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A subject taken by some students at Hogwarts is Arithmancy.

Throughout the Harry Potter series, we don't seem to be given much information as to what arithmancy actually is.

For example, Defence Against the Dark Arts involves spells and techniques to battle dark creatures/wizards, History of Magic is... supposed to be history of magic (but under Professor Binn's tutorship is mostly just goblin rebellions), Muggle Studies is the study of Muggles, Transfiguration is turning one object into another, Divination is trying to see into the future and Astronomy is studying the sky, stars and constellations and what they mean.

What actually is arithmancy?

Is it just Muggle mathematics, or is it a complicated business used in spell creation (a theme often seen in fanfiction), or...?

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Arithmancy (in the real world, not in the Harry Potter books) is not really mathematics—it's more like number-based divination. I don't see much of a reason to believe it's something else in the Potterverse. – Janus Bahs Jacquet Jan 31 at 3:03
Arithmancy is a Freudian slip by JKR and the main reason she wrote the books: you put a maths problem in, magic happens, and you get the solution out. – Deer Hunter Jan 31 at 9:55
Just for comparison, the Laundry series by Stross, has as one of its key concepts, the idea that certain obscure forms of mathematics can act as spells. Not unreasonable if one accepts that spellcasting is performed by manipulating symbols according to certain rules. (Author's warning: These stories will be getting progressively darker as the Great Old Ones gain strength.) – keshlam Feb 1 at 0:10
The art of the mathemagician – colmde Feb 1 at 16:27
@DavidBanner Spells only work when they're in mangled Latin. Teaching students proper Latin is counterintuitive. – Axelrod Feb 1 at 22:55
up vote 49 down vote accepted

From this article in the reasonably reliable HP Lexicon (emphasis mine):

Arithmancy is a branch of magic that is concerned with the magical properties of numbers; someone who practices Arithmancy is called an Arithmancer. For example, in the 1200s, Bridget Wenlock, a famous Arithmancer, discovered the magical properties of the number seven. An O.W.L. in Arithmancy is required to apply for a curse-breaker's job at Gringott's.

Arithmancy at Hogwarts is taught by Professor Vector. In her class, students are expected to write essays and to be able to understand complicated number charts, which are part of their homework. Hermione Granger appears to be the only Gryffindor in her year who attempted an O.W.L. in this subject (which is her favourite).

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“Professor Vector”. Nice math pun. – Arturo Torres Sánchez Jan 31 at 8:30
The number 7 had been associated with magical properties far earlier than the 1200s. Seems like a silly claim to make on the Lexicon's part. – KRyan Feb 1 at 1:00
@KRyan Sure, but in the Potterverse this is canonical - see here. – Rand al'Thor Feb 1 at 1:03
@randal'thor Yeah, it really wasn't a criticism of the answer, just commentary that the canon is silly. – KRyan Feb 1 at 1:06
@KRyan A young bespectacled orphan saves the world by shouting faux Latin very loudly, and you're complaining that a scientific/mathematical proof came after a bunch of folklore going "This seems to work"? Interesting calibration on your suspension of disbelief. – deworde Feb 1 at 9:31

From JK Rowling Herself.

Stephen Fry:What is Arithmancy?

JK Rowling: Well your guess is as good as mine Stephen. Arithmancy is predicting the future using numbers. I’ve decided there’s a bit of numerology in there as well but how you do it I really don’t know.

This is about all we know other then that Hermione talks about it and they talk about the numbers and figures she deals with being complex.

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If Stephen Fry doesn't know then it really is a mystery. – maguirenumber6 Jan 31 at 9:18
@maguirenumber6 If neither Stephen Fry not JKR knows, then it really is a mystery! – Janus Bahs Jacquet Jan 31 at 17:30
Predicting the future using numbers? Sounds like an actuary to me... – crunch Feb 1 at 11:08
@crunch A late relative of mine was an actuary and joked that an actuary can walk into a room and tell you how many people will die, a Sicilian actuary can walk into the room and tell you which ones. – Kevin Rubin Feb 1 at 13:43
predicting the future sounds like divination to me, and Hermione disliked that, so why would she like Arithmancy if this is what it really is? – Michael Feb 1 at 17:01

Not original with Rowling, it's a real word, albeit rare. The online OED defines "arithmancy" as "divination by numbers" (also called "arithmomancy") and gives two quotations:

1577 W. Harrison Hist. Descr. Islande Brit. i. ix. f. 28/2, in R. Holinshed Chron. I An old kind of arithmancie, fathered on Pythagoras, yet never invented by him.

1878 J. H. Gray China II. xvii. 25 Other systems of telling fortunes are in vogue, as for instance..arithmancy.

The following quotation from "Turjan of Miir" by Jack Vance, about mathematics and magic, is probably not what JKR had in mind:

In this fashion did Turjan enter his apprenticeship to Pandelume. Day and far into the opalescent Embelyon night he worked under Pandelume's unseen tutelage. He learned the secret of renewed youth, many spells of the ancients, and a strange abstract lore that Pandelume termed "Mathematics."

"Within this instrument," said Pandelume, "resides the Universe. Passive in itself and not of sorcery, it elucidates every problem, each phase of existence, all the secrets of time and space. Your spells and runes are built upon its power and codified according to a great underlying mosaic of magic. The design of this mosaic we cannot surmise; our knowledge is didactic, empirical, arbitrary. Phandaal glimpsed the pattern and so was able to formulate many of the spells which bear his name. I have endeavored through the ages to break the clouded glass, but so far my research has failed. He who discovers the pattern will know all of sorcery and be a man powerful beyond comprehension."

So Turjan applied himself to the study and learned many of the simpler routines.

"I find herein a wonderful beauty," he told Pandelume. "This is no science, this is art, where equations fall away to elements like resolving chords, and where always prevails a symmetry either explicit or multiplex, but always of a crystalline serenity."

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Arithmancy is close to a synonym of data science in the muggle world. It is about inferencing and prediction from numbers.

The fact that it has numerology in it, is the only thing that makes it different from present-day data science (or more precisely predictive analytics).

So, Arithmancy = (Present day predictive analytics + Numerology)

The proof for the above is an interview of Stephen Fry with JKR:

Stephen Fry: Can you explain in words of less than two syllables what Arithmancy is?

JK Rowling: Well your guess is as good as mine Stephen… Well, really it's predicting the future using numbers, but I've also decided there's a bit of numerology in there as well.

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It's like data science but magical ... so data magic then? ;-) – Rand al'Thor Jan 31 at 16:00
@randal'thor haha Being a professional DS myself, I envy those kids :D – Dawny33 Jan 31 at 16:02
+1. @randal'thor: Data Science is magical. – Wayne Jan 31 at 16:07

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