Sugar, Cubedby BlazzingInfernoChaptersEarly Morning ChoresA Meeting of the Unsuspecting MindsLessons in NumbersTheory to ApplicationEarly Morning Chores“What’s Pa doing out there?” Applejack whispered. The view from the little filly’s bedroom window made no sense. Pa was standing in front of an apple tree without a barrel, a rake, or even a watering can. He just stared at the tree without bothering to buck the glistening, red apples off the branches. For minutes on end he’d stand there, only pausing on occasion to glance at a small book resting on his hoof. There was barely enough sunlight out there to work in, let alone read by. Nopony else would be up for a half hour. Her hoofsteps were nearly silent as she crossed the hallway. If she woke up Ma or Granny Smith this early, she’d never hear the end of it. Her big brother was a different story. She pushed open his door and approached the bed. “Hey, Big Mac.” The sleeping form under the covers didn’t move. “Big Mac!” Finally he stirred. “Huh? AJ?” “Pa’s doing something outside; looks mighty strange to me.” “Pa’s just being Pa, and you’re supposed to be in bed. Sun’s not up yet.” “But–” “Nope.” “I just–” “Nope.” She scowled. “Fine.” Her hoofsteps were equally noiseless as she made her way down the stairs, including the hop at the end to skip the creaky step. She couldn’t count the times Big Mac had put his full weight on the thing after being out late with his friends. Even if the groaning wood didn’t wake her up, the inevitable scolding from Ma certainly would. Soon she was standing outside and at the edge of the orchard. She crouched behind a tree trunk and watched Pa continue his strange ritual. He studied the nearest tree, once again without bucking even a single apple, and then consulted with his little book. From this perspective she could see the pencil he was holding in his mouth. Pa was the biggest stallion her young eyes had ever seen. The first time she saw him knock an apple out of a tree, she’d been sure the tree trunk would be the next thing to hit the ground. Seeing him standing here, still and silent with a book on his hoof, was like looking at another pony entirely. “You gonna hide back there all morning, AJ?” His voice was as deep as rolling thunder. She froze. Did he know she was there, or just suspect? Could she just take a few careful steps back and pretend she’d never left her room? It wasn’t worth trying, not when it meant lying to Pa. Instead she stepped out of her hiding place and hung her head. “Sorry, Pa. I know I’m not supposed to be out this early. I just wanted to see what you were doing.” He rolled the pencil between his lips. “What do you think I’m doing?” “Can’t say. You’ve just been staring at those trees, and reading… only why would you ever write in a book? Wouldn’t that ruin it?” “Why don’t you come on over here, and I’ll show you.” To her surprise the only text in the book was hoofwritten, and most of it was numbers. “What is this?” “Just take a look at this tree; tell me how many apples there are.” One glance at the tree was all she needed. “Ten.” “Right, and here’s the ten in my book.” She followed his gaze down the columns of numbers until she found a freshly drawn one and zero. “So you’re counting all the apples?” “Kinda, but there’s more than that. See, I’ve got numbers for how many apples each tree produced for nigh on thirty years. Same goes for the date they started producing, when they stopped, when the rainy season was…” “But why?” He flipped the pages until they reached the end. “Know how the pegasi give us a weather forecast?” “You mean like when they’re gonna make it rain?” “Right. Well, with all these numbers, I can give you an apple forecast.” “That’s just crazy talk. How can anypony know how many apples there’re gonna be in advance?” He tousled her mane. “Oh it’s not easy, Sugar, but it’s not crazy either. You just gotta track everything a tree cares about for enough seasons, then–” “Fifty-seven.” “Pardon?” She pointed to the last column on the page where he’d added up the crop yields for the last few trees. “You should’ve written fifty-seven here, not sixty-three.” He rolled the pencil between his teeth while he redid the sum. “Well I’ll be, you’re right. You learning arithmetic in school this year?” “Yep. Teacher says I’m top of the class when it comes to math. Don’t know why the other fillies have so much trouble with it; it’s just numbers.” “You don’t say… you know why you’re not allowed up so early?” She frowned and hung her head again. “I’ll be too tired for all my chores after school.” “Right again. So how about we change things just a bit?” “How do you mean?” “We’ll change what chores you need to do. How’d you like to get up bright and early with me and count apples? You can make sure I get the sums right, and I’ll tell you all about statistics and apple forecasts.” Her leap of joy nearly brought her to eye level with him. “You mean it, Pa? Just you and me?” He grinned. “Just you and me.” “Sounds great, only… what’s statistics mean?” “We’ll get to that in due time, Sugar, we’ll get to that.” A Meeting of the Unsuspecting MindsTwilight couldn’t help but smile. She was standing in Ponyville Town Hall with no less than fifty other ponies. For the Ponyville chapter of the Equestrian Math Club, fifty ponies was a gathering of epic proportions. Normally five or six of them would squeeze into a member’s house for the monthly meeting, but not today. The banner hanging over the stage only made her smile broaden: “144th Annual Competition: Regional Judging.” Her hooves guided her closer and closer to the hallowed podium where the winner would be announced. She’d seen this spectacle every year since she joined the club as a filly and never tired of it. Winning in this contest demanded the very best research papers and theories, and the ponies who dared to enter never failed to rise to the challenge. A solid bump against another pony brought her immediate surroundings back into focus. “Oh, I’m so sorry I didn’t see…” The pony she’d bumped into pushed her Stetson out of her eyes. “No problem, I was…” “Applejack?” Applejack cringed. “Uh… Hi, Twilight.” “What are you doing here?” “Uh… I mean… doing where?” Twilight looked over their surroundings. “At the Equestrian Math Club. I didn’t expect to see any of my friends here for–” her face lit up “–are you a member too? Why don’t you ever come to our meetings?” Applejack’s eyes darted around, and she started backing away. “Math Club? You don’t say… Guess I must be in the wrong place… yep. Best be going back to the farm, lotsa chores to do…” “What?” “Yep. I couldn’t possibly be in the right place, what with this being a math competition and all.” Twilight darted forward and locked eyes with her. “The prime factors of forty-two are two, three, and…” Applejack smirked. “Seven of course.” Her breath caught in her throat and her eyes darted back and forth. “Wait… I mean ten! Ten!” “Aha!” “Horseapples…” Twilight threw her hooves in the air. “You are a math enthusiast! This so great; I never have anyone to go with to these meetings. I can’t even get Spike to…” Her enthusiasm drained away when she realized her friend was staring at the floor. “Applejack, what’s wrong?” “It’s nothing, Twilight… Why don’t you just tell me about what I’ve gotten myself into?” Twilight looked from her friend to the stage. “They’re announcing the regional winner for the national competition today. I’m so glad they’re doing it in Ponyville; it’s brought in members from all over.” Applejack looked over the crowd and took a few steps back. “Might bit busy in here… maybe I should go.” “Applejack are you… nervous?” She pulled off her Stetson and fanned herself with it. “A bit.” “Why?” “I… I entered the competition.” Twilight’s jaw dropped. “You submitted a research paper? What’s it about?” “Oh just a little something I’ve been working on… nothing special.” “I’m sure it’s special, Applejack. I can’t wait to see it.” Applejack found a nearby chair and sat down. “So… you come to these meetings often?” “Every month. Normally there’s just a few of us. We discuss our new findings, read the minutes from last time, send out the newsletter and minutes to… That’s why I never see you at the meetings! You just read the letters we send out to all the local members.” She nodded. “Guilty as charged.” “But I send out those letters myself; there’s no Sweet Apple Acres in the membership address list, and no Applejack.” “I rent a box at the post office under the name SC.” “SC?” She managed a grin. “Sugar Cubed.” Twilight resisted the urge to cheer. “I’m so happy you’re here! I finally have a close friend to talk math with.” “About that… I’m not sure I want this getting around.” “That you’re in this club?” “That I’m into math at all. Most ponies just think I’m a farm hoof, and that’s how I like it.” “But why? What’s so wrong about celebrating your talents and interests?” Applejack twisted her hat in her hooves. “Nothing. I suppose that’s why I entered the contest this year, it’s just…” A pony in a suit walked across the stage and tapped his hoof on the microphone. “Good afternoon, everypony, and welcome to the regional judging round of the Equestrian Math Club’s annual contest. We’ll be announcing the winners in just a few minutes. All contestants are encouraged to sit in the first two rows so we can all see you.” Twilight pulled Applejack out of her chair. “That’s you, SC. Let’s get you up front.” “Now, Twilight…” “Oh come on, since when does Applejack ever back down from a challenge?” She sighed. “Fine. Let’s get this over with.” The first row was completely packed, and the second wasn’t far behind. Once they found a pair of seats, Applejack pulled her hat over her eyes, and Twilight resumed her giddy pony-watching. “Oh, there’s Double Factorial! He’s the chairpony of the math department at Canterlot University; I heard he’s one of the judges this year. I should introduce you after this is over.” Applejack’s head sank even deeper into her hat. “Cool it, Twi, I’m perfectly fine keeping a low–” A deep blue hoof clad in a silver shoe touched the back of Twilight’s chair. “Why, Twilight Sparkle, are you here to compete against me, Princess of the Night?” Twilight jumped up and then bowed. “Princess Luna! I didn’t expect to see you here. Won’t you join us?” Luna smiled and took the seat next to them. “Thank you. My treatise on planetary motion is complete at last, and what better way to share it with ponykind than a friendly competition?” “But why here in Ponyville? Why not in the Math Club’s Canterlot chapter?” Luna’s smile faded. “There has been some… unpleasantness between myself and the other members in Canterlot as of late.” “Oh no, what happened?” “The debate on gravitation at the last meeting became intense and I… might have threatened the chapter president with getting to witness the full lunar cycle in person. I was joking of course, but apparently Princesses should not even jest over such things.” Twilight held back a laugh. “Well, you’re more than welcome here.” Luna’s smile returned in an instant. “And what did you submit to the contest, Twilight?” “Oh I’m just here to watch. Applejack’s the reason we’re seated in the second row.” Applejack felt her hat levitate off of her head, bringing her nose to nose with Luna. “H-howdy, Princess. Come to compete in our little contest?” “Indeed I have. It’s an honor to engage in an intellectual pursuit with a pony such as yourself, Applejack.” Applejack smiled. “Why that’s awful big of you, Princess. I never thought I’d ever compete hoof to hoof with royalty. You said your entry’s about the motion of the planets?” “Yes, and I could not feel better about my chances. I have raised and lowered the moon for thousands of years, and now I have updated physics itself to properly account for the forces involved. What, pray tell, have you submitted?” Her smile faded. “Well…” Twilight grinned. “You might as well tell us, Applejack. All the entries are published right after the contest anyway.” Applejack sighed. “It’s actually about the farm… or farming in general I guess. My Pa tracked our crop yields his whole life, and I created a statistical model for it. I call it the Apple Distribution.” Twilight’s mouth hung open. “You invented a new statistical model? That’s amazing! How come you’ve never mentioned this before?” “It’s… a bit of a complicated story.” Lessons in NumbersAs always, Applejack and Pa were up before the sun. This time Applejack was the one holding the book on her hoof. “This tree makes two hundred sixty-seven apples, right in line with your notes.” Her Pa was a few feet away inspecting a neighboring tree. “Yep. Not bad.” “Not bad? It’s great! Why I bet next season you’ll have the whole harvest predicted down to the barrel.” He laughed. “Now don’t go inflating my ego, Sugar Cubed; Ma wouldn’t care for that one bit.” “But it’s true, you’ve got apples figured out.” “That I might. Still I need to formalize the whole thing.” “How do you mean?” “Just flip through that book a bit. What do you see?” She knew the answer without touching the pages. “Good notes.” “Numbers, just numbers. See, for this to really fly we need more than that, we need an equation that tells us all the numbers we don’t have.” “How do you mean?” “Say one year we had an extra two acres of trees that’d been given half as much fertilizer. How many apples would we get? Or what if we had five days less rain than usual? All those things are just numbers. What we need is an equation to plug them all into to tell us what kind of crop we’re looking at. When we can do that, when we can say right at planting time how many barrels we’re expecting at harvest and figure in everything that happens in between, then we’ve got apples figured out, skin to core.” Another stallion’s voice called out across the fields. “A little early for your numbers, isn’t it, Apple?” Pa sighed. “Run along, Sugar Cubed.” “But, Pa–” “Run along.” Applejack passed him the book and took off into the trees. After running for a few minutes she found a good hiding spot and held her ears up high. The still morning air carried voices further than most ponies would guess, especially a deep one like Pa’s. “…And how I run my farm isn’t any concern of yours.” “To hay it ain’t. All your talk about seeing the future isn’t doing any of us a lick of good, your family included. You need to quit stealing our business with these lies, Apple.” “It’s not lies, Carrot, and I don’t see the future. It’s some calculations I’ve been doing.” “It’s a sham, and it’s gonna stop right now. I know you’ve been stealing our fertilizer for your own crops; that’s the only explanation. Why, my bean crop’s been so bad this year I wouldn’t be surprised if you went and salted the ground too. You’re nothing but a thief and a liar.” “This is my farm we’re standing on, and if you think you can come over here and–” Pages fluttered as the book sailed through the air. A thud and a grunt followed. “Maybe it’s time the boys and me teach you a thing or two.” Applejack raced back to find Pa rubbing his side while one of the Carrots brandished a hoof. “You leave my Pa alone!” Before any of the adults could react, she spun around and bucked Pa’s attacker square in the jaw. A tooth flew out of his mouth and nearly caught one of his brothers in the eye. She shouted as loud as she could, just to hide the quiver in her voice. “And… and if you ever come back again… I’ll… I’ll…” She couldn’t hold back the tears in her eyes, or the shiver in her legs. “I’ll–” “That’s enough, Applejack.” Her Pa’s stern voice froze her in place. “But, Pa…” “You’ve done plenty already. This is just a little discussion between adults, no need to get all worked up over it.” The oldest Carrot brother pushed her aside. “A little worked up? You gonna stand for this?” He parted his lips to show off the new gap in his teeth. “Why if my little Golden Harvest ever–” Pa was standing on three hooves in an instant; the fourth was busy pinning the other pony to the ground. Applejack’s gentle giant of a Pa had been replaced with a monster: fiercer than a timberwolf and twice as big. “I do intend to stand for it, and if you so much as say a word I’ll be planting a full set of teeth instead of apple seeds this year. We clear?” The remaining Carrots backed away. “Whatever you say, Apple.” Pa nodded. “Now get off my farm.” Applejack’s tears wetted the ground while the bullies ran for it. “Pa… Pa, I’m sorry… I…” “It’s all right, Sugar Cubed. Ol’ Carrot had that one coming, even if it should’ve been from me.” He chuckled. “In a year or two you’re gonna be as good an apple bucker as Big Mac.” She wiped her nose with her hoof. “But they… why’d they run all of a sudden?” He stepped to the side of the tree and retrieved the records book. One of the edges was wet with mud. “It’s a mite bit complicated.” “They were calling you a liar, and a thief! Why didn’t you just make ’em leave right off? Why let them call you that?” “Sugar… I let them. It wouldn’t be the first time, either.” She gasped. “But… why?” He brushed off the book and handed it to her. “Figuring out apples isn’t an easy thing, Sugar Cubed; same goes for ponies. Some love you for your talents, some don’t.” “But the Carrots… they–” “They don’t understand how we’re increasing our apple yields season after season, and it bothers them to no end. It bothers them so much that every once in a while they come over and give me some hay about it. They burn off some steam, and then we all get back to work. It’s never gotten physical before; never figured the Carrot boys were fool enough to take a swing at me. I don’t know how I’m gonna explain this to Ma.” They both looked at the bruise forming on his side. She started crying again. “It still ain’t right.” His hoof touched her chin, raising her gaze up to meet his. “Hey now, bruises aren’t nothing to worry about.” “But…” His hoof tapped her forehead next. “It’s what’s in here that counts. Even if nopony ever knows it’s there but you. It’s what’s in here that’s gonna take you places. Why, by the time you reach my age you’ll probably have some fancy degree and a whole lot of better things to do than count apples with your old Pa.” She wrapped her hoof around his leg. “Never, Pa. Fancier math or not, I’ll always count apples with you.” He coughed twice. The force of it shook them both. “We should get inside.” “You okay, Pa?” He coughed again and nodded. “I’ll be fine. Just head on in, and tell Ma I fell off the ladder to the hay loft.” Theory to ApplicationDouble Factorial stood at the podium. “And the regional winner of the one hundred forty-fourth annual math competition of the Equestrian Math Club, who will progress to the final round, is–” a hush fell over the audience “–Maud Pie, for her unprecedented solution to Furmat’s Last Theorem.” The cheers that erupted through the crowd were mixed with gasps. Twilight and Luna stared at each other. Luna pointed at the stage. “Did he say…” “Furmat’s Last Theorem? That problem’s been unsolved for… for…” Luna nodded. “Two thousand years.” Double Factorial tapped on the microphone again. “Care to come up and share a few words, Maud? Perhaps a preview of your formal proof?” The crowd fell silent again as Maud left the first row and stepped onto the stage. When she reached the microphone, she stared out at the crowd with a perfectly stone-faced expression. “I work on a rock farm. Last month when I was rotating granite in the South field, I accidentally found a link between elliptic curves and modular forms, two previously unrelated branches of mathematics. A proof to Furmat’s theorem was the inevitable consequence. I don’t yet know how this will apply to my larger body of work in geology.” Her emotionless stare was met with slowly growing applause. By the time Double Factorial had resumed his position at the microphone, the crowd seemed to have regained its full enthusiasm. When they had finally quieted down he tapped on the microphone once more. “On behalf of myself and the other judges I’d like to thank all of you who put so much time and effort into advancing not only mathematics, but the pony way of life that’s increasingly dependent on it. Advance copies of all the contest entries, including Maud’s groundbreaking work, are available at the back of the–” Twilight’s focus on the stage broke when she heard her friend sniffling. “Applejack? What’s wrong?” “It’s nothing Twi, just let me be. I should’ve never come here.” Ponies left their seats as Double Factorial adjourned the meeting. Applejack stayed seated, and Twilight didn’t leave her side. “Applejack, you’ve been acting weird ever since I ran into you. I’m your friend. Please tell me what’s wrong.” Applejack pulled off her hat and wiped it across her tear-streaked face. “I know it’s silly, but part of me actually thought I’d win this thing. Not for me, but for my… my dad. These numbers… this math was his life, and because of him it’s been part of mine too. He smiled through things that would’ve plumb sent me over the edge. He lived his whole life on the farm without any special schooling for his talents, and after he and Ma… after they were gone, I just did the same. I never told anypony because… well, I don’t rightly know anymore, just fillyhood fears about how I’d get treated.” Twilight stared at the floor. “Applejack, I… I can’t imagine what you’ve gone through. I’m so sorry if I made it worse.” Applejack wiped her eyes one more time and returned the now-damp hat to her head. “It’s not on you, Twi; it’s me. I passed up college, stallions, and plenty more to keep the family together and the farm alive. Pa deserved some recognition for all he did, and some fool part of me thought I could give it to him.” “Excuse me, Miss Applejack?” She and Twilight looked up to see Luna and Double Factorial standing in front of them. She blinked away the last few tears. “Yes?” “Princess Luna here tells me that you’re the author of the Apple Distribution? You’re SC?” “That’s right. Doesn’t quite measure up to cracking some two-thousand-year-old puzzle, I guess.” “Yes, well, I daresay Miss Pie’s talents are something else entirely… but I came over here to discuss your work.” “What about it?” He adjusted the glasses perched on his nose. “Well… how do I put it… this contest only bothers with first place. If we were a tad more broad in our recognition, you could’ve easily captured third or even second; no offense intended, Princess Luna.” Luna rolled her eyes and sighed. “None taken. Please continue.” “I suppose what I mean to say is, this contest highlights one big, flashy contribution to a field of study that most ponies consider boring. Maud’s proof will make headlines, but your work has a chance of bettering our way of life. That’s why I started in this field, and I’m sure many would say the same. I’d like to shake your hoof and say I look forward to whatever you decide to work on next. Where did you receive your degree?” She opened her mouth but didn’t speak for a moment. “That’s… that’s some high praise for a farmer like me. I don’t have any degree, unless you count bucking apples.” His eyebrows shot up, which prompted him to adjust his glasses again. “You mean to say you have no advanced mathematical education, that with no formal training you… my word… would you be interested in a scholarship? I’ll have my secretary draw up the paperwork and send it by mail; please do consider it.” She looked just as surprised as he did. “Scholarship? You’d admit an old farm hoof like me to–” “Excuse me.” Maud was standing on the other side of Luna, still bearing the same emotionless expression. “I just read your paper. It was brilliant.” Luna smiled. “Why thank you, Maud, I’ve studied planetary motion for–” “Oh, sorry. I meant her.” Applejack stared at the hoof pointing at her. “You read my whole paper, just now? How’d you even know it’s mine?” “I read all of them. I singled you out through process of elimination. Yours was my favorite.” “But… but you won, Maud; you won hooves down.” “Your discovery might actually be applicable to my field. I’d like to try your distribution against my work in rock farming.” Applejack matched her blank stare. “Can’t really say that apples and rocks have that much in common, but suit yourself I guess.” Maud nodded. “I’ll keep you apprised of my findings.” As Maud walked away, Luna gave her a withering glare. “I have been doing vector calculus since her precious rocks were formed from dust… What ever happened to all the theorists and astronomers?” Twilight put a hoof around her friend. “I think you just won your dad some pretty big recognition, Applejack. A chairpony from the biggest university in Equestria, and… well Maud’s going to be in history books.” Applejack gave a tiny nod. A hint of a smile was forming on her face. “I guess I did. Thanks, Twi. I wouldn’t have been able to see this through without a good friend like you by my side.” Twilight pulled her into a hug. “Any time, Applejack. I can’t wait to see what you work on next.” “Next?” “I doubt your dad wanted you to stop after just one paper. I’m sure he would’ve wanted you to pursue your talents and be happy.” Applejack took a deep breath and stood. “You’re right, and I’m never gonna be happy if I keep this up.” “Huh?” “The Apple Distribution was his work, Twilight; I just put the final touches on what he wasn’t around to finish. I’m glad I did it, but it’s high time I moved onto some research of my own.” “That’s great! What’re you going to study?” She shrugged and smiled big. “Don’t quite know yet. Give me a lifetime, I’ll think of something. Just make sure you save me a spot at the next club meeting.”
Early Morning Chores“What’s Pa doing out there?” Applejack whispered. The view from the little filly’s bedroom window made no sense. Pa was standing in front of an apple tree without a barrel, a rake, or even a watering can. He just stared at the tree without bothering to buck the glistening, red apples off the branches. For minutes on end he’d stand there, only pausing on occasion to glance at a small book resting on his hoof. There was barely enough sunlight out there to work in, let alone read by. Nopony else would be up for a half hour. Her hoofsteps were nearly silent as she crossed the hallway. If she woke up Ma or Granny Smith this early, she’d never hear the end of it. Her big brother was a different story. She pushed open his door and approached the bed. “Hey, Big Mac.” The sleeping form under the covers didn’t move. “Big Mac!” Finally he stirred. “Huh? AJ?” “Pa’s doing something outside; looks mighty strange to me.” “Pa’s just being Pa, and you’re supposed to be in bed. Sun’s not up yet.” “But–” “Nope.” “I just–” “Nope.” She scowled. “Fine.” Her hoofsteps were equally noiseless as she made her way down the stairs, including the hop at the end to skip the creaky step. She couldn’t count the times Big Mac had put his full weight on the thing after being out late with his friends. Even if the groaning wood didn’t wake her up, the inevitable scolding from Ma certainly would. Soon she was standing outside and at the edge of the orchard. She crouched behind a tree trunk and watched Pa continue his strange ritual. He studied the nearest tree, once again without bucking even a single apple, and then consulted with his little book. From this perspective she could see the pencil he was holding in his mouth. Pa was the biggest stallion her young eyes had ever seen. The first time she saw him knock an apple out of a tree, she’d been sure the tree trunk would be the next thing to hit the ground. Seeing him standing here, still and silent with a book on his hoof, was like looking at another pony entirely. “You gonna hide back there all morning, AJ?” His voice was as deep as rolling thunder. She froze. Did he know she was there, or just suspect? Could she just take a few careful steps back and pretend she’d never left her room? It wasn’t worth trying, not when it meant lying to Pa. Instead she stepped out of her hiding place and hung her head. “Sorry, Pa. I know I’m not supposed to be out this early. I just wanted to see what you were doing.” He rolled the pencil between his lips. “What do you think I’m doing?” “Can’t say. You’ve just been staring at those trees, and reading… only why would you ever write in a book? Wouldn’t that ruin it?” “Why don’t you come on over here, and I’ll show you.” To her surprise the only text in the book was hoofwritten, and most of it was numbers. “What is this?” “Just take a look at this tree; tell me how many apples there are.” One glance at the tree was all she needed. “Ten.” “Right, and here’s the ten in my book.” She followed his gaze down the columns of numbers until she found a freshly drawn one and zero. “So you’re counting all the apples?” “Kinda, but there’s more than that. See, I’ve got numbers for how many apples each tree produced for nigh on thirty years. Same goes for the date they started producing, when they stopped, when the rainy season was…” “But why?” He flipped the pages until they reached the end. “Know how the pegasi give us a weather forecast?” “You mean like when they’re gonna make it rain?” “Right. Well, with all these numbers, I can give you an apple forecast.” “That’s just crazy talk. How can anypony know how many apples there’re gonna be in advance?” He tousled her mane. “Oh it’s not easy, Sugar, but it’s not crazy either. You just gotta track everything a tree cares about for enough seasons, then–” “Fifty-seven.” “Pardon?” She pointed to the last column on the page where he’d added up the crop yields for the last few trees. “You should’ve written fifty-seven here, not sixty-three.” He rolled the pencil between his teeth while he redid the sum. “Well I’ll be, you’re right. You learning arithmetic in school this year?” “Yep. Teacher says I’m top of the class when it comes to math. Don’t know why the other fillies have so much trouble with it; it’s just numbers.” “You don’t say… you know why you’re not allowed up so early?” She frowned and hung her head again. “I’ll be too tired for all my chores after school.” “Right again. So how about we change things just a bit?” “How do you mean?” “We’ll change what chores you need to do. How’d you like to get up bright and early with me and count apples? You can make sure I get the sums right, and I’ll tell you all about statistics and apple forecasts.” Her leap of joy nearly brought her to eye level with him. “You mean it, Pa? Just you and me?” He grinned. “Just you and me.” “Sounds great, only… what’s statistics mean?” “We’ll get to that in due time, Sugar, we’ll get to that.”
A Meeting of the Unsuspecting MindsTwilight couldn’t help but smile. She was standing in Ponyville Town Hall with no less than fifty other ponies. For the Ponyville chapter of the Equestrian Math Club, fifty ponies was a gathering of epic proportions. Normally five or six of them would squeeze into a member’s house for the monthly meeting, but not today. The banner hanging over the stage only made her smile broaden: “144th Annual Competition: Regional Judging.” Her hooves guided her closer and closer to the hallowed podium where the winner would be announced. She’d seen this spectacle every year since she joined the club as a filly and never tired of it. Winning in this contest demanded the very best research papers and theories, and the ponies who dared to enter never failed to rise to the challenge. A solid bump against another pony brought her immediate surroundings back into focus. “Oh, I’m so sorry I didn’t see…” The pony she’d bumped into pushed her Stetson out of her eyes. “No problem, I was…” “Applejack?” Applejack cringed. “Uh… Hi, Twilight.” “What are you doing here?” “Uh… I mean… doing where?” Twilight looked over their surroundings. “At the Equestrian Math Club. I didn’t expect to see any of my friends here for–” her face lit up “–are you a member too? Why don’t you ever come to our meetings?” Applejack’s eyes darted around, and she started backing away. “Math Club? You don’t say… Guess I must be in the wrong place… yep. Best be going back to the farm, lotsa chores to do…” “What?” “Yep. I couldn’t possibly be in the right place, what with this being a math competition and all.” Twilight darted forward and locked eyes with her. “The prime factors of forty-two are two, three, and…” Applejack smirked. “Seven of course.” Her breath caught in her throat and her eyes darted back and forth. “Wait… I mean ten! Ten!” “Aha!” “Horseapples…” Twilight threw her hooves in the air. “You are a math enthusiast! This so great; I never have anyone to go with to these meetings. I can’t even get Spike to…” Her enthusiasm drained away when she realized her friend was staring at the floor. “Applejack, what’s wrong?” “It’s nothing, Twilight… Why don’t you just tell me about what I’ve gotten myself into?” Twilight looked from her friend to the stage. “They’re announcing the regional winner for the national competition today. I’m so glad they’re doing it in Ponyville; it’s brought in members from all over.” Applejack looked over the crowd and took a few steps back. “Might bit busy in here… maybe I should go.” “Applejack are you… nervous?” She pulled off her Stetson and fanned herself with it. “A bit.” “Why?” “I… I entered the competition.” Twilight’s jaw dropped. “You submitted a research paper? What’s it about?” “Oh just a little something I’ve been working on… nothing special.” “I’m sure it’s special, Applejack. I can’t wait to see it.” Applejack found a nearby chair and sat down. “So… you come to these meetings often?” “Every month. Normally there’s just a few of us. We discuss our new findings, read the minutes from last time, send out the newsletter and minutes to… That’s why I never see you at the meetings! You just read the letters we send out to all the local members.” She nodded. “Guilty as charged.” “But I send out those letters myself; there’s no Sweet Apple Acres in the membership address list, and no Applejack.” “I rent a box at the post office under the name SC.” “SC?” She managed a grin. “Sugar Cubed.” Twilight resisted the urge to cheer. “I’m so happy you’re here! I finally have a close friend to talk math with.” “About that… I’m not sure I want this getting around.” “That you’re in this club?” “That I’m into math at all. Most ponies just think I’m a farm hoof, and that’s how I like it.” “But why? What’s so wrong about celebrating your talents and interests?” Applejack twisted her hat in her hooves. “Nothing. I suppose that’s why I entered the contest this year, it’s just…” A pony in a suit walked across the stage and tapped his hoof on the microphone. “Good afternoon, everypony, and welcome to the regional judging round of the Equestrian Math Club’s annual contest. We’ll be announcing the winners in just a few minutes. All contestants are encouraged to sit in the first two rows so we can all see you.” Twilight pulled Applejack out of her chair. “That’s you, SC. Let’s get you up front.” “Now, Twilight…” “Oh come on, since when does Applejack ever back down from a challenge?” She sighed. “Fine. Let’s get this over with.” The first row was completely packed, and the second wasn’t far behind. Once they found a pair of seats, Applejack pulled her hat over her eyes, and Twilight resumed her giddy pony-watching. “Oh, there’s Double Factorial! He’s the chairpony of the math department at Canterlot University; I heard he’s one of the judges this year. I should introduce you after this is over.” Applejack’s head sank even deeper into her hat. “Cool it, Twi, I’m perfectly fine keeping a low–” A deep blue hoof clad in a silver shoe touched the back of Twilight’s chair. “Why, Twilight Sparkle, are you here to compete against me, Princess of the Night?” Twilight jumped up and then bowed. “Princess Luna! I didn’t expect to see you here. Won’t you join us?” Luna smiled and took the seat next to them. “Thank you. My treatise on planetary motion is complete at last, and what better way to share it with ponykind than a friendly competition?” “But why here in Ponyville? Why not in the Math Club’s Canterlot chapter?” Luna’s smile faded. “There has been some… unpleasantness between myself and the other members in Canterlot as of late.” “Oh no, what happened?” “The debate on gravitation at the last meeting became intense and I… might have threatened the chapter president with getting to witness the full lunar cycle in person. I was joking of course, but apparently Princesses should not even jest over such things.” Twilight held back a laugh. “Well, you’re more than welcome here.” Luna’s smile returned in an instant. “And what did you submit to the contest, Twilight?” “Oh I’m just here to watch. Applejack’s the reason we’re seated in the second row.” Applejack felt her hat levitate off of her head, bringing her nose to nose with Luna. “H-howdy, Princess. Come to compete in our little contest?” “Indeed I have. It’s an honor to engage in an intellectual pursuit with a pony such as yourself, Applejack.” Applejack smiled. “Why that’s awful big of you, Princess. I never thought I’d ever compete hoof to hoof with royalty. You said your entry’s about the motion of the planets?” “Yes, and I could not feel better about my chances. I have raised and lowered the moon for thousands of years, and now I have updated physics itself to properly account for the forces involved. What, pray tell, have you submitted?” Her smile faded. “Well…” Twilight grinned. “You might as well tell us, Applejack. All the entries are published right after the contest anyway.” Applejack sighed. “It’s actually about the farm… or farming in general I guess. My Pa tracked our crop yields his whole life, and I created a statistical model for it. I call it the Apple Distribution.” Twilight’s mouth hung open. “You invented a new statistical model? That’s amazing! How come you’ve never mentioned this before?” “It’s… a bit of a complicated story.”
Lessons in NumbersAs always, Applejack and Pa were up before the sun. This time Applejack was the one holding the book on her hoof. “This tree makes two hundred sixty-seven apples, right in line with your notes.” Her Pa was a few feet away inspecting a neighboring tree. “Yep. Not bad.” “Not bad? It’s great! Why I bet next season you’ll have the whole harvest predicted down to the barrel.” He laughed. “Now don’t go inflating my ego, Sugar Cubed; Ma wouldn’t care for that one bit.” “But it’s true, you’ve got apples figured out.” “That I might. Still I need to formalize the whole thing.” “How do you mean?” “Just flip through that book a bit. What do you see?” She knew the answer without touching the pages. “Good notes.” “Numbers, just numbers. See, for this to really fly we need more than that, we need an equation that tells us all the numbers we don’t have.” “How do you mean?” “Say one year we had an extra two acres of trees that’d been given half as much fertilizer. How many apples would we get? Or what if we had five days less rain than usual? All those things are just numbers. What we need is an equation to plug them all into to tell us what kind of crop we’re looking at. When we can do that, when we can say right at planting time how many barrels we’re expecting at harvest and figure in everything that happens in between, then we’ve got apples figured out, skin to core.” Another stallion’s voice called out across the fields. “A little early for your numbers, isn’t it, Apple?” Pa sighed. “Run along, Sugar Cubed.” “But, Pa–” “Run along.” Applejack passed him the book and took off into the trees. After running for a few minutes she found a good hiding spot and held her ears up high. The still morning air carried voices further than most ponies would guess, especially a deep one like Pa’s. “…And how I run my farm isn’t any concern of yours.” “To hay it ain’t. All your talk about seeing the future isn’t doing any of us a lick of good, your family included. You need to quit stealing our business with these lies, Apple.” “It’s not lies, Carrot, and I don’t see the future. It’s some calculations I’ve been doing.” “It’s a sham, and it’s gonna stop right now. I know you’ve been stealing our fertilizer for your own crops; that’s the only explanation. Why, my bean crop’s been so bad this year I wouldn’t be surprised if you went and salted the ground too. You’re nothing but a thief and a liar.” “This is my farm we’re standing on, and if you think you can come over here and–” Pages fluttered as the book sailed through the air. A thud and a grunt followed. “Maybe it’s time the boys and me teach you a thing or two.” Applejack raced back to find Pa rubbing his side while one of the Carrots brandished a hoof. “You leave my Pa alone!” Before any of the adults could react, she spun around and bucked Pa’s attacker square in the jaw. A tooth flew out of his mouth and nearly caught one of his brothers in the eye. She shouted as loud as she could, just to hide the quiver in her voice. “And… and if you ever come back again… I’ll… I’ll…” She couldn’t hold back the tears in her eyes, or the shiver in her legs. “I’ll–” “That’s enough, Applejack.” Her Pa’s stern voice froze her in place. “But, Pa…” “You’ve done plenty already. This is just a little discussion between adults, no need to get all worked up over it.” The oldest Carrot brother pushed her aside. “A little worked up? You gonna stand for this?” He parted his lips to show off the new gap in his teeth. “Why if my little Golden Harvest ever–” Pa was standing on three hooves in an instant; the fourth was busy pinning the other pony to the ground. Applejack’s gentle giant of a Pa had been replaced with a monster: fiercer than a timberwolf and twice as big. “I do intend to stand for it, and if you so much as say a word I’ll be planting a full set of teeth instead of apple seeds this year. We clear?” The remaining Carrots backed away. “Whatever you say, Apple.” Pa nodded. “Now get off my farm.” Applejack’s tears wetted the ground while the bullies ran for it. “Pa… Pa, I’m sorry… I…” “It’s all right, Sugar Cubed. Ol’ Carrot had that one coming, even if it should’ve been from me.” He chuckled. “In a year or two you’re gonna be as good an apple bucker as Big Mac.” She wiped her nose with her hoof. “But they… why’d they run all of a sudden?” He stepped to the side of the tree and retrieved the records book. One of the edges was wet with mud. “It’s a mite bit complicated.” “They were calling you a liar, and a thief! Why didn’t you just make ’em leave right off? Why let them call you that?” “Sugar… I let them. It wouldn’t be the first time, either.” She gasped. “But… why?” He brushed off the book and handed it to her. “Figuring out apples isn’t an easy thing, Sugar Cubed; same goes for ponies. Some love you for your talents, some don’t.” “But the Carrots… they–” “They don’t understand how we’re increasing our apple yields season after season, and it bothers them to no end. It bothers them so much that every once in a while they come over and give me some hay about it. They burn off some steam, and then we all get back to work. It’s never gotten physical before; never figured the Carrot boys were fool enough to take a swing at me. I don’t know how I’m gonna explain this to Ma.” They both looked at the bruise forming on his side. She started crying again. “It still ain’t right.” His hoof touched her chin, raising her gaze up to meet his. “Hey now, bruises aren’t nothing to worry about.” “But…” His hoof tapped her forehead next. “It’s what’s in here that counts. Even if nopony ever knows it’s there but you. It’s what’s in here that’s gonna take you places. Why, by the time you reach my age you’ll probably have some fancy degree and a whole lot of better things to do than count apples with your old Pa.” She wrapped her hoof around his leg. “Never, Pa. Fancier math or not, I’ll always count apples with you.” He coughed twice. The force of it shook them both. “We should get inside.” “You okay, Pa?” He coughed again and nodded. “I’ll be fine. Just head on in, and tell Ma I fell off the ladder to the hay loft.”
Theory to ApplicationDouble Factorial stood at the podium. “And the regional winner of the one hundred forty-fourth annual math competition of the Equestrian Math Club, who will progress to the final round, is–” a hush fell over the audience “–Maud Pie, for her unprecedented solution to Furmat’s Last Theorem.” The cheers that erupted through the crowd were mixed with gasps. Twilight and Luna stared at each other. Luna pointed at the stage. “Did he say…” “Furmat’s Last Theorem? That problem’s been unsolved for… for…” Luna nodded. “Two thousand years.” Double Factorial tapped on the microphone again. “Care to come up and share a few words, Maud? Perhaps a preview of your formal proof?” The crowd fell silent again as Maud left the first row and stepped onto the stage. When she reached the microphone, she stared out at the crowd with a perfectly stone-faced expression. “I work on a rock farm. Last month when I was rotating granite in the South field, I accidentally found a link between elliptic curves and modular forms, two previously unrelated branches of mathematics. A proof to Furmat’s theorem was the inevitable consequence. I don’t yet know how this will apply to my larger body of work in geology.” Her emotionless stare was met with slowly growing applause. By the time Double Factorial had resumed his position at the microphone, the crowd seemed to have regained its full enthusiasm. When they had finally quieted down he tapped on the microphone once more. “On behalf of myself and the other judges I’d like to thank all of you who put so much time and effort into advancing not only mathematics, but the pony way of life that’s increasingly dependent on it. Advance copies of all the contest entries, including Maud’s groundbreaking work, are available at the back of the–” Twilight’s focus on the stage broke when she heard her friend sniffling. “Applejack? What’s wrong?” “It’s nothing Twi, just let me be. I should’ve never come here.” Ponies left their seats as Double Factorial adjourned the meeting. Applejack stayed seated, and Twilight didn’t leave her side. “Applejack, you’ve been acting weird ever since I ran into you. I’m your friend. Please tell me what’s wrong.” Applejack pulled off her hat and wiped it across her tear-streaked face. “I know it’s silly, but part of me actually thought I’d win this thing. Not for me, but for my… my dad. These numbers… this math was his life, and because of him it’s been part of mine too. He smiled through things that would’ve plumb sent me over the edge. He lived his whole life on the farm without any special schooling for his talents, and after he and Ma… after they were gone, I just did the same. I never told anypony because… well, I don’t rightly know anymore, just fillyhood fears about how I’d get treated.” Twilight stared at the floor. “Applejack, I… I can’t imagine what you’ve gone through. I’m so sorry if I made it worse.” Applejack wiped her eyes one more time and returned the now-damp hat to her head. “It’s not on you, Twi; it’s me. I passed up college, stallions, and plenty more to keep the family together and the farm alive. Pa deserved some recognition for all he did, and some fool part of me thought I could give it to him.” “Excuse me, Miss Applejack?” She and Twilight looked up to see Luna and Double Factorial standing in front of them. She blinked away the last few tears. “Yes?” “Princess Luna here tells me that you’re the author of the Apple Distribution? You’re SC?” “That’s right. Doesn’t quite measure up to cracking some two-thousand-year-old puzzle, I guess.” “Yes, well, I daresay Miss Pie’s talents are something else entirely… but I came over here to discuss your work.” “What about it?” He adjusted the glasses perched on his nose. “Well… how do I put it… this contest only bothers with first place. If we were a tad more broad in our recognition, you could’ve easily captured third or even second; no offense intended, Princess Luna.” Luna rolled her eyes and sighed. “None taken. Please continue.” “I suppose what I mean to say is, this contest highlights one big, flashy contribution to a field of study that most ponies consider boring. Maud’s proof will make headlines, but your work has a chance of bettering our way of life. That’s why I started in this field, and I’m sure many would say the same. I’d like to shake your hoof and say I look forward to whatever you decide to work on next. Where did you receive your degree?” She opened her mouth but didn’t speak for a moment. “That’s… that’s some high praise for a farmer like me. I don’t have any degree, unless you count bucking apples.” His eyebrows shot up, which prompted him to adjust his glasses again. “You mean to say you have no advanced mathematical education, that with no formal training you… my word… would you be interested in a scholarship? I’ll have my secretary draw up the paperwork and send it by mail; please do consider it.” She looked just as surprised as he did. “Scholarship? You’d admit an old farm hoof like me to–” “Excuse me.” Maud was standing on the other side of Luna, still bearing the same emotionless expression. “I just read your paper. It was brilliant.” Luna smiled. “Why thank you, Maud, I’ve studied planetary motion for–” “Oh, sorry. I meant her.” Applejack stared at the hoof pointing at her. “You read my whole paper, just now? How’d you even know it’s mine?” “I read all of them. I singled you out through process of elimination. Yours was my favorite.” “But… but you won, Maud; you won hooves down.” “Your discovery might actually be applicable to my field. I’d like to try your distribution against my work in rock farming.” Applejack matched her blank stare. “Can’t really say that apples and rocks have that much in common, but suit yourself I guess.” Maud nodded. “I’ll keep you apprised of my findings.” As Maud walked away, Luna gave her a withering glare. “I have been doing vector calculus since her precious rocks were formed from dust… What ever happened to all the theorists and astronomers?” Twilight put a hoof around her friend. “I think you just won your dad some pretty big recognition, Applejack. A chairpony from the biggest university in Equestria, and… well Maud’s going to be in history books.” Applejack gave a tiny nod. A hint of a smile was forming on her face. “I guess I did. Thanks, Twi. I wouldn’t have been able to see this through without a good friend like you by my side.” Twilight pulled her into a hug. “Any time, Applejack. I can’t wait to see what you work on next.” “Next?” “I doubt your dad wanted you to stop after just one paper. I’m sure he would’ve wanted you to pursue your talents and be happy.” Applejack took a deep breath and stood. “You’re right, and I’m never gonna be happy if I keep this up.” “Huh?” “The Apple Distribution was his work, Twilight; I just put the final touches on what he wasn’t around to finish. I’m glad I did it, but it’s high time I moved onto some research of my own.” “That’s great! What’re you going to study?” She shrugged and smiled big. “Don’t quite know yet. Give me a lifetime, I’ll think of something. Just make sure you save me a spot at the next club meeting.”
