A Man of Science and Engineering in Troubled Times Wandering in the Late Qing Dynasty

At the beginning of the 20th century, India was the largest and most important colony of the United Kingdom. Every year, the United Kingdom recruited a group of British students.

For example, the University of Cambridge recruits about 20 Indian students every year, and there are almost more than 1000 Indian students scattered in various colleges in the UK.

Most of these people are from upper castes, at least Vaishyas (third caste).

Brahmins are the highest caste in India and are mainly clergy, accounting for about 5% of the population.

The second caste, Kshatriyas, is the least, with only about 3%. The living conditions of these people are truly favorable.

A considerable number of the students were from the third caste, Vaishyas - Gandhi was also a Vaishya.

Although Ramanujan is a Brahmin, the highest caste, his family does not have much money, at least not enough to study abroad.

After Hardy received Ramanujan's letter last year, he wanted to bring Ramanujan to Cambridge, so he wrote to Indian officials and conveyed Ramanujan's letter at the same time.

As a result, the Indian civil servant in charge of overseas students was very unhappy after reading it and wrote back to Hardy: "The recent letter surprised me. It seems that you encouraged Ramanujan before he was sure of the source of his expenses for going to England. OK. I have seen too many situations where Indian students don’t have enough money after coming to the UK, and all they get is disappointment and misfortune.”

Later, Hardy and Littlewood prepared to pool money together, but the two of them could not bring out much for pure mathematics. At most, 50 pounds per year was far from enough for studying abroad. Fortunately, Ramanujan finally secured a scholarship program.

India and China are still different. The Chinese attach too much importance to education. As early as the late Qing Dynasty, they vigorously promoted studying abroad, and a large number of them studied abroad at public expense.

But India is a non-sovereign country. It can decide very few things on its own and relies on charity from the colonizers.

Indian students in Cambridge are easy to identify, and Li Yu even felt the caste system's huge constraints on Indians.

When he was in the restaurant, Li Yuduo paid more attention and found that there were not many Indian students in the first place, and they basically did not cluster together, or rather they clustered in small clusters - they gathered according to caste.

It should also be noted that each caste is actually subdivided into many smaller castes, which has simply divided Indian society.

Within the same caste, people can sit and eat together, but across castes, this rarely happens.

For a time traveler like Li Yu, it is very difficult to understand, not to mention that he is from China, which should be the only country that has eliminated the so-called aristocratic class in the purest way.

In the past, a Chinese businessman went to India to do business. During lunch, the Chinese businessman called the Indian driver to the table. As a result, other Indians were dumbfounded.

The driver burst into tears of gratitude and said that this was the first time he sat down to eat with such a distinguished person.

Because in India, foreigners basically belong to high castes.

The real upper castes in India do not even bother to share water pipes with lower castes.

Li Yu sat opposite Ramanujan and saw that he ate very simple vegetarian food, including bread, lentils and a glass of milk.

"Will eating like this make you hungry easily?" Li Yu asked.

Ramanujan did not answer Li Yu's question. Instead, he looked around and asked in surprise: "Chinese people also like to chat?"

Li Yu was puzzled by the question: "What's so confusing about this?"

Ramanujan said: "After I came abroad, I found that all the people here were reserved or indifferent, to the point of irritation, and often rejected people thousands of miles away. It is difficult for each of us Indian students to accept it."

"Perhaps due to cultural differences, the British have to maintain their so-called gentlemanly demeanor. Of course, it cannot be ruled out that some are superior national prejudices," Li Yu said, and then asked a question that had been doubting him for a long time, "Mr. Hardy said, Your formulas were all told to you by the goddess in your dream, what kind of goddess is she?"

Ramanujan said: "It is my faith, Goddess Namageli."

Li Yu had never heard of the name of this goddess at all. His understanding of Brahmanism or Hinduism was the three main gods of Brahma, Shiva and Vishnu.

Add at most one prototype of the legendary Sun Wukong - the Indian monkey god Hanuman. (I don’t know if this statement is reliable. Many self-media have said so. After all, the Great Sage has no shortage of traffic.)

Li Yu asked: "Who is this goddess Namagiri?"

Ramanujan said: "She is the consort of Narakhimo, who is also called the Lion God and is one of the incarnations of Vishnu."

Finally, I mentioned a god I had heard of.

Li Yu said: "It feels very similar to Chinese Taoism, with many gods and goddesses."

Ramanujan made an astonishing statement: “To me, it is more or less true that all religions, whether Christian or Buddhist, are equally true.”

Li Yu was very stunned and could not understand the Indian religious views.

Ramanujan asked again: "Does Mr. Academician also have faith?"

Li Yu shook his head: "I am an atheist."

Ramanujan said: "It's such a pity. If you also have faith, you might get instructions from God."

Li Yu smiled and said, "Maybe I don't need it anymore."

Ramanujan said: "Goddess Namakri gave me endless help. Originally, according to the teachings, I could not leave India, but the goddess told me in a dream that I could leave, so I boarded the ship to London."

Li Yu didn't dare to ask more questions. At this time, Indians really couldn't leave Indian soil casually unless there was some reason.

Gandhi was expelled from his caste for leaving India.

But Brahmins themselves are priests and can explain religion, so...

Li Yu smiled and said: "God has arranged the best, and the goddess also wants you to come to London."

Ramanujan said: "But my family and friends disagreed. My father-in-law asked me why I couldn't study mathematics in India. I explained to him for a long time, but he still couldn't understand. My friend also thought that this was a mistake that belonged to his family. It is a despicable way to smuggle the glory of India to a British university. My mother is worried that I will not be able to adapt to the British weather, that there is no good Indian food here, that I will be discriminated against by the British, and that she is even worried that I will be raped by a British girl. Hang on and never return to China."

Li Yu has watched "The Big Bang Theory" and knows that Indians have very traditional views on marriage and love. People who are successful in Silicon Valley have to return to their country to get married, and they must report their caste. If you are of a lower caste, even if you are in Silicon Valley No matter how awesome you are, you still have to squat.

Before Ramanujan left India, some English women came to see this mysterious genius who was about to go to Cambridge, shook hands with him, and made his mother very angry.

Li Yu spread his hands: "Since you're here, just do what you want to do first."

Ramanujan said: "That's what I think. Mr. Academician's deeds are very exciting to me."

Li Yu smiled and said: "To each other."

Ramanujan finished his meal in several bites and said, "Yes, let's go find Mr. Hardy. We have to discuss a key issue today."

Li Yu asked again: "Do you really only eat this much?"

Ramanujan said: "My mother's worries are not unreasonable. There is too little food in the UK." Ramanujan is very picky about food.

Peaceful times were fine, but World War I broke out half a year later, and the British supplies were in short supply. Bread was in limited supply, so where could we find more vegetables?

Ramanujan happened to be in the period of scientific research at that time. He ate very casually and rested even more casually. In this state, he was most likely to get sick.

The key point is that Ramanujan was not obedient in the hospital. He always complained about pain here and there. He was even a little willful and did not believe in medicine.

Many doctors in London said: "Few doctors are willing to bring Ramanujan to their own medical clinics. No one can stand his temper."

In short, various factors led to his illness.

If future generations adhere to vegetarianism, it will actually have little impact. However, in the early 20th century, when this kind of medicine was just beginning, vegetarianism was still somewhat risky.

Ramanujan's early death was probably due to his weakened immunity and contracting tuberculosis.

As mentioned before, one-third of the world's population is infected with tuberculosis, but the human body's immunity prevents 90% of people from getting the disease. However, once the immunity drops significantly, there is a danger.

Some trace elements are difficult to provide or provide in small amounts on a vegetarian diet, such as vitamin D. Perhaps it was its lack that caused Ramanujan to contract tuberculosis.

Unfortunately, it will take several years for the role of vitamins to be slowly confirmed.

In addition, compared with life in Britain and India, there is at least one thing missing - sunshine.

Sunlight helps the body synthesize vitamin D. However, the weather in the UK meant that there were very few opportunities to bask in the sun. In addition, he had been doing research in the house all year round. As time went by, his body collapsed sooner or later.

On the way, Ramanujan asked curiously: "Mr. Academician is also from the East. You have left your homeland. Don't you miss your hometown?"

Li Yu said: "In fact, I often return to China."

"I'm so envious!" Ramanujan said, "I have only been away from India for a few months, and I already miss my hometown very much. The streets there are full of bullock carts, the bells jingle on the painted horns, and the men are topless and surrounded by trousers. Loincloths, women in saris, nose rings and bangles shining against dark skin.”

Listening to Ramanujan's narration, it seems that he lived in the countryside.

The genius lived a lonely life in England for several years, with few friends and only mathematics as his companion.

Li Yu said: "I can understand your mood."

The two walked into Hardy's office. He was writing and drawing on a small blackboard. When he saw Ramanujan coming, he said:

"I have already thought about it. If you want the entire British mathematics community to know your name, you can choose the topic of integer splitting. Professor McMahon, who specializes in combinatorial mathematics in the office next to him, has spent more than ten years on this and has not figured it out yet. He has a clue, but your formula has a perfect approximation effect. We will spend some time and give a more professional mathematical proof, and his jaw will definitely drop."

Ramanujan said: "If I can publish a paper, I will definitely cooperate with your work."

Hardy took a puff on his pipe and said: "I know you have a lot of things you want to publish, but we have to do it bit by bit and make choices. After the extremely difficult result of integer splitting is achieved, I might be able to help you apply. to a researcher position, that way we have more time.”

Ramanujan said: "I understand, thank you Professor Hardy."

The integer splitting that the two people did belongs to the field of number theory, which is very easy to understand and can be understood by elementary school students.

The so-called integer splitting is to express a positive integer into several different addition combinations.

比如数字3，有3，1+1+1，1+2三种组合方式。

数字4，有1+1+1+1，1+1+2，1+3，2+2，4，一共五种拆分方式。

Then suppose there is a function p(n), which represents how many ways a certain number n can be split.

Obviously,

P(3)=3

P(4)=5

What Ramanujan and Hardy want to do is to find the expression of this integer split function p(n).

Does it sound as simple and easy to understand as Fermat's last theorem and Goldbach's conjecture?

But it is quite difficult to get the function P(n).

Because the divergence speed of this function is very scary. Even though the first few items are very small and harmless to humans and animals, when it reaches p(50), it reaches 204226.

And p(100) is about 2 million!

Clearly exponential growth.

The first person to study integer splitting was Euler, the god of mathematics, but he failed to do it.

Ramanujan somehow wrote an approximate formula of p(n). The key is that the larger n is, the more accurate it will be. It is difficult to say that it was made up casually.

Littlewood put a pile of materials on the table: "This is Professor McMahon's calculation. We can verify it slowly."

Then he said to Ramanujan: "I really want to know how you got this weird result, but I know you will definitely say it was the instructions of the goddess, just like Joan of Arc in France said, 'I Locking myself in a small attic for a day and a night, God told me that I would become a general in the kingdom of heaven and lead the French army to drive out the British."

Hardy said: "This is the mysterious Eastern power."

"It's really too mysterious," Littlewood said. "According to the usual mathematical logic, once we know the result in advance, we can spend time slowly finding the correct form of the function. But the key is, how does Ramanujan know that there will be A correct form? He even gave a very good formula! If explained by theoretical insights, his ability is hard to believe! Because for the integer split function, no numerical results can give him such a strong hint The conclusion. I can only say it is a stroke of genius."

Hardy laughed loudly: "I have given up thinking about this problem! Why not continue to verify it."

The integer splitting function diverges very quickly, and Professor McMahon had previously calculated the first 200 P(n) values ​​by hand through Euler's early work.

Perseverance is also strong enough.

The first thing Ramanujan and Hardy had to do was to verify the accuracy of the formula given by Ramanujan, and just use McMahon's data.

The results are quite encouraging and the approximation is very good.

Poor McMahon was simply struck by dimensionality reduction.

打个比方，之前他是通过1000 001个29相加来计算29+29+29+…，得到了结果29 000 029。

Now Ramanujan and Hardy multiply directly to calculate 29×1000001.

However, the specific process is definitely more complicated and uses a lot of modern mathematics results.

Some people find number theory boring, but those who like it really like it and love it to their core.