1. Indian Teenager Dancing with Numbers
Nobody knows Srinivasa Ramanujan, the poor Indian teenager without any education, scribbling How did those formulas on the ground, on the table, on paper come from? Even he himself can only explain: "They just appeared, appeared in my mind".
Those endless positive integers, changing various forms of existence, are like an endless dance, attracting Ramanujan to seek, discover and describe their delicate and graceful dance steps.
In 1913, Ramanujan wrote his formulas to GH Hardy, a famous mathematician at Trinity College, Cambridge, UK.
As Hardy himself said: "There is no precedent or regulation by which people's heartfelt thoughts can be judged." In this way, Hardy helped Ramanujan to come to England.
The teenager who dances with numbers has since become attached to Science, Trinity College, the mathematician Hardy, and Hardy's mathematician friends.
2. The reckless teenagers in the scientific world
arrived at Trinity College at the beginning of the year. Everything here is different from the mud and beaches in his hometown. Even in the air, there are faint thoughts and wisdom from the depths of history floating in the air.
Now, Ramanujan is very close to Trinity College, but how far is he from science?
Ramanujan came to publish his manuscripts, but Hardy arranged some lessons for him. Hardy told him: "I would also like to publish it at the right time, but we first have to prove your formula, using a more formal algorithm." The
genius boy naturally disagreed: "Professor Howard's class is always about derivation and proof. , I don't understand, I have the formula and can get the result directly, why waste time on these proofs?"
3. The beauty of intuition and the pride of science
Hardy saw Ramanujan's formulas, he felt their value, and he liked them very much.
But what is science?
Like Euler, the most creative mathematician of the 18th century in his youth, and Jacobi, the most puzzling mathematician of the 19th century, Ramanujan also displayed the same qualities everywhere: right Intuition and love of form. It is their own form, an art for themselves, it shows the truth.
However, both Euler and Jacobi, their scientifically recognized results were completed in the second half of their lives. Because, "Science must be proven and reproducible, and must stand up to scrutiny", otherwise, those intuitions and forms will only be considered "conjuring tricks".
So, "I need you to take the course, to study the proof".
"Not only do we have the responsibility to use scientific methods to prove your beautiful intuition formulas, but also, when we are ready to challenge the field of science, we cannot afford to fail the proof."
Intuition has the beauty of intuition, and science has the pride of science, When they joined hands, it was Ramanujan who met Hardy.
Intuition suggests the direction for science, and science keeps intuition from getting lost.
4. The pride and humility of science
Hardy's good friend, the mathematician JELittlewood, wrote to Hardy: "I absolutely believe that any positive integer is a good friend of Ramanujan. , you have a responsibility to take care of him and make sure that his work is fruitful. In a way, this is also a war for you.”
Ramanujan and Hardy had an argument over Hardy's questioning of the prime number formula. However, what Ramanujan did not know was that his first paper had been successfully published in Mathematical Sciences at Hardy's recommendation. Hardy, the famed mathematician, helped Ramanujan correct and revise his proof of the formula while worrying about how to protect the digital teenager from the war.
The distribution formula is so beautiful that it was a shared surprise for Ramanujan and Hardy. Hardy introduced Ramanujan to Major Macmahon, the authoritative mathematician of distributional formulae. The proud major saw Ramanujan's proof, and he liked the exotic teenager very much.
With the efforts of Hardy and his friends, Ramanujan was finally elected as "Academician of the Royal Academy" and "Academician of Trinity College, Cambridge" successively.
Proud science, ready to drop his stature at any time and humbly follow in the footsteps of those who push science forward.
5. The significance of pure mathematics
To quote a speech given by Hardy when he recommended Ramanujan as a Fellow of the Royal Academy:
"When I met Ramanujan, the limitations and depth of his knowledge were astonishing. Manujan's work, we may disagree on its importance, and its impact on the future of mathematics is unknown, but what it shows is its profound originality.
… Manukin once told me: 'A formula means nothing to me unless it expresses the mind of God'. Leaving aside the question of my beliefs, I'd say maybe he's right. That's not what pure mathematics is all about Can it be said that we are all explorers of infinity in pursuit of absolute perfection, we did not create these formulas, they already exist, waiting to be perceived and proven by a brain as intelligent as Ramanujan. Without thinking, how can we question Ramanujan? Let alone God."
6. Some Notes
(1) Srinivasa Ramanujan (1887.12-1920.4), Died of tuberculosis at the age of 32.
(2) In 1976, the "lost manuscript" in which Ramanujan proved his new formula in the last year of his life was found. These manuscripts, currently on display in the Wren Library at Trinity College, are comparable in importance to Beethoven's posthumous manuscript, the Tenth Symphony. These formulas were later used to understand "black hole behavior".
(3) In 1992, American writer Robert Kanigel's biography "The Man Who Knew Infinity" (The Man Who Knew Infinity) won the "American Book Critics' Biography Award".
(4) In 1997, the Ramanujan Journal was launched to publish research papers on "Mathematical Fields Influenced by Ramanujan".
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