I Am the Crown Prince in France

Early winter of 1787, East Palace of Versailles.

The young man was sitting in a room covered with rococo-style golden decorations and large oil paintings, shaking his head and smiling bitterly at the test paper in front of him.

The candlelight of the luxurious crystal chandelier with a diameter of two meters dances, reflecting on his fair skin and young and delicate facial features, making him look like the handsome Paris in the oil painting.

Beside him, an old man with a white curly wig and a lace scarf sighed. Disappointment flashed in his brown eyes. He leaned over and said to him: Your Highness, if you find it difficult, maybe you can learn the basic course first. …”

The young man who was called the Crown Prince was startled, and immediately recovered from his fugue. He nodded politely to the old man:

Mr. Lagrange, I think you may have made a mistake. I meant the graduation examination for your course, not the entrance examination.

Yes, this little old man with an unattractive appearance is the founder of analytical mechanics, the pioneer of group theory, and the famous French mathematician and physicist known as the Prince of Mathematics - Lagrange.

Graduation assessment? Lagrange frowned and looked at the thirteen-year-old boy in front of him, Your Highness, I teach university courses. You are afraid...

The richly dressed aristocratic young men around him who were answering papers immediately turned their heads and looked over, their eyes full of curiosity.

At this time, there was a young man about sixteen years old, wearing a silk coat with a lace collar, a look of disdain, and said loudly:

His Royal Highness the Dauphin, I remember that you should have two years to complete the basic course. He nodded to the old man, Mr. Lagrange often said that the ladder of mathematics must be climbed step by step. If you aim too high, you will fall and break your head. Blood flow. I think His Royal Highness the Crown Prince should also remember this motto.

The young man ignored him and said seriously to Lagrange:

Sir, I have studied college mathematics courses by myself. I really need to take the graduation exam.

The old mathematician sighed helplessly, turned to his assistant and said, Andre, please bring the exam paper at the bottom of my book folder.

Okay, Professor.

Soon, several test papers were placed in front of the young man.

He quickly browsed through it and found that the difficulty had increased several times compared to the previous one, but most of it was still at the high school level of later generations, involving a small amount of calculus content, and it was really not difficult for him.

Yes, more than half a month ago, he was still in the second year of graduate school in the 21st century. That day, he went to France with his tutor to work on a wind turbine project. He accidentally fell from the top of the tower. When he woke up, he found that he was dressed as the eldest son of King Louis XVI of France. , Louis Joseph. Perhaps due to the influence of time travel, Joseph was born a few years earlier than in history, and was already thirteen years old at this time.

Under Lagrange's scrutinizing gaze, Joseph quickly wrote the answer to the first question, but he was thinking about the historical direction of France: next year the French Revolution will break out, and the entire royal family will be destroyed. As the king, he The prince will definitely not be able to escape... King Louis XVI knows nothing but repairing locks. France owes more than 2 billion in foreign debt, but its annual income is only 500 million.

Due to the financial collapse, civil servants were not paid their salaries, the daily operations of the government were difficult, foreign trade was stagnant, and the colonies were declining day by day. In order to replenish the finances, the cabinet had to increase taxes massively, which almost sucked the bones out of the people at the bottom, while the nobles with tax-free rights spent their money like water and drank and drank meat all day long.

In addition, France will encounter severe hailstorms next summer, and coupled with the effects of drought in previous years, a nationwide famine will occur. Next came the riots of hungry people, the dungeon of the Bastille, the opening of the Da Ge Ming expansion pack, the country was in turmoil, and hundreds of thousands of people were guillotined...

Therefore, if he wanted to save his head, he counted on his fingers: first, he had to solve France's financial deficit; second, he had to get enough food to avoid starving to death; third, he had to deal with the nobles with evil intentions; finally, he had to deal with The British and Prussians were eyeing him.

The famine would begin in July, leaving him with only a little more than half a year. He rubbed his forehead irritably, because he was young and could not get involved in state affairs, so he had nothing to do with his energy.

It's a completely hellish start, with little chance of survival...

Not far away, the stern young man saw his actions and thought he was worried because he couldn't do the questions. He immediately snorted with disdain: This idiot came to say that he knew how to take college courses. It was simply embarrassing. ! Why is this idiot the crown prince, but I am not? !

While thinking about how to save his life, Joseph quickly wrote the answers and quickly completed the first page of the test paper.

He turned the pages impatiently. If he passed Lagrange's exam, he would have completed his studies at the University of Paris!

More than half a month ago, he proposed to Queen Mary, his cheap mother, that he should join politics in an attempt to reverse the situation of certain death, but the latter politely refused, asking him to rest his studies and wait until he was successful.

So he had to make an agreement with the queen to officially participate in politics after he completed his courses at the University of Paris.

Of course, with his level, he is a fighter among top academics in this era. In the past half month, he had completed most of the subjects, but this was due to the delay in memorizing wrong knowledge - much of the knowledge that is regarded as truth in this era is actually fallacy.

Lagrange watched the Crown Prince writing quickly, no longer paying attention to the other students, and his eyes widened.

This is a question that requires five years of study at the University of Paris to complete. The Crown Prince answered it effortlessly and with clear thinking. One correct answer!

He is only 13 years old and he is self-taught! Lagrange was shocked. Could it be that another Leibniz was born?

Lagrange suddenly glanced at his assistant, his eyes narrowed slightly, wondering if André had missed the question for the Crown Prince? After all, the crown prince behaved too strangely. You know, a super prodigy like Leibniz did not start college until he was 14 years old.

He immediately took out a pen and paper, wrote down a few lines, handed it to Joseph and said:

Your Highness, you don't need to do the rest. As long as you complete these questions, I will consider you to have passed.

Seeing this, the young boy with stern eyes sneered secretly: Ha, Lagrange is just trying to see if he doesn't know how to do it, are you going to let him go? Idiot who clings to the royal family! I'll have to find a way to show everyone the Crown Prince's exam papers later and make him look embarrassed.

Joseph looked at the paper in surprise. There were only 5 questions. The difficulty had not changed, but the number of questions had decreased. Good thing.

He quickly finished the first two questions and saw that the third question was Please write the proof process of Rolle's theorem. He was very familiar with this and wrote in the blank space without thinking:

Rolle's theorem, let f be continuous in the closed interval [a, b] and continuous in the open interval (a, b). If f (a) = f (b), then at least in the open interval (a, b) There is a point where the value of its derivative function is zero.

Proof: Because the function f(x) is continuous within [a, b], the maximum value (M) and minimum value (m) obtained in the closed interval...

Joseph finished writing in a few seconds, but suddenly he felt that Lagrange next to him was breathing rapidly. He looked up quickly and saw that the old mathematician looked excited and stared at the exam paper as if he had seen his first love.

Joseph immediately lowered his head and scanned the question, and hesitated: I shouldn't have written it wrong, right?

Lagrange grabbed the test paper, read the proof process carefully several times, and murmured: It turns out that it is also true for differentiable functions! Why didn't I think of it?

He looked at Joseph again, his eyes as hot as fire: Your Highness, how did you come up with this idea?

Ah? Isn't it... Joseph suddenly remembered that Rolle simply proved that between two adjacent real roots of a polynomial equation, the equation has at least one root. It was not until the 19th century that anyone generalized it to a feasible level. Microfunction category.

I was careless and didn't flash...

Ahem! He quickly took back the test paper and changed the subject, Mr. Lagrange, I'm going to do the next two questions.

The new book has set sail. I beg you to collect it and comment. Please give me your support. Tianhaishan is grateful!