In December 1889, Ramanujan had smallpox but luckily he passed. It was a miracle, when the other 4,000 people living in the county he lived in had died from a terrible disease.

In late 1909, after getting married, he contracted testicular vitreous disease (hydrocele testis). The disease is easy to cure, just surgery is healthy again but the Ramanujan family has no money for treatment. Fortunately, in January 1910, a doctor volunteered to perform the surgery for free.

Ramanujan's health condition has been weaker and weaker during the working days in England.

But by the end of 1910, Mr. Ramanujan was seriously ill. Fearing he could not survive, he asked his friend to hand the math notebook to Singaravelu Mudaliar mathematics professor or English professor Edward B. Ross. However, he survived and received his precious book.

Ramanujan's health condition has been weaker and weaker during the working days in England. While keeping a religious diet while living through the harsh state of war, he was diagnosed with tuberculosis and severe vitamin deficiency. Ramanujan returned to his hometown of Kumbakonam and died shortly after, on April 26, 1920, at the age of 32.

Ramaujan's mathematical notes are aggregated and sent to individuals who can understand them. As for Ramanujan's wife, Janakiammal, has benefited from a plethora of funds - research units deeply mourning the passing of a prominent mathematical genius of human history. She died in 1994.

Also in 1994, DA B Young, a doctor, analyzed and re-diagnosed Ramanujan's pathology, found that most likely the mathematical genius had an amoeba infection, a very common disease in Ramanujan's homeland, not tuberculosis. When not properly treated, the illness can last for many years before it becomes ill. At that time, if it was true that Ramanujan had a disease caused by amoeba, he was promptly cured.


In a lecture in India in 2011, American math professor Bruce Carl Berndt said that for the past 40 years, nearly all of the theorem that Ramanujan mentioned had been proved to be correct. Attention became more and more attention to his genius and genius, as brilliant achievements spread to all areas of modern mathematics and physics.

Over the past 40 years, nearly all of Ramanujan's theorem has been proved to be correct

The science journal Nature named Ramanujan one of the most prominent individuals in human history. His hometown of India issued a stamp with his picture in 1962, to celebrate the 75th anniversary of Ramanujan's birth, in memory of the brilliant genius. On December 26, 2011, the stamp was redesigned.

Also in 2011, India announced it would select December 22 - Ramanujan's birthday - as the National Mathematics Day. Another way to remember the merits that genius has brought to mankind.

Ramanujan will be alive as long as the numbers no longer make sense. That also means "immortal".

Address: Head Office at 29 Nguyen Thi Minh Khai, Pham Ngu Lao Ward, District 1, Ho Chi Minh City, Phone: 088 3925 9999
Copyright © 2015 - NEAS. All rights reserved