Ella closed the book with mixed emotions.
In Archimedes' time, this was a mathematical message that no one could understand. So much so that the manuscript was purged and replaced by ignorant people with prayers.
However, the strong will remaining on the manuscript miraculously defeated time and finally came to Ella's hands safely.
Ella wiped away the tears that had filled her eyes for some time.
Then, she solemnly opened the door and stepped into the abyss.
"Come here, Infinite, I'm not afraid of you!" She shouted towards the abyss, "Give me a fulcrum and I can move the earth!"
Ella's voice angered the monster. Ella saw only a black mist rising upward from the abyss. That fierce
The monster was hidden in the black mist. Soon, from the abyss to the clouds, the entire world in front of him was covered with black mist.
There were countless eyes exposed in the black mist, all of them staring at Ella.
Ella looked down at the straw in her hand and shook her head.
"This kind of thing cannot be measured to infinity."
She dropped the straw on the ground. At the same time, a series of formulas appeared. They shone faintly in the black mist, swirling around her—that was all the mathematics Ella had mastered so far. They protected her from the darkness of the mist.
Ella stretched out a hand towards the black mist and chanted like magic: "Pythagoras' theorem."
A string of glowing formulas shot towards the black mist. After an explosive collision, the black mist became thicker and thicker. The thing in the black mist hit the land where Ella was. The earth shattered into pieces as it trembled, and Ella lost her footing and plummeted toward the abyss.
Ella stared at the countless eyes in the black mist and stretched out her hand in the air again.
"I'm not the only one challenging you!" she shouted. "Try this—Archimedes' integral method!"
The mathematical knowledge from Archimedes' manuscript shines with dazzling light and flies into the black mist. Amid the explosion, an almost blinding flash of light shone between heaven and earth.
The black mist was dispelled, and the monster showed its shape in front of Ella: it was as black as a ball of liquid; it was so huge that it even topped the sky; it was covered with eyes, Ears, and tentacle-like arms all over the body. It is infinite, and people know nothing about it.
The disappearance of the black mist made it furious. It stretched out its tentacles, rolled up Ella in the air, and lifted her into the air. Ella was completely unable to withstand its anger. With only a slight twist of its tentacles, Ella's already fragmented spirit body was shattered again. With red eyes, Ella relied on her will to forcibly reunite the fragments into shape, but was bound by its tentacles again.
In the intense pain of being on the verge of disappearing, Ella bit the sticky tentacle hard.
"Knowledge from Mr. Gottfried - the formula for the sum of squares of infinite polynomials!"
The tentacles exploded, and Ella fell from the air to the ground. This further aroused the monster's anger, and with an almost crazy scream, its entire body pressed toward the ground where Ella was like an overwhelming force.
Just the sum of squares formula is not enough. After using the exhaustion method to convert the integral into an equation, an infinite series with various powers appears. The sum of squares formula only addresses the tip of the iceberg.
Unless... beyond the sum of squares formula.
In Ella's mind, a series of mathematical proofs were going on rapidly. Before the monster crushed the entire earth, Ella stretched out her hand with difficulty.
Taking the formula of the sum of squares of infinite polynomials as a special case, we get a more general formula for the sum of positive integer powers!
"This is the most powerful attack I can use,"
After a sudden crash, a light that was more dazzling than any previous formula flashed out. Under the illumination of this light, the huge monster melted like an iceberg.
Ella laughed hard. She had used all her wits to deal with the monster.
However, before she could get up, the crazy screams suddenly came from all directions!
Ella only felt cold all over. She watched in horror as points poured out from every direction, from the front, back, left, and right, surrounding it like a cage. It turned out that the huge monster before was just a small part of its body.
Nothing is left, the whole world is surrounded by this dark monster.
Ella cried. There was really nothing she could do.
"God of Wisdom... If you really exist, if infinity can really be measured, then please show me a way."
This plea is meaningless. The god of wisdom is Hermes in the magic system of the Seven Hills Empire. But as far as Ella knows, Hermes' wisdom is completely reflected in alchemy. That "Jade Record", the top comes from the bottom, the bottom comes from the top, etc., has nothing to do with mathematics.
"The bottom comes from the top, and the top comes from the bottom?"
Ella suddenly realized something. Use countless shapes to approximate the curve and calculate the sum of the areas of these infinite shapes. This area summation operation performed in an infinite number of fields was affectionately called 'integral' by Gottfried - which is the name of the monster in front of him.
If the integral belongs to "upper", then what should the corresponding "lower" be?
--differential.
In the void, the stone slab engraved with "Jade Record" emerged. A voice like a god solemnly read out the words in "The Jade Record":
——"This is the unquestionable truth"
——"The superior comes from the lower realm, and the inferior comes from the upper realm. The creation of miracles originates from one, just as all things are born from one and ruled by one."
Ella looked up at the monster that blocked the sky, and then looked at the inconspicuous differential at hand - it was lying quietly in the corner of a pile of mathematical formulas, glowing dimly.
The upper ones originate from the lower world, and the lower ones originate from the upper world. Could it be said that integral comes from differential and differential comes from integral?
She grasped it tentatively.
——“Rising from the earth to the sky, and descending from the sky to the earth.”
——"Thus, gain the power of the Supreme and the Low."
——"In this way, you can get the light within the light and escape from the darkness and ignorance."
In the reading of "Jade Record", a great god-like formula showed its shape between heaven and earth:
∫????f(x)dx=F(b)-F(a)
At that moment, the entire space was filled with light, as if a thousand suns had risen!
——"It can conquer all subtleties and drive away all roughness."
——"This is how the world was created, and it will be incredibly changed from then on. And this is the way."
The infinite monster screamed, deformed and shrank under the same infinite light, and finally turned into a lake. Although it is still wide, it is no longer the monster that covered the sky and the sun before.
And the reading continued:
——"I am the triple great Hermes, for I possess the wisdom of the three parts of the world."
——"This is the great work of which I am speaking."
Barcelona's Restoration Diary
