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"Double Divination this afternoon," Harry groaned, looking down. Divination was his least favorite subject, apart from Potions. Professor Trelawney kept predicting Harry's death, which he found extremely annoying.

"You should have given it up like me, shouldn't you?" said Hermione briskly, buttering herself some toast. "Then you'd be doing something sensible like Arithmancy."

JK herself says of Arithmancy:

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.

As we all know, Hermione absolutely loathes Divination, harbouring a great skepticism for it , as does Professor McGonagall.

However, she loves Arithmancy to the point where she (I believe) calls it her favourite subject.

So, given her hatred of Divination, the art of predicting the future, why does she have such a love for Arithmency, which JK says is basically predicting the future in a different way?

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    Predicting the future using numbers? Climatologists, stockbrokers, physicists and economists do that... – leftaroundabout Mar 20 '17 at 19:06
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    I thought hpmor had something to say about Arithmancy—basically that they hadn't even gotten past trigonometry—but I can't find it just now. :) – Wildcard Mar 21 '17 at 1:13
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    Arithmancy is predicting the future using numbers. That's pretty much exactly what Physics is. Just, it presumably also incorporates divination magic to go beyond what real-world Physics can, which would it make stupidly awesome. – Nat Mar 21 '17 at 9:06
  • I think it's the exact same difference between numerology and numerics and astrology and astronomy: The former reacts to the successor with indifference, the latter reacts to the predecessor with undiluted hatred. – Thorsten S. Mar 21 '17 at 12:07
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    Arithmancy looks an awful lot like Psychohistory, which is described as a hard science in Asimov books... – Lorenzo Dematté Mar 21 '17 at 16:13
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Arithmancy was a very different subject from Divination

You're right to say that Hermione saw Arithmancy as her favourite subject. She continued studying it right up to her sixth year. However, her explanation of why she loved it so much was - tantalisingly - interrupted by Ron's discovery of Scabbers's faked death.

“Why don’t you just drop a couple of subjects?” Harry asked, watching her lifting books as she searched for her rune dictionary.
“I couldn’t do that!” said Hermione, looking scandalized.
“Arithmancy looks terrible,” said Harry, picking up a very complicated-looking number chart.
“Oh no, it’s wonderful!” said Hermione earnestly. “It’s my favorite subject! It’s -"
But exactly what was wonderful about Arithmancy, Harry never found out. At that precise moment, a strangled yell echoed down the boys’ staircase. The whole common room fell silent, staring, petrified, at the entrance. Then came hurried footsteps, growing louder and louder - and then Ron came leaping into view, dragging with him a bedsheet.
(Prisoner of Azkaban, Chapter 12, The Patronus).

It's clear, however, that it wasn't the prophetic aspect of Divination that Hermione had a problem with. She expresses no scepticism whatsoever about the concept of prophecy when Harry relays the contents of Trelawney's prophecy to Dumbledore; she takes it at face value. She has no problem with the notion of predicting the future using magic. She even goes as far as to defend Divination against Ron's scorn after she comes across legitimate prophecy.

"Bet Dumbledore wishes he could've got rid of Trelawney for good," said Ron, now munching on his fourteenth Frog. "Mind you, the whole subject's useless if you ask me, Firenze isn't a lot better..."
"How can you say that?" Hermione demanded. "After we've just found out that there are real prophecies?"
(Order of the Phoenix, Chapter 38, The Second War Begins).

It seems to be partly Trelawney's classroom methods that she objects to.

“Professor Trelawney said you didn’t have the right aura! You just don’t like being bad at something for a change!”
He had touched a nerve. Hermione slammed her Arithmancy book down on the table so hard that bits of meat and carrot flew everywhere.
“If being good at Divination means I have to pretend to see death omens in a lump of tea leaves, I’m not sure I’ll be studying it much longer! That lesson was absolute rubbish compared with my Arithmancy class!
(Prisoner of Azkaban, Chapter 6, Talons and Tealeaves).

That conversation is the only time that we hear Hermione directly compare the two subjects. It seems that she believes that Divination involves making things up whereas Arithmancy has a more precise, objective, rational methodology. Additionally, she had something of a personal feud with Professor Trelawney, which she didn't have with Professor Vector.

Some further supplementary reasons why Hermione may have liked Arithmancy include:

  • She believed that it was a "sensible" subject, as the quote in the question points out.
  • Arithmancy involves numbers and mathmatics. That makes it very different from the more emotive and vague Divination.
  • Arithmancy was very difficult and, as we know, Hermione likes a challenge.

    “Only four exams left,” said Parvati Patil wearily as they headed back to Gryffindor common room.
    “Only!” said Hermione snappishly. “I’ve got Arithmancy and it’s probably the toughest subject there is!”
    (Order of the Phoenix, Chapter 31, O.W.L.s).

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    Yup, Hermione hates divination because it's a "soft science." – MissMonicaE Mar 20 '17 at 15:44
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    "Professor Vector", teaching a class about numbers... Well played, JK. – DisturbedNeo Mar 20 '17 at 15:54
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    So Hermione actually doesn't have a problem with Divination, just with Trelawney? Actually, that makes a lot of sense. – DisturbedNeo Mar 20 '17 at 15:55
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    @DisturbedNeo see also "Sprout", "Sybil Trelawney", "Remus Lupin", "Sirius Black", "Peeves"... Some of the students have insignificant names, but pretty much everyone else.. well, there's a reason that every character page on the Harry Potter wikia has an "etymology" section. – Tin Man Mar 20 '17 at 18:22
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    Arithmancy seems to be a for-realz science/maths. Right up Hermione's alley. – DVK-on-Ahch-To Mar 20 '17 at 21:43
14

One big part of it is that Arithmancy is something one can learn from books, and book-learning is Hermione's strength. Trelawney herself explicitly states that only those with special aptitude will do well in Divination, studying the text will be of little use; we see immediately that this puts Hermione 'off her game', and it is only natural that she would resent that.

Another big part of it is that Hermione is on the whole a Rationalist and a Skeptic. She is one of the few that can see immediately that Trelawney is a fraud trying to bluff her way through the class (through life, really - hence the copious amounts of sherry), and is not afraid to call her out. On some implicit level Trelawney realizes this and is striking back in her own way. Whoever is teaching Arithmancy doesn't have that problem - they really know the material - and as Hermione is doing as well in that class as in others then that teacher probably likes her as well as most of the other teachers.

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3

Someone answered the question very well already, but from the description you give, Arithmancy sounds like it's very close to Psychohistory from Asimov's Foundation series. Pioneered by Hari Seldon, it's meant to be the science of using laws pertaining probability applied to large numbers of people to plot the course of human history. In some of the later books we see Hari's "master equation", meant to be the entirety of human civilisation over a thousand year period, and it definitely looks far more concrete than the wishy-washiness of Divination. It's possible Rowling was drawing inspiration.

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2

From the Wikia page on Arithmancy:

Hermione has expressed open contempt for the subject of Divination, yet has also proclaimed that Arithmancy (in which numerology is prominent) is her favourite subject. While this may seem contradictory at first, it should be remembered that Arithmancy applies much more rigorous and mathematical approaches to predicting the future (which the scientifically-inclined Hermione would respond to), unlike Divination, which she detested because it seemed to be "a lot of guesswork."

Hermione likes Arithmancy because it's precise and calculable, not because it doesn't involve making predictions. The clockwork universe theory states, essentially, that the future has already been set and that, if you knew all the variables, you could predict exactly what it's going to be. The pre-Cursed Child Harry Potter universe, it can be argued, subscribed to this theory with its use of causal loops.

Basically, while Divination involves guessing the future, Arithmancy involves calculating it.

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    That "Behind the scenes" bullet point on the Wikia doesn't have a citation. That's not to say I don't like your answer, it makes a lot of sense, but technically speaking it is without a valid, canon reference. – DisturbedNeo Mar 20 '17 at 15:25
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    Exactly this. Plus Trelawney doesn't help her own cause, she "predicts" things she has direct control over (such as what will be on the exam) or that are common knowledge (Harry having a powerful enemy) while most of her other predictions are the kind of vague tricks employed by contemporary "psychics". That is bound to grate on someone as sceptical and grounded as Hermione. And to add to this, Prof McGonagall is quite disparaging of divination. – delinear Mar 20 '17 at 15:29
  • @DisturbedNeo You're right, it doesn't. Hermione's quote appears to be from Prisoner of Azkaban, but since I don't have the books in front of me I don't have a page number. – PlutoThePlanet Mar 20 '17 at 15:40
  • Well, PoA is the only book in which she took Divination before storming out, so I reckon you're probably right. – DisturbedNeo Mar 20 '17 at 15:51
1

Maybe Arithmancy is some sort of magical statistics, with logical rules and theorems. I would certainly see Hermione enjoying that.

Personally, I have always seen Arithmancy related to Asimov's psychohistory, only with more magic in it.

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