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The Arithmancer by White Squirrel is a Harry Potter Alternate Universe Fanfic in which Hermione Granger is a mathematics prodigy. It is complete and covers Years 1-4, with a completed sequel, Lady Archimedes, covering Years 5-7. A third story, Annals of Arithmancy, which is set after graduation, was finished in March 2019.

Unmarked spoilers below.


Tropes:

  • Adaptational Badass: In addition to Hermione being such a math whiz, there is also Ron's chess skills, and the whole trio's, plus Professor Vector's, actions in the Chamber of Secrets.
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  • Adaptational Villainy: In the sequel the author manages to pull this off with Umbridge — who was already a villain in the original novels.
  • Adult Fear: The Grangers are creeped out that the Wizarding World can track one's movements unless concealed with magic.
  • Alternate History: In this fic, the witch hunts began much earlier being an occurrence as early as the 9th century.note  King Malcolm III didn't like that his predecessor was getting help from witches, and started an active persecution of witchcraft.
  • Alien Geometries: Hogwarts runs on this. Not only do the interior's measurements not match the outside, the corridors have different measurements across different floors.
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  • Anger Born of Worry: George to Hermione in the sequel's Chapter 57 when her insomnia-derived recklessness caused her to Apparate in front of the Weasley's shop during an Death Eater attack and nearly get hit with a Killing Curse.
  • Armed with Canon: Christian wizards and witches point out that the Bible only bans divination and necromancy.
  • Ascended Extra: Professor Septima Vector.
  • Attention Deficit... Ooh, Shiny!: Played for Drama. In the sequel, Hermione when she's on the run from the Death Eaters. She has so many projects and problems facing her that she has a hard time focusing on the most important ones.
  • Badass Boast: Hermione to Draco at the end of fifth year.
    Hermione: Anyone who resorts to Unforgivable Curses doesn't have an ounce of creativity.
  • Badass Bookworm: In this Alternate Universe, Arithmancers tend to be this.
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  • Black Dude Dies First: Lee Jordan dies in the battle of the Department of Mysteries, making him the first character to die "onscreen".
  • Blood Knight: Blaise Zabini, the only marked Death Eater to be considered innocent, joins the Reconciliation Committee established after the war. He's the most militant and bloodthirsty of all members, basically demanding the death penalty for all of the Death Eaters.
  • Corporal Punishment: It was never formally banned at Hogwarts, but Dumbledore used his power to forbid it. Umbridge, however, brings it back when she becomes headmistress.
  • Day of the Jackboot: Voldemort takes over the Ministry in Chapter 47 of the sequel, a few months earlier than canon due to Dumbledore's death.
  • De-Power: Septima Vector loses her ability to use arithmancy after she suffers traumatic brain injury due to being Crucioed.
  • Deconstruction Fic: Not the most extreme example, but the fic does point out certain inconsistencies in the characters' behavior, as well as the general weirdness of the wizarding world.
    • The first arc does a Decon-Recon Switch of the Chronic Hero Syndrome, pointing out that first years simply do not know enough magic to face a troll, which is defeated with a non-lethal One-Hit Kill spell cast by Professor Vector.
    • Kid Hero is deconstructed too, as everyone points out that a first year at Hogwarts would be curbstomped in a fight against an adult wizard and Harry's attempts to get to the Philosopher's Stone are seen as suicidal.
    • Later, the obstacles get a Difficulty Spike and Quirrelmort got through by cheating, using an obscure charm to make Vector's enchanted statues color-blind and causing a system failure that opens the doorway.
    • Hermione points out that Mandrakes are literally Person of Mass Destruction due to their lethal scream. If a malicious wizard put an amplifying charm on the plant it would result in the death of thousands. However Professor Sprout points out that the lethal effects are not instantaneous and that the scream cannot be reproduced artificially, such as recording the scream. And that a silencing charm will render the mandrake harmless.
  • Despair Event Horizon: The Basilisk attacks on muggleborns have such an impact on Hermione that by Christmas she's ready to either give up magic altogether or be transferred to another school.
  • Doorstopper: The first two books have over half a million words each.
  • Dramatic Irony: Played for Laughs; Hermione's letter home after the troll incident includes the phrase "It's not like an evil psychopath sneaks in and tries to kill somebody every year or something." In canon, almost every book focused on exactly that.
  • The Dreaded: Voldemort to the Wizarding World. After an earlier death of Dumbledore, Voldemort curses his own name so that Death Eaters can track down his greatest enemies. Hermione uses a ritual to bind her tongue, which prevents her from speaking his name and triggering the Taboo Curse, which has a creative effect that the narrator refers to him as You-Know-Who.
  • Get Out!: The Grangers have a downplayed version when McGonagall tries to recruit Hermione for Hogwarts, at least until she proves magic does exist.
  • Education Mama: Downplayed. The Grangers are distraught to find out that Hogwarts favors magic over science and muggle history, but when McGonagall informs them that it's possible to hire tutors and that magical education is only compulsory up to fifth year, they back down. For the most part they're the Open-Minded Parent.
  • Eldritch Abomination: The giant blob of dust and woodchips that appeared in the Battle of Hogwarts. Considering that it seemed to be the last thing to come down from the upper floors of the Grand Staircase, it was probably the top of the Grand Tower. But it was still animated by McGonagall's spell, and it still fought for Hogwarts.
  • Eldritch Location: The upper floors of the Grand Staircase, as Hermione finds out.
  • Fate Worse than Death: Beyond their already bad canon characteristics, ghosts also can't grow mentally and are trapped in whatever mental state they were in when they died and cannot get new memories.
    • Septima Vector gets this in the sequel, where she's Crucioed by the Carrows in such a way that her head cracks. While Madam Promfrey is able to save her, Vector suffers from traumatic brain injury which strips Septima of her ability to use arithmancy.
  • Foregone Conclusion: Hermione's attempts to ensure that her map of the castle is architectonically correct fails because Hogwarts is always changing. She still tries to create a map without the correct measurements, though.
  • Fox-Chicken-Grain Puzzle: The Ravenclaw door gives puzzles in lieu of a password, of which this is one. Ginny suggests Cutting the Knot by casting Freezing Charms on the animals and conjuring a bigger boat, which the door deems an "acceptable alternative".
  • Friend to All Living Things: Hermione, though she takes exception at Dementors.
  • Gilligan Cut: After Harry and Ron miss catching the train in second year, all their friends are discussing how Molly and Arthur probably used the Floo Network to get them to Hogsmeade and are enjoying butterbeer. Cut to Harry and Ron on the Knight Bus.
  • As the Good Book Says...: As she studies soul magic in order to understand Horcruxes (including the one in Harry), Hermione purchases religious books. She later "borrows" a Bible while on the run from the Death Eaters.
  • Good with Numbers: Hermione; that's the main premise.
  • Happily Adopted: The son of Bertha Jorkins and Barty Crouch Jr, who is adopted by Septima Vector after the Battle of Hogwarts.
  • Homeschooled Kids: In her fifth year, Hermione leaves Hogwarts after Christmas and gets tutorship from Slughorn.
  • If You Ever Do Anything to Hurt Her...: Subverted when Dan has "obligatory father-daughter's boyfriend talk" with George; he says This Is the Part Where... he's supposed to threaten a root canal without anaesthesia, but admits that Hermione is far more threatening than he is, and if George hurts her, she will take revenge.
  • Intrinsic Vow: Hermione's devotion to maths means that she is able to throw off the Imperius Curse when told to write 2+2=5.
  • In Spite of a Nail: Because of The Stations of the Canon being at play, this trope is played straight such as in these cases:
    • The barrier at King's Cross is still sealed and Ron still gets a Howler from his mother.
    • Dumbledore still dies but it's Draco not Snape who does it.
    • The Ministry still falls to the Death Eaters.
  • It Is Pronounced Tro Pay: Ginny's name is Ginevra, not Virginia which is why she's annoyed when Rita Skeeter misnames her in one of her articles.
  • Literal Metaphor: Cedric survives in this continuity, but as Hermione puts it, it cost "an arm and a leg, and no, that's not a figure of speech".
  • Loophole Abuse:
    • Quirrelmort gets through Professor Vector's trap by using a color-blind charm on her enchanted statues.
    • Underage wizards and witches can use wandless magic outside of school, as long they do not use it in front of Muggles that are not a Secret Keeper.
    • Runes can be used to replace wands in potion making, allowing muggles to brew potions.
  • Medieval Stasis: Played for Drama and Played with. The Wizarding World seems perpetually stuck in the 17th/18th centuries, with an extremely authoritarian government that literally controls the press and exerts influence over education and academia, as well as seeming to lack any concept of civil liberties. On the other hand, the Wizarding World seems to be ahead of the muggle world regarding religious tolerance and sexuality (remembering of course that Harry Potter is set in The '90s).
  • Mindlink Mates: After doing a Hollywood Exorcism ritual to remove the Horcrux inside Harry, one of the consequences of the light magic is that it turns Harry and Ginny into light-oriented horcruxes for each other, and at first, they can't look each other in the eyes without massive pain.
  • Misfit Mobilization Moment: After spending a year and half on the run from the Death Eater-controlled Ministry, the Battle of Hogwarts is this for Dumbledore's Army and the Order of the Phoenix.
  • Monumental Damage: Hogwarts Castle was so badly damaged by The Siege laid by Voldemort's forces, that in the aftermath McGonagall declared the castle uninhabitable and the survivors had to create a tent camp by the carriage stand.

  • Mundane Solution: Basilisk kills with a stare? Use Sunglasses with lenses of a certain color designed to filter out the yellow of its eyes.
    • Although "Mundane" is selling what they do a little short — while the initial method of wearing sunglasses works, Hermione invents a spell on the fly to figure out the precise wavelength of light needed to block it out. And better? With them, she's able to look the Basilisk in the eye and only feel like she's got a migraine, rather than getting knocked out, paralyzed, or killed.
    • Instead of waiting a long time to get the Firebolt checked out by the teachers, they just send it back to the manufacturers and borrow a loaner until it can get checked.
    • Instead of flying a car to Hogwarts when Dobby seals the platform, Ron and Harry take the Knight Bus.
    • When trying to get at the stone, Quirrel just steals the mirror the Stone is inside of, rather than just sitting around and trying to puzzle it out in Hogwarts. He's still stopped, though.
  • A Nazi by Any Other Name: The Death Eaters and later the Ministry when they take over.
  • Not His Sled: The climax of each year is always different than it is in the books.
  • "Not Making This Up" Disclaimer: Hermione decides to prove the existence of a sixth Principal Exception to Gamp's Law of Elemental Transfiguration, namely, radioactive material, not for the prestige such an accomplishment would bring, but because she's terrified that someone might try transfiguring antimatter, and proving the impossibility of radioactive transfiguration is the first step in proving the same of antimatter. When she explains this to her parents in a letter home, she has to clarify that it wasn't a joke.
  • O.C. Stand-in: Being told from Hermione's perspective, we get to see the teachers that she, rather than Harry, interacts with, particularly Vector.
  • Oh, Crap!: Professor Vector gets a fairly large one when Hermione reveals that her experiments could potentially create antimatter. Or at least, she gets one once Hermione explains what antimatter is.
  • Our Ghosts Are Different: Ghosts are Barred from the Afterlife and exist in an endless cycle, unable to grow mentally or gain new permanent memories.
  • The One Thing I Don't Hate About You: Snape begrudgingly admits that Hermione's potions publication was impressive and that he wouldn't be opposed to teaching her if she elected for independent study.
  • Pet the Dog: Hermione helps Filch make a potion using rune clusters as part of her paper. He's so happy that the Twins thought it was the end of times.
  • Pædo Hunt: Downplayed. When they read Hermione's Hogwarts letter they're creeped out that wizards can track the movements of children.
  • Pinch Me: Daniel Granger pinches himself when McGonagall transforms his table into a tortoise in an attempt to prove that magic exists.
  • Powder Keg Crowd: Umbridge's attempt to stop Septima from rescuing Harry and Hermione from the Ministry of Magic marks the final straw for Dumbledore's Army, resulting in a riot that ends with Umbridge getting blasted across the room.
  • Queen of Pranksters: Fred and George slowly come to see Hermione as this due to the increasingly risky, highly illegal means she uses to deal with the dangerous occurrences at Hogwarts.
  • Rape Is a Special Kind of Evil: Bertha Jorkins was held hostage and brutally raped by Barty Couch Jr for four years, and eventually became pregnant. She's rescued by Snape when the DA takes over Hogwarts from the Death Eaters.
  • Reality Ensues: Hermione's parents grow increasingly distrustful of Hogwarts' commitment to student safety with each passing year. After she is nearly kissed by a Dementor, the Grangers force her to transfer to Beauxbatons.
  • Real Witches Love Jesus: It seems that Hermione is a Christian (probably a Cafeteria Christian) in that she believes in God and immortal souls. This is why she is so shocked to find out that the Dementors might be capable of destroying souls.
  • Reasonable Authority Figure: Arithmancy Professor Septima Vector is this to Hermione.
  • Refuge in Audacity: After Umbridge passes an Educational Decree banning teachers from teaching outside of their schedule or curriculum, Hermione points out that classes that aren't accredited by the Ministry don't require a teaching certificate, allowing her to continue the studies with Professor Vector. But when Umbridge finds out, she bans that too.
  • Ritual Magic: Used in the sequel. Hermione uses one to remove the Horcrux on Harry's mind, and in the process make him and Ginny into Light-aligned Horcruxes. Another ritual is used to kill Voldemort.
  • Rooftop Confrontation: Deconstructed when Hermione fights Bellatrix in the Great Hall rooftop after killing Voldemort for good, she slides down the rooftop, suffering tears in her robes and scraps. It's even given a Lampshade Hanging that rooftop fights are not as easy as in movies.
  • Rules Lawyer: In the sequel, Umbridge and Hermione have this back and forth, with Umbridge having the upper hand because she has the backing of the Ministry.
  • Shame If Something Happened: As Hermione protests the blood quill detention Umbridge prepared for her, the witch threatens her family because truancy is illegal in the Wizarding World. note .
  • The Stations of the Canon: Played with, but mostly played straight. All the events of the books occur with only superficial changes. Umbridge is much meaner than in canon, Dumbledore is killed by Draco a few months earlier, the Death Eaters take over the Ministry a few months earlier.
  • Super Window Jump: During her duel with Bellatrix, Hermione out of a window.
  • Take Our Word for It: Hermione says this to Bill Weasley as she's explaining to him the concept of continental drift, which he finds preposterous.
  • Take That!: The last section of Chapter 68 is one to the Fandom-Specific Plot of magically arranged marriages.
  • There Are No Therapists: Averted, Hermione saw a counsellor during the summer after her traumatic experiences in her first year.
  • This Is for Emphasis, Bitch!: Hermione to Umbridge when she has George Weasley attached to a whipping post at the end of fifth year.
  • Torches and Pitchforks: A mob of angry Slytherins run Harry out of Hogwarts in mid-sixth year, as Voldemort consolidates his control over the Ministry.
  • Voice of the Resistance: In the sequel there are two. Potterwatch on the Wizarding Wireless and the Liberator newspaper.
  • You Are Better Than You Think You Are: Hermione points out that while Ron sees himself and his family as normal, not one member of his family doesn't excel at what they do.
    • She has to verbally beat both of her friends into submission to take more advanced classes than the "easy O" classes of Divination and Care of Magical Creatures, pointing out that the two are actually really good at what they do — Harry's mind is fine enough for Arithmancy (with the added benefit of him having muggle schooling, which is better at maths than the wizarding counterpart), and Ron is better at Runes than Hermione is.
  • The Unpronounceable: Parodied with the infamous Welsh town which Harry, Hermione, George and Ginny visit while on the run from the Death Eater-controlled Ministry.
  • Walpurgisnacht: The Battle of Hogwarts occurs during this.
  • "Where Are They Now?" Epilogue: The Annals of Arithmancy which, while mostly focusing on Hermione, are this.
  • White Magic: Usually especially on the sequel. The horcruxes in Harry and Ginny created accidentally by Hermione and the ritual to kill a dementor in order to restore Luna's soul are good examples of this. However, the text itself refers the trope by Light Magic.
  • A Wizard Did It: Played for Drama regarding Hogwarts' Alien Geometries.

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