The days of learning black magic in another world

Riemann is a little puzzled: "But we are constantly coming up with new mathematical theorems, and obviously this behavior is encouraged."

Heller scratched his head: "How is this the same? This is mathematics!"

Riemann: "Is there any difference between mathematics and the laws you want to prove?"

Heller gasped: "Of course it's different!"

"What's the difference?"

"This... this..." Heller scratched his head more frequently. He paced around with a tangled expression, as if Riemann asked some questions like "Why do you eat every day?"

He walked back and forth in the same place, and finally straightened out the logic: "Nature is the law that God has set for us. Since He has established such a law, we just need to believe it. It is an offense to God to doubt and wonder rashly. , mathematics is different, mathematics exists naturally, and the sages of the past have already studied mathematics to the extreme, but their achievements have not been preserved and have been lost in the inheritance from generation to generation. What we have to do is to find again It's something that the predecessors have already found."

"This is an inheritance rather than an offense to the sages, isn't it?"

Riemann: ...

Riemann was shocked. Although he also learned about the ideas of some medieval mathematicians when he was studying the history of mathematics in his previous life, he just watched the fun at the time and forgot after reading it. Now facing this self-deceiving idea, he This kind of person who can answer anything can't say the right words for a while.

He was silent for a long time, and finally patted Heller's shoulder: "I understand, but I think God is very magnanimous, and he shouldn't mind your offense. You see, three years have passed, and he hasn't sent down the holy light." To destroy you, you have to believe in God’s tolerance.”

Heller: "What you said makes sense... Forget it! Don't talk about it, Riemann, you are such a good person! I was still hesitating whether to invite you to my family's banquet tonight. This banquet is actually mine Entrance celebration banquet... I originally thought that uh... a super young genius like you must be very lonely. It would be too humiliating to invite you to this kind of banquet. After all, I am the Springs who bite the bullet College, my father actually wants to hold a banquet to celebrate, my God..."

Riemann now sees the stalwart halo of his own scientist. Although he feels that it is a bit troublesome to go to the banquet, he simply nodded and added a sincere consolation: "Brother Heller, don't underestimate yourself."

……

The mansion of the Velen family is very close to Springs College. Heller Velen simply invited Riemann to his house for lunch. As a disciple of Achill Monroe, Riemann was warmly received by General Velen. Terrible treat, he felt he was one step closer to tearing apart the teleportation scroll and teleporting to the Dark Forest.

Just after lunch, Heller was lazily lying on the sofa, but when he heard Riemann saying that he was going out to buy the latest "Mathematics and Physics" magazine, he woke up suddenly.

"The latest issue... Do you mean the one that Chester just kept telling you to follow the method above?"

Riemann nodded.

Heller gasped: "You mean you haven't seen it yet?!"

Riemann frowned at his volume: "Yes."

"My God, my God...you haven't watched it yet?! Then how dare you promise Chester!"

"Oh! Oh no, you are a genius, you must be able to write it right away, right?! I'll get it for you right now!"

The expression on Heller's face changed from messy to self-comforting. He roared and ran upstairs, and came down with two more magazines in his hand.

"This is from the last issue, and this is from the previous issue...To be honest, I didn't listen to Chester's speech at all, and I don't know which one it is, you can find it yourself..."

Riemann: "Thank you."

He flipped through the two magazines and glanced at them. Heller was standing next to him with folded hands and staring at him nervously, for fear that he would suddenly say something—"I don't think I should agree to Chester."

Fortunately, Riemann did not say such words that would cause him to have an instant myocardial infarction. The black-haired and black-eyed boy flipped through "Mathematics and Physics" at his own pace. His slender fingers paused for a long time on one of the pages. After a while, Only then did he raise his head and said to Heller, "Can you lend me a pen and two pieces of paper?"

Heller put down the half-gnawed finger, and then rushed upstairs to get the parchment and pen.

Riemann took the pen and paper from Heller and fell into deep thought.

The principle of the square root method proposed in this magazine is very simple, it is the binomial theorem, and then some computational labor, repeated approximation, if Riemann wants to complete the young man named Chester The task assigned to him is not difficult, but... the binomial theorem, he has other ideas.

Since he came to Wangcheng, although most of the time he has been busy upgrading, looking for materials, and fooling the little duke, he has not forgotten his plan to consolidate his status as a mathematician by means of calculus...

The problem is that he thought hard, but he didn't think of how to gradually let people of this era accept the idea of ​​calculus.Which undergraduate student is not told "when Δx approaches infinite hours..."

But people in this era still regard the concept of "infinity" as a scourge, and feel fear and headache when they think of infinity.

When he thought that the pale-faced Mr. Rochester was actually a student taught by the greatest mathematician of this era, and he also scoffed at Riemann's idea that the circle should be infinitely divided, Riemann felt that the task of promoting calculus was a bit difficult.

But the binomial theorem... to be exact, Newton's generalized binomial theorem...

Riemann felt that the fog in his mind had been cleared away. Anyone who has learned infinite series knows that some infinite series can be summed, that is, they are so-called convergent.

For example, "several commonly used Maclaurin formulas" that every advanced mathematics student should keep in mind.

Since I don't know how to play formulas in Jinjiang, here is only one of the best ones, which is also the most counter-intuitive at first glance:

e^x=1+x+x^2/2! +...+x^n/n! +... (x can be taken from negative infinity to positive infinity)

Don't get bogged down in the details, we just need to notice one shocking fact - infinite numbers add up to get an exact value!

What an amazing fact!

And for the mathematicians of this era, once Riemann laid it out and proved it, he could convince others that infinity can be conquered!It can be incorporated into the mathematical system and used in an open manner!

Thinking of this, Riemann felt a little enthusiasm for a while. Once the concept of infinity was accepted, would it be difficult to slowly throw out calculus?Wouldn't his troubles be easily solved?

So, he immediately started writing.

""On Some Properties of Sequences of Numbers I Call Infinite Series""

"From the square root method mentioned by Mr. Perrol in the last issue of "Mathematics", we can clearly see that..."

Wait a minute—Riemann stopped writing, as if it wasn't particularly obvious.

His thinking jumped from the square root method of this article to the binomial theorem to the generalized binomial theorem and finally to the series, but what he actually wanted to write was only the series, but he directly picked out the series It's too... Literally speaking, it's like an antelope hanging horns, making people wonder where his idea came from.

Riemann hesitated for a while with a pen, and finally decided to write down all this string of ideas.

"From the method of rooting mentioned by Mr. Perrol in the last issue of Mathematics, it is evident that...

"I call this the binomial theorem... When the case is generalized to the rational numbers...

"I call this the Generalized Binomial Theorem...Finally, it is evident that..."

Heller looked at Riemann's pen and paper, writing like flying, and immediately felt relieved.