I am the prince of France

Early winter of 1787, East Palace of Versailles.

The young man sat in a room filled with rococo-style golden decorations and large oil paintings. He looked at the test paper in front of him, shook his head and smiled bitterly.

The candlelight of the luxurious crystal chandelier with a diameter of two meters danced, 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 wearing 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 courses first." ..."

The young man known as the prince was stunned and immediately came back from his fugue. He nodded politely to the old man:

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

Yes, this ugly little old man 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 college courses, and you are scared..."

The richly dressed aristocratic young people around them who were answering their papers suddenly 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, with a disdainful look on his face, and said loudly:

"Your Highness, 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 have high aspirations, He will fall down, break his head, and bleed. I think His Highness the Crown Prince should also remember this motto."

The young man ignored him and said seriously to Lagrange:

"Sir, I taught myself a college mathematics course and I really need to take the graduation exam."

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

"Okay, Professor."

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

He browsed it quickly and found that the difficulty had increased several times compared to before, but most of it was still at the high school level and involved a small amount of calculus, which was indeed not difficult. he.

Yes, more than half a month ago, he was still a second-year graduate student in the 21st Century. That day, he went to France with his mentor to work on a wind turbine project. He accidentally fell from the top of the tower. When he woke up, he found himself 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: The French Revolution will break out next year, and the entire royal family will be destroyed. As a king, his prince would definitely not be able to escape...King Louis XVI knew 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.

And the famine would start in July, leaving him 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. After passing Lagrange's subject, 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 want to join politics in an attempt to reverse the situation of certain death, but the latter rejected him neatly, asking him to rest his mind on his studies and wait until he was successful in his studies.

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 as fast as he could, no longer paying attention to the other students, his eyes widening.

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 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 man with stern eyes sneered secretly: Ha, Lagrange just wants to see that he can't do it, will you let him go? The idiot who clings to the royal family! Later, I have to find a way to show the prince's test paper to everyone and embarrass him.

Joseph looked at the paper in surprise. Only 5 questions. The difficulty has not changed, but the number of questions has decreased. nice one.

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 so familiar with this that he wrote in the margin 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 there is at least one point in the open interval (a,b) whose derivative function value 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 quickly looked up and saw the old mathematician looking excited, staring at the test paper, as if he was seeing 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 muttered: "It turns out that the same is 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 wasn't until the 19th century that anyone promoted it to a feasible level. Micro function class.

I wasn't careful and didn't dodge...

"Ahem!" He quickly took back the test paper and changed the subject: "Mr. Lagrange, let me do the next two questions."