I were chatting with a friend of mine, not really a Harry Potter fan, but we were talking about the subjects taught at Hogwarts and what the corresponding real life subjects would be and all that. Then we came on the field of mathematics, and our discussion took an unexpected turn, and progressed like this:

Her: So do they have math at Hogwarts?
Me: Not math exactly, but Arithmancy is sort of like math.
Her: Arithmancy?
Me: The easiest way of explaining it would be... It's about studying the magical properties of numbers and predict the future.
Her: So it's like - probability calculations or something?

And I was stuck, because I always thought of like, heart numbers and stuff when it comes to Arithmancy, but if it can be used like she asked, a wizard sufficiently adapt at Arithmancy could theoretically through some quick thinking achieve something akin to precognitive sight. Now that would be actually kind of cool! :-D

 

There's nothing mentioned about Arthimancy in canon aside from the fact that it's very difficult and not at all like Trelawney's Divination classes.

 

Here's what we know about arithmancy:

1. It's "predicting the future with numbers".

2. It's less "woolly" than Divination.

3. You need it to be a curse breaker.

4. Numbers have magical properties (horcruxes).

What can we take away from this? I think 1 and 2 are the most important, because it presents a contradiction that requires an explanation: it's about telling the future but it isn't divination. How can you tell the future without being a branch of divination? I think the answer is that you tell the future based on the known present - the only way to avoid the woolliness of Divination is, in my mind, to base your prediction on that which is known. That is, arithmancy is the magical equivalent of a model (in the sense of "economic model"). Everything in the world would have some numerological value associated with it, and you can predict the likely behaviour of the world by using arithmetical laws to combine those values and interpret the meaning of the result.

It's easy to see how this would be of value to curse-breakers: it allows them to evaluate the potential success of a curse-breaking strategy without having to actually do it, meaning they can minimise their risk. Like, you take the numerology of the spell you're thinking of using, and the numerology of the curse you're wanting to counter, and use arithmetical laws to analyse how the two interact.

 

You just blew my mind. THAT'S how awesome you just are. :O

 

So in other words it's a magical version of probability and statistics?

 

That's how I understood it, but Taure made it sound way cooler.

 

comparing it to probability and statistics is an insult to the former math fields.
We do not know, why it is required in order to become a curse breaker.
It could be just a Ministry requirement, that has nothing to do with the field of curse breaking.
It could be considered a noble art that somehow related to Wizardry culture, and due to the Ministry "control" on registration you require to have OWL or higher degree in it.
We have no link between Enchanting and arithmancy in canon.
All we have that the class mindset is different from Divination, it lie with the teacher and not the subject.

 

I think that she has gotten it right. Because in my opinion it is pretty similar to probability because you are looking at possible ways the future might be going too.

 

I think Arithmancy sits perfectly with real life beliefs such as Numerology and Gematria. They are systems used to analyze the world (mystically) using numbers and their importance, and can be used for predictions. Those systems also regard 7 as the most magically powerful number. "The Black Arts" by Richard Cavendish explains it pretty well. It has very little to do with Math as it's taught to us. It predicts the future in the sense that "if 13 people sit at a table, the first to rise will be the first to die" and so on, not in the sense that "if a train travels at X speed and has Y number of miles to go, it will arrive at its destination in Z amount of minutes".