What a relief to be back. This, Harry thought, as they walked into the great hall and took their seats at the Gryffindor table, this was his home. This was the place where he grew into his mind and magic, where he read and practiced and competed, where he forged himself into what he was now. This is what he lived for. And number 4 Privet Drive? That, that wasn't anything worth discussing, his own personal Azkaban, nothing but bad muggle food, silence and a productive yet staggeringly lonely retreat into arithmancy.
"I've been reading some of his publications," Hermione said, looking up at Harry, her lips pinching together into a tight smile as she said the words, the wavering illumination of the candlelight making her sharp features wander casually in and out of visibility. "The man's brilliant, you have to admit that."
"When I say I dislike him," Harry said, "I mean just that: I don't like him. He's a genius potions master and, " Harry grinned, "a greasy git." He paused, "Cardano's pri…"
"Cardano's principle of non-exclusivity,' Ron mumbled. "Merlin, Harry, we get it you're good at arithmancy. It's no surprise Cho dumped you. Can you imagine what the pillow talk was like," he said, smirking at Hermione.
Hermione smirked right back, "You're as elegant as the numeric isomorph of a shield charm. Your bosom is as fulsome as Flamel's derivation of…"
"Ok, ok,' Harry said, "cease fire on the arithmancy jokes. And like I said in June, I broke up with Cho."
"Sure you did," Ron muttered.
They went back and forth like this for a while, the conversation sputtering out. From the next table over, a girl's shrill giggle broke through the chattering din. The truth was he wasn't sure if he did break up with Cho. She had said the words, but he just sort of shut off at some point, a comet propelled out of orbit by chaotic warbles in its trajectory too subtle to calculate, even in hindsight. His magic became more pressing, obligations to her more irritating. Whatever that step was, when you start to love a person. Where you start to care about them more than you care about being with them, that hadn't happened with Cho, even after months. He wondered if he was broken. If those years unloved, alone had taken some toll.
"I'm bunking off," Harry said. That whole Cho train of thought was leaving him feeling depressed.
"Sorry," Hermione said, elbowing Ron. "We shouldn't have brought Cho up."
"It's not that," Harry said, cooly. Hermione pursed her lips. "It's just I'm not hungry, and if I have to hear that bloody hat sing for a seventh time I might just off myself."
Harry stood up and headed for the exit, catching Hermione angrily whispering at Ron as she did. Even after taking a few steps, he felt his mood brightening. It was hard to stay down in this place. The hall was glorious, candles floating above the four sturdy tables, the enchanted ceiling brimming with stairs, friends and rivals reuniting, laughing and shouting, casting utterly useless spells just for the sheer joy of using magic again. Yes, It was very hard to stay in a sour mood. He looked back at Hermione and Ron; They seemed to have made up rather quickly, her leaning against him now, his arm around her shoulder.
OOOoooOOO
"Madame Pince," Harry said, looking at the sharp-eyed librarian. She was sitting at her desk, right by the entrance to the library, performing some subtle classification magic on a ratty tome, whose title Harry could just barley make out. It saidThe Sacred Charms. "I expected you would be at the feast."
"And what use to me, Mr. Potter, is a feast? Will I bind books better if I eat a rich meal? Will my sorting charms become more efficient if I prattle on with the staff and listen to that insufferable hat sing." She looked back down at the book, whispered a soft spell, then tapped its cover with her wand. The book stood up on the table, like some drunk sobering up. It was as if it had spent its whole life listening and that spell was first dollop of good sense it had heard. What has become of me, Harry imagined the book thinking, I don't belong on a desk, alone without peers. It bristled its pages, flew off Pince's desk, and delicately shelved itself in the back-left corner of the restricted section.
"And why aren't you at the feast, Mr. Potter," Pince said, her tone implying a complete lack of interest. It was as if conversation and politeness were things she knew were of some importance to other people, but never could quite figure out the precise reason why.
"You've seen it six times," Harry said, " you've seen it seven." Pince nodded, pulled another book from the bin beside it and began examining it with more of her subtle librarian magic. Harry smiled and made his way to his favourite table, sat down and started working.
She had a poor reputation, but Madame Pince wasn't so bad. So long as you didn't write in a book's margins, or bend its spines too far back, or cast carless search charms, or neglect to a cast a silencing charm before conversing in the library, she was perfectly civil. Harry had made all these mistakes and more in his first year at the school, and been shouted down and given detention several times. But now he was an old pro at the library, with a pass to the restricted section and a pavlovian terror of writing notes in the margins.
"Potter," Terry Boot whispered, startling Harry out of his trance. How long had he been sitting there? He'd been so focused on the equations, on the tick in his head, he'd lost track of time. Was the feast over already?
"Hermione told me I could find you here," Terry Boot said, taking the seat opposite Harry. Harry waved his wand and cast a sound-proofing charm.
"Is the feast over already?" Harry said.
"Not quite,' Boot said, "Just thought I'd find you so I could see if you've been working on anything interesting."
Harry had known Boot since third year, and they weren't exactly friends. Rivals maybe? That mysterious intuition Harry had for arithmancy, Boot had that, too. He was the only other person in all of Hogwarts Harry would admit to be his equal in the subject. Both had demonstrated themselves to be startlingly precocious in third year, when they first took up the class, which Harry found incredibly unchallenging and thus incredibly boring. It got to the point where he was talking Hermione's ear off, as she diligently worked through the problem set, disrupting her and the rest of the class. Boot was having similar issues. He once set fire to his textbook while mindlessly practicing charms, having finished his problem sets well before the rest of the class, aside from Harry of course, were even half way through.
After a few months of this, Vector announced, "Boot, Potter please see me after class."
The two boys lingered after the other children left (Ron and Hermione giving Harry mocking looks as they did) and warily approached the large, oak desk behind which Vector was sitting. She was a pretty young women, of medium stature, who wore no makeup around her eyes, but seemed to have charmed her lips to take on a deep rose colour. Looking at her, one might think every one of her male students (and a good portion of the female ones) would have a crush on her. But like arithmancy itself, her beauty was abstract and beyond physical, subtly alien, exuding an exactness that neutralized all attempts at romanticization.
She cleared her throat. "You two are constantly disturbing the class." Harry and Boot both tried to interrupt but Vector raised her finger. "And I know why. This is all too easy for you. You're bored. I suspect you've both studied this subject extensively before you started this class?"
"Yes, ma'am," Terry said, "I've been teaching myself the subject since first year.
Vector turned to Harry. "Err, yeah. I've been working on arithmancy in my free time since last year," Harry said, nervously. "I found a book in the library, and it just sort of clicked, I guess."
She nodded, their answers exactly as she expected. She reached into her desk and pulled out two large textbooks. "These are the fifth year textbooks," She said, then pointed at a table at the back of the classroom. "From now on in my class, you two will work on the fifth year problem sets at that back table and at your own pace. I'll supply you with more-advanced books as needed. Though Hogwarts doesn't allow me to move you into my more advanced classes," she crinkled her nose disdainfully, "I am still given full discretion when it comes to grades. You two have gotten perfect scores on all the examinations I've given so far. So long as this continues and I'm satisfied with your progress in the more advanced material, I will exempt you from all homework.
Terry looked pleased but very shocked, "You'll exempt us? Really?"
"Yes, Mr. Boot. I'll exempt you. Unlike most my students," she smiled, "you two actually enjoy arithmancy. Enforced homework is necessary to ensure most students achieve competence. You two have glimpsed the beauty of the subject, which few do. I have no doubt you will continue studying on your own."
Harry nodded. Boot did too. It was perfectly true. Harry and Boot did continue to study on their own. By the end of their second year in the class, they had worked their way through every arithmancy textbook in the Hogwarts curriculum. And now they studied independently under Vector's supervision, constantly trying to one-up each other, to see who could impress Vector with their performance on masters-level problem sets, and, increasingly in the last two years, independent research.
"It's been frustrating," Harry said, reaching into his bag and grabbing two fresh sheets of parchment. He silently cast the protean charm on the pages - a trick Hermione had worked out the year before. The charm caused anything written on one sheet to appear on the other. Hermione used it to send messages to Ron and Harry while in class. The connection would fizzle out if the sheets were more than a few miles apart so it was no replacement for an owl, but it worked well for passing notes and even better for arithmancy, a shared workspace for demonstration and cooperation. Harry passed one of the sheets to Boot, and started scribbling on it with his quill.
"So there's the proof, right, the Aparecium charm is in this whole region of stable magics. It's far from optimal, and there exists a possible path to a much stronger revealing spell."
'But it's non-constructive," Boot said. It was true. It was non-constructive. It proved the existence of such a spell, but didn't derive it. It was very frustrating, like having a word at the tip of your tongue. There existed stable magic just beneath the surface of the proof, a discovery, an original one at that was just beyond his grasp. "Still," Boot said, noticing Harry's face fall, "This is very good work. Now that we know its possible, we should be able to derive it. Walk me through the proof."
Harry, raised an eyebrow, "I just did." Boot told him that he'd shown him the proof, but didn't walk him through how he got where he did from the ground up, saying he wanted a higher-level view of the problem. Harry dug around in his schoolbag and pulled out a notebook. "Here's all the dead ends," Harry said, his stomach rumbling now, "Tell me if you get anywhere. If we derive a new spell we should be able to get published." Boot nodded and Harry stood up. "Come on, let's catch the end of the feast, I'm bloody starving."