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“This thesis…”
Lord Percival didn’t finish reading. In fact, the mont he saw the title and the author, he had already guessed much.
He had thoroughly read this thesis by Sirius ten years ago, during a seminar suggested by his ntor, Bodoro.
Percival still rembered that afternoon. The first ti he read the thesis, he felt an electrical current running through him. He couldn’t believe that Sirius, soone his own age, had reached such heights.
While their peers were still worrying about dinner and tomorrow’s weather, Sirius had already set his sights on the distant stars.
However, this thesis had a fatal flaw: Sirius had introduced imaginary numbers.
Undoubtedly, imaginary numbers did not exist in the real world. They were purely conceptual, difficult to understand, and had no real-world application.
At that seminar, Bodoro had expressed the sa opinion. Despite the thesis’s elegant and concise formulas, they were aningless.
Now, Percival couldn’t believe that this thesis had resurfaced before him.
Another discussion eting, another young and talented mage presenting it. Percival felt a sense of déjà vu.
As Percival was lost in thought, Roger had already finished reading the thesis.
He put it down and spoke.
“Absurd, absolutely ridiculous!”
Clearly, he also didn’t believe in the existence of imaginary numbers and thought it was pure imagination.
“Imaginary numbers? Square root of -1? What was the author thinking?”
As Roger spoke, the others also finished reading the thesis.
Bel remained silent. His mathematical skills were lacking, so he refrained from comnting.
Hannah glanced at Percival before speaking.
“This is a purely mathematical thesis. The concepts seem forcibly created to solve problems. Honestly, I don’t see the point of imaginary numbers.”
Igor, after hearing the others’ comnts, glanced at Reiner and spoke slowly.
“Uh, I think this thesis might be better reviewed by a mage specializing in this field. So of the mathematical concepts are beyond my knowledge.”
Savros shook his head, keeping his thoughts to himself.
Seeing everyone’s reactions, Reiner was prepared.
Ten years ago, no one could accept the existence of imaginary numbers. How could people’s views change so easily ten years later?
He stood up and spoke,
“Everyone, you must be puzzled by the imaginary numbers in this thesis, thinking they are aningless in the real world.”
“Aren’t they?” Roger retorted sarcastically. “If I have one apple, that’s normal and reasonable. But if I say I have i apples, what exactly do I have in my hand, Reiner? Can you show ?”
He used a very realistic example, earning a nod from Hannah beside him.
“Of course, I can’t show you, Lord Roger.” Reiner replied calmly to Roger’s near-mocking question.
“A number that cannot exist in reality is aningless. Even if the theory of imaginary numbers is complete, it’s just a calculation on paper. How does it relate to our real lives?”
Roger continued, seeking agreent from others. “The reason not many invest ti in pure mathematics is not just the lack of real-world feedback, but because pure number gas can easily beco aningless theories like imaginary numbers, becoming mathematics for mathematics’ sake.”
His words made everyone ponder. Indeed, if a theory couldn’t be applied to practice, no matter how ingenious and sophisticated, it was useless. The developnt of magic has always been about solving real problems, not exploring knowledge without practical significance.
This was exactly the pragmatism of the mage, a matter of efficiency.
Everyone looked at Reiner, waiting for his explanation.
“Lord Roger, I think I need to educate you on mathematics.” [1]
Reiner walked to the blackboard and picked up a piece of chalk.
“W-What did you say?” Roger was angered by Reiner’s attitude and wanted to stand up, but his reason restrained him.
Reiner smiled and drew a horizontal line on the blackboard, adding an arrow.
“This is a number line we often use in mathematics. Now, I’ll mark three points: -1, 0, and 1. These are integers and negative numbers, the most basic concepts even six year olds know.”
The Thesis Review Committee mbers watched as Reiner continued to mark the number line, adding 0.5 between 0 and 1.
“Integers can’t fill the entire x-axis because there are also decimals. Between 0 and 1, there are countless decimals. But even then, the number line isn’t filled.”
Reiner drew a square and its diagonals.
“The square root of 2, an irrational number, also exists on the number line. By now, rational and irrational numbers have filled the number line.”
After hearing Reiner, Roger spoke.
“If the number line is full, where do imaginary numbers fit? Aren’t they on this board?”
He intended to mock Reiner, but Reiner unexpectedly nodded.
“Imaginary numbers don’t fit on this line, but they at least exist on this board.”
“What?”
Even Percival questioned, looking at the number line again. Rational and irrational numbers filled it completely, leaving no place for imaginary numbers.
“Imaginary numbers exist here.”
Reiner marked a point above 0 on the number line.
“Are you kidding !?”
Roger stood up, thinking Reiner was mocking him, ready to confront the young mage, but Bel stopped him.
“Let’s hear him out, Roger.”
Bel sensed sothing and looked at Reiner.
“The imaginary number i is one unit above the origin.”
Reiner’s words seed strange, but Igor quickly realized it. In his mind, the number line shrank, and the entire blackboard appeared in his eyes.
“Yes, a single number line can’t represent all points on a plane, but adding another axis creates a coordinate system to represent all points.”
Igor realized the Cartesian coordinate system was already widely accepted. People had long accepted using two numbers to represent a point’s coordinates. The existence of imaginary numbers was akin to adding an additional axis, expanding the world a hundred tis!
Such a simple concept, yet none of the mid-level mages present had thought of it before Reiner’s demonstration.
Their imagination limited their knowledge!
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T/N:
[1] Burn
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