***
From that day on, I shut myself in my room, deep in thought.
I read my worn-out magic space book thoroughly, trying to absorb every bit, but I still couldn’t decide what kind of magic to present.
In truth, the best way to gain recognition in a magic presentation contest is to showcase a new spell.
However, there’s a big problem with that.
And that is… to demonstrate a new spell, I’d need a completely new mathematical formula!
Magic in this world is fundamentally based on mathematics, so this was only natural.
But how on earth was I supposed to come up with a new mathematical formula? If I could do that, wouldn’t I have already been working in a math research institute in my previous life? I might even have won a Fields Medal* by now.
No, I must keep my hopes up. Perhaps there’s a slight difference between the mathematics in this world and the one I knew. I could use something that hasn’t been introduced here yet.
Let’s see… What would work best? What kind of mathematics is usually used in novels?
“Aha! This is called zero!”
Damn it! That’s not going to work! If zero didn’t exist in this world, all the magic and everything else would’ve already been in chaos!
“Aha! This is called the multiplication table!”
“Aha! This is known as the Pythagorean theorem!”
Of course, these won’t work either. I realized that most fundamental theories had already been presented.
‘Wait, hold on…’
Great! I just got a brilliant idea!
How about proving existing theories in a simpler way?
For example, proving that 1+1=2 could be straightforward, and perhaps it hasn’t been officially presented yet in this era.
The way to prove 1+1=2 is as follows. First, we need to define natural numbers using *Peano’s axioms:
1. 1 is a natural number.
2. If \( n \) is a natural number, then \( n’ \) (the successor of \( n \)) is also a natural number.
3. There is no natural number \( n \) such that \( n’ = 1 \).
4. If \( m’ = n’ \), then \( m = n \).
5. If \( P(1) \) is true, and \( P(k) \) implies \( P(k’) \), then \( P \) is true for all natural numbers.
Next, we define addition:
1) For any natural number \( n \), \( n + 1 = n’ \).
2) For any natural numbers \( n \) and \( m \),
\( n + m’ = (n + m)’ \).
Therefore, according to the definition of addition, \( 1 + 1 = 1′ \), and by Peano’s axioms, \( 1′ = 2 \).
Hence, we can conclude that 1+1=2….
‘Oh no, at this rate, people are going to get bored and lose interest!’
To summarize, I might be able to prove that 1+1=2 in a simplified way!
So, I asked Ghieuspe about the proof for 1+1.
“Are you referring to Peano’s axioms?”
“Darn! It already exists here!”
This cursed world had academic progress exactly matching my previous one! I knew this, but to be confronted with it again was frustrating!
And so, my grand “Aha, 1+1 equals 2!”—”Wow! Amazing! 1+1 is 2!”—”Genius!” strategy failed miserably.
“So, what exactly am I supposed to prove?”
Am I expected to tackle a Millennium Problem? Prove the Riemann Hypothesis? Solve the Yang-Mills mass gap conjecture? If I knew how to do that, would I be a fantasy writer—or, rather, an average math instructor? I’d already have a Fields Medal, my biography in history books, and countless handshakes from admirers around the world!
But if I were to say something like, ‘I have solved the Riemann Hypothesis but lack the space to write it all out,’ I’d be ridiculed!
As I sat there with a gloomy expression, Ghieuspe, noticing my troubled look, spoke up.
“Seraphina, there’s no need to put so much pressure on yourself. You’re already a talented mage.”
“But I don’t think I can create a new spell.”
“That’s naturally difficult. Just presenting an existing spell skillfully is more than enough. Spatial mages are rare.”
Yet, I didn’t want to be recognized just because of this lucky talent for spatial magic. I wanted to achieve something through my own efforts!
“What should I do….”
As I was idly scribbling math formulas to pass the time, none other than Arkhangelo came to see me.
“Hmph, you look stupid.”
“Arkhangelo… Why are you here?”
“You say that like I’m not supposed to be here!”
“Well, this is a lady’s room after all. Normally, it’s not a place you’re supposed to be.”
“…Don’t win by stating facts so bluntly!”
After muttering nonsense, Arkhangelo sat in the chair across from me, slouching comfortably. He then began speaking.
“What’s got you so troubled? You’re already an exceptional mage. Why not just show the abilities you already have? It seems like you’re overthinking this in front of someone like me who doesn’t even have any magical talent.”
“But I want to show something more impressive. It doesn’t feel good to be looked down on.”
“Hmph, whatever the reason, those who look down on others are in the wrong.”
Surprisingly, Arkhangelo began saying something sensible.
“Whether you’re full of magical talent or not, no one has the right to belittle you! They’re only trying to hold you back because you’re aligned with the First Prince.”
“That’s… true.”
“No one has the right to disregard you because of your magical skills. Even if you weren’t an outstanding mage, you still deserve respect!”
“Arkhangelo…”
As I looked at him, touched by his words, he delivered his final line.
“Because you’re a friend of the great me!”
“Oh, uh… sure…”
Although his final words ruined the mood a bit, Arkhangelo’s advice was still somewhat helpful.
“Have confidence in yourself.”
Right, as Arkhangelo suggested, maybe I had been lacking in self-confidence. But even realizing that, it wasn’t easy to act with confidence.
“How can you be so confident, Arkhangelo?”
When I asked him, looking into his fiery red eyes, Arkhangelo tilted his head and answered in a relaxed tone.
“Hmph, I have never had any doubts about my self-confidence…”
“But when you fought those bandits… Ah, though you did recover quickly then too.”
“Yes, I love my opera singing, and therefore, I love the person singing it—me. Whenever my confidence wanes, I just think about my opera.”
“Hmm, I think I understand what you mean.”
Back in my previous world, I was respected as a top instructor by many people. Even now, in this world, my core self hasn’t changed. Maybe I just need to regard myself highly here too.
But…
“What are you afraid of?”
Arkhangelo looked me straight in the eye as he asked.
“What is it that makes you lack confidence?”
“…I’m afraid of making mistakes and being laughed at. I’m afraid of being criticized and dismissed. I’m also afraid of being left out.”
Mathematics was something I had learned gradually over my entire life in my previous world.
But here, learning and adapting to magic so quickly made me afraid of making mistakes.
“Then it’s important to change your mindset.”
“How?”
“What does it matter if you make mistakes? What’s the big deal if people criticize you? They can’t do anything to you.”
“But if my reputation falls, it bothers me, and I get scared of how I’ll be seen.”
When I was teaching, my students rated me.
★★★★★
I moved up from level 2 to level 1!
★
Lacks humor—Megalodon’s Mr. Kim Math seems more fun.
Though I was in a teaching position, I was still someone who was evaluated by others. Maybe that shaped my personality this way.
“Remember, no matter what, they can’t actually change anything about you.”
As he said this, Arkhangelo looked at me with a gaze that was firm, lacking his usual sharpness, but filled with strong conviction.
“No one can influence your inner self. Only you can change your inner self. No matter what external events may try to shake you, you will remain unchanged.”
“I’m the only one who can change myself….”
🍓;
*Fields Medal is one of the most prestigious awards in mathematics, often considered the equivalent of a Nobel Prize in the field. Established in 1936 and awarded every four years, it recognizes outstanding achievements in mathematics and is given to up to four mathematicians under the age of 40.
*Peano’s Axioms, also known as the Peano Postulates, are a set of foundational principles for the natural numbers (0, 1, 2, …). They were formulated by the Italian mathematician Giuseppe Peano in 1889. These axioms define the arithmetic properties of natural numbers in a formal logical framework, providing a basis for number theory.
*Riemann Hypothesis is one of the most famous unsolved problems in mathematics. It is a conjecture related to the distribution of prime numbers, proposed by Bernhard Riemann in 1859. The hypothesis is part of the Millennium Prize Problems, meaning a correct proof or disproof would earn a $1 million prize from the Clay Mathematics Institute.
*Yang-Mills Mass Gap Conjecture is a central open problem in theoretical physics and mathematics, specifically in the study of quantum field theory. It is one of the seven Millennium Prize Problems posed by the Clay Mathematics Institute, with a reward of $1 million for a correct solution.
