Starlight stared at Twilight for a good ten seconds, trying to process what she had just said. "So... you've spent ... half of your life... trying to divide by zero?"
Twilight blushed and looked away. "Well it isn't really half my life. I've taken cracks at it whenever I have time or if I just feel like challenging myself, but most days I forget about it entirely."
Starlight rolled her eyes. "I'm going to be completely honest here. If I was in your position, I would have just given up the moment I reached that conclusion. "
Starlight was then forced to backpedal as Twilight once again teleported directly in her face. "But don't you see?! That's the idea! If I could reconstruct the process of creating a base spell and publish the results. The awards! The fame! I might even become a prin-"
Twilight quickly caught herself and blushed. "Hehe, sorry about that Starlight, just got caught up again in the moment." She sat on her haunches before unfurling her right wing and staring at it. "A very old moment..."
Starlight cleared her throat to break the silence before it became any more awkward. "Ahem anyway so about your project..."
Twilight shook her head a little to clear her thoughts. "Right, sorry. I've tried almost everything I could think of! At first, I thought I could just skip the last step all together and cast the construction matrix by itself."
In a bright flash, she teleported to the other side of the room and gestured with a hoof to the surrounding walls and floor. "You can tell how well that went."
Starlight glanced around the room again, paying much closer attention to detail, and did a double take upon noticing that what she had initially thought were intricate wall and floor patterns looked very similar to char marks from an explosion. She cast a basic scanning spell on the room and blanched at the results. Two of the crystal walls and parts of the ceiling had been magically regrown in the last hour.
Starlight turned back to Twilight with a confused expression. "Wait, I'm sensing that you magically repaired the room, so why are there still so many scorch marks?"
Twilight laughed nervously, her wings twitching ever so slightly. "Yeaahhh about those. Let's just say that those are from ONLY my last attempt. I've been at this for four hours already."
Starlight's jaw dropped. That's a lot of damage. "Why are you suddenly so obsessed with this?! In all the time I've known you, I've never seen you spend so much time on one task before on..." She thought a little more about what she had just said. "Forget I said that. What I meant to say is that whenever you got obssessed over something, it was because of some new and sudden development, like when we found Starswirl's old journal, or that one time you told me about when you thought Celestia was going to give you some big test but ended up just sending you to the Crystal Empire to deal with Sombra. Why did this come up just now?"
Twilight turned away and muttered under her breath. "I don't know about obsessing, but..."
"Whatever you say."
Twilight rolled her eyes. "To answer your first question, Spike and I were almost done reshelving the castle library yestersay afternoon when he came across one of the journals I used to keep as a filly. Most of it were just notes from Celestia's lectures during my time as her student, bu-"
"Wait, Celestia actually taught you herself?!" Starlight interjected, trying to form the image in her mind of the solar diarch standing in front of a chalkboard with a pointer stick in hoof. She failed. "I mean, I knew you were her 'personal protégé', but I always thought it was a metaphor for you being the valedictorian."
Twilight giggled briefly to herself before continuing. "Yes, Starlight, Celestia was my teacher, what did you think? That's not the whole truth though; even as her personal protégé, I still attended classes with the other ponies at CSGU, but those were just for subjects like math, history, and Ponish. I also took my General Education classes later on with everypony else, but every Tuesday I would have weekly sessions with the princess for advanced magic exploration. But yeah it also meant I was technically the valedictorian."
A thought came to Starlight. "Did you ever try asking the princess for help?"
"I did." Twilight groaned in exasperation. She trotted back to her desk and sat down. "Every. Single. Week. She just kept chuckling and telling me that, while it was nice that I was trying to go beyond expectations, that she was already proud of me and to not be blinded by my ambitions. Now that I think of it, she always seemed a little sad every time she told me that."
Starlight followed Twilight to her desk and sat down on the ground next to her. She put a hoof to her chin in thought. "What if you didn't need to blatantly divide by zero?"
Twilight glanced at Starlight in confusion. "What do you mean? "
"I'm saying what if you just figure out what the value is going to be instead of what it is straightforward?" Starlight trotted over to one of the nearby bookshelves, scanned the titles of the top row, and levitated out a thick, dusty tome. She started for Twilight with it in tow. "You can just plot out the function for the total magic divided by a number. If you track the value of the function as that number approaches zero, you might be able to calculate the-"
"Limit?" Without even throwing a glance behind her, Twilight lit her horn and snatched the book out of Starlight's magic aura, opening it and turning precisely to the third chapter before promptly shoving it back into Starlight's face. "Yes, I've studied singlevariable Hoofulus years ago, Starlight. Oh how I wish it was just as simple as that!"
Twilight leaned in her seat until she could rest her head on the desk. Her magic cut off, letting the book fall onto Starlight's face. "The function's behavior matches that of a normal inverse function, since it's basically a constant divided by a number. But if you try taking the limit as that number approaches zero, it just keeps going without bounds! It doesnt exist!"
An irritated Starlight levitated the heavy book off her face before teleporting it into one of the Dragonland's many active volcanos. "What about a reverse sequence? "
Twilight threw her hooves up in annoyance. "Yes I tried a sequence! The stupid thing just ended up diverging. I though of trying a series as well out of desperation, but then I remembered that because of the nonexistent limit, it would have ended up diverging as well because of the divergence test."
"The what?"
Confused, Twilight looked at Starlight, who in turn looked away in embarrassment. "You don't know about testing for divergence in series? Which university did you go to?"
Starlight blushed. "I never went to any. After high school i told my dad that I was going on a journey of self-discovery, then spent the next few years researching and experimenting with my unmarking spell, developing my... erm... ideology, and creating the foundations for my village."
Now it was Twilight's turn to drop her jaw. "Are you serious?! But your magic is so powerful! Did you ever have some sort of professional magic teacher during high school?!"
"Nope, none at all." Starlight shrugged and lit her horn. Twilight felt the surrounding air getting dryer and dryer until, to her astonishment, a strange sort of mist became visible in front of Starlight. After a few seconds, the mist had coalesced into a small ball of water about the size of her eye. "I should probably rephrase something I said earlier. Whenever I've said how long I've studied magic, I meant that's how long I've PRACTICED it. Magic always felt natural to me; as long as I knew what I wanted to do, I could figure out how to do it. When I was younger my biggest problem was really just knowing the solution. Sunburst would always come up with solutions for me that I could implement in the blink of an eye."
Starlight's horn grew a few lumens brighter, and the ball of water slowly morphed and froze into a solid block of ice. It rose higher and higher until it reached the ceiling, where it burst into a minute flurry of snow. "To do this, you would probably research individual spells and determine what order to cast them, then experiment until you succeed. I simply... do it. I don't worry about the specifics of how it works and just trust my magic and my emotions to work together with what I'm trying to accomplish. As long as it's nothing too complicated, like my unmarking spell."
Starlight then looked Twilight dead in the eye. "Maybe you it's impossible to approach this problem through math. Maybe you can use magic to solve it. Based on what I can read from your loose paper, you've only been attempting mathematical approaches, then magically implementing the last step."
"Hmmmmm that could work." Twilight pondered the idea in her head for a few seconds. "Well if you think it's worth a shot, we could... maybe..."
A look of horror flashed on Twilight's face. Starlight cocked her head in confusion. "We could... what? Is something wrong?"
With a flash of light, a small clock materialized in front of Twilight, confirming her fears. "No no no no no no no no no no I was so focused on this problem that I completely lost track of time! I was supposed to start teaching another history lecture ten minutes ago!"
Twilight quickly disappeared in burst of magic, leaving Starlight to awkwardly stand by herself before she reappeared in front of her. "I'm really sorry, I'll talk more about this with you tomorrow if you want. Anyways I have to go. I'll see you at the castle tonight!!"
With one final mini explosion, Twilight teleported to the school. Starlight glanced around the room at the all the scorch marks before turning to leave.
Impossible, you say?
Starlight paused mid-trot right outside the room and turned to face the desk once more. She lit her horn and all the scattered paper and books glowed in an identical light before neatly stacking themselves on the desk.
Not if I have anything to do about it.
Starlight took one last glance around the hallway for any prying ponies. Satsfied, she turned back to the room and trotted inside. The door was wrapped with a light teal light before slowly closing behind the unicorn.