Maths- An Art or a Science?

rage against the leaving

What do ye think?

I've always been on the science side, but a lot of people see it as an art.

On a side note, is there any difference between a BA in Maths and a BSc in Maths?

LeixlipRed

Didn't we have this thread before? It's both. QED.

Fremen

Neither.

Just to be controversial.

LeixlipRed

Lizard?

Anonymo

Well as LeixlipRed said it's both. Usually it is regarded as the purest of the sciences, with the possibility of getting an exact answer given a (well-posed) problem. And of course, as an art, maths can be regarded as providing a web of patterns. However, I think a more topical debate would be the question as to whether maths should be taught as an art or a science. To my mind there is no doubt that arguments in favour of teaching as a science are much stronger. However some of the lads who lectured me during my undergrad had the opinion that it was an art and attempted to teach it as such. There is, I think, a big difference between the two. As a science, maths is taught as a toolkit to help solve different problems. As an art, it's taught as a complete piece whose structure is to be uncovered. I'd like to know if others agree with this summary and which approach to teaching others would endorse.

Pherekydes

rage against the leaving wrote: »

On a side note, is there any difference between a BA in Maths and a BSc in Maths?

Without giving a rigorous proof, no. Or yes.

Fremen

Well, arts degrees tend to be three years long, whereas science degrees tend to be four. That means 33% more maths in a science degree, all other things equal.

Pherekydes

Fremen wrote: »

Well, arts degrees tend to be three years long, whereas science degrees tend to be four. That means 33% more maths in a science degree, all other things equal.

In Maynooth, the BSc comprises the following modules (Maths only):

Year 1: 4 modules
Year 2: 4 modules
Year 3: 6 modules
Year 4: 4 compulsory modules, plus up to 8 additional modules.

The BA comprises:

Year 1: 8 modules
Year 2: 6 compulsory modules, plus 2 optional modules in the 40/20 credit version
Year 3: 4 compulsory modules, plus up to 8 optional modules

The total numbers of modules (all of 5 credits each) is:

BSc 26, BA 28.

Note that in the BA program, level 100 and level 200 modules are covered in year 1. In other words, they "catch up" the BSc by doing twice as much Maths in first year. In conclusion, I don't think there's any difference between a BA and a BSc in Pure Mathematics.

You can also do a BA in Maths Studies, followed by a PGDip in Pure Maths, which together are equivalent to a BA or BSc in Maths.

Eliot Rosewater

Do the BSc students take modules in "understanding humour online" instead?

COUCH WARRIOR

It's neither. It's a bit like asking if bacteria are animals or plants. Is logic an art or a science?

fergalr

There's a big debate about what science is, and isnt.
But if you require testable hypotheses, and think this idea that you can find things out by making claims that are refutable, and testable by experiment, as core to science, then maths isn't really a science.

There's a lot in common to how the practice of certain kinds of maths and science are conducted, but philosophically, you wouldn't say its a science.


Art is notoriously hard to define.
You think its about paintings and stuff, and then someone puts their soiled bed in a gallery.


But if you are going to say that maths is discovered, rather than created, its hard to see how you'd call it art.
It might be beautiful, but its beautiful in the way a spectacular view of a natural landscape that you stumble upon is beautiful.

You wouldn't call that art.



You might say there is artistic value in the choices we make about sort of maths to study, and to do; what axioms to postulate.
Maybe that is art; but maybe its really like choosing where to go for the walk.


Is a photograph of a beautiful thing, art?
The photographer is more choosing how to compose the picture, and from what perspective to take it, rather than creating what is in the picture. The art of the photographer is where to position their viewpoint in the world.


I guess, if you take that view of photography, and agree that its art, you could argue that a mathematician, by virtue of choosing what perspective to look from, might be making art.


Perhaps a good math paper, describing something beautiful, might be art, in the way a photograph of a beautiful landscape is.
But maybe then, its the paper that is the art, and the maths remains separate from the artefact.

I guess you could still say the practice of mathematics is art, in the way photography is.



I'm not sure.
I think the question is more about how you define the word 'art', rather than one whose answer will tell us anything interesting about maths.

I'd love to hear more about this, from people have that thought more about it.

(edit: I think we should exclude people talking about 'the art of doing maths' or 'the art of logic' or some such - because thats really a different meaning of 'art', and means closer to 'practice')