Is Mathematics an art or a science?

Science is usually a field of observation, whereby we can test and prove things using empirical evidence from experiments. This is not true for mathematics.

What do you guys think?

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Reply 1

racheltriggs4

What a lovely question.

It's generally accepted that mathematics is objective rather than subjective, and most people argue that therefore it means it isn't art.

However, I think it kind of is if you think about it, art is where you take an idea and express it in a different way. You could paint about world peace, sing about love, photograph the bond between a mother and son or write a poem about the colour blue. With maths, you take something that's not necessarily numerical and convert it into numbers and wonderful algebraic formulae. I read a book not long ago that expressed population as a formula (more about that here), and I think to be able to do that is art.

Reply 2

username2130115

Original post by High Stakes

Science is usually a field of observation, whereby we can test and prove things using empirical evidence from experiments.

I think that definition is too narrow for science. There are many different types of science; life science, natural science, physical science, mathematical science, and social science. Defining science as a field that proves things in its subject by 'empirical evidence from experiments' would discount all the mathematical sciences as a science because the mathematical sciences such as Computer Science or Pure Mathematics do not use empirical evidence to prove the truth or falsity of a hypothesis. For instance, to prove an autopilot algorithm will not fail under any given circumstances, you would not use it to fly a plane under loads of different weather conditions, you'd use formal methods to prove the algorithm is correct. This is similar to the type of proof used in the mathematical sciences, e.g. proof by induction; to prove Gauss' summation formula, you wouldn't do it by seeing if it gives the correct answer for the sum of the first 10, first 20, first 30, first 40 integers, and so on, you'd use a more rigorous method like proof by induction. None of these mathematical proof methods rely on experimental evidence. Therefore, I think it is better to think of science as a field of systematic study which tries to prove hypothesises related to physical or abstract structures by inductive arguments (experimental observation) or deductive arguments (mathematical proof).

(edited 8 years ago)

Reply 3

ChaoticButterfly

I'd class it as a part of philosophy.

Reply 4

username1539513

Original post by High Stakes

Science is usually a field of observation, whereby we can test and prove things using empirical evidence from experiments. This is not true for mathematics.

What do you guys think?

It is a language; albeit a scientific one

It is a means of expressing concepts that would be impossible to express well with mere words

Reply 5

username2151383

mathematics is the art of self hatred

Reply 6

EricPiphany

An art and a philosophy.

Reply 7

whydoidothis?

Some of it is a branch of philosophy.

Reply 8

Smaug123

Why is the answer not "both"?

Reply 9

Juichiro

Original post by High Stakes

Science is usually a field of observation, whereby we can test and prove things using empirical evidence from experiments. This is not true for mathematics.

What do you guys think?

You have reached the conclusion. It is not a science. That does not mean that it is not important and stuff but it is not science.

Original post by racheltriggs4

What a lovely question.

1. It's generally accepted that mathematics is objective rather than subjective, and most people argue that therefore it means it isn't art.

However, I think it kind of is if you think about it, art is where you take an idea and express it in a different way. You could paint about world peace, sing about love, photograph the bond between a mother and son or write a poem about the colour blue. With maths, you take something that's not necessarily numerical and convert it into numbers and wonderful algebraic formulae. I read a book not long ago that expressed population as a formula (more about that here), and I think to be able to do that is art.

1. Just because something is not art does not mean that it is science. :smile:

Math is neither art or science.

1. No, it isn't.
2. You are begging the question. Social science, biology/chemistry and physics are all empirical.
3. That's right. And that is why CS and Maths are not sciences.
4. True.
5. It does not follow from your premise. Nor do you explain why it is "better" beyond "I think that definition is too narrow". Someone could come alone and say: hey, I think your definition is too narrow. In the religious sciences, we prove things by faith. Therefore, I think it is better to think of science as a field of systematic study which tries to prove hypothesises related to physical or abstract structures by inductive arguments (experimental observation), deductive arguments (mathematical proof) or faith (spiritual observation). And someone else could come and widen the definition and so on until the definition of science is so general that literally everything is a science. I don't see the point of trying to include maths in the category of science. You can't add it without changing the definition of science itself. That should be telling enough that maths does not belong there.

Reply 10

username2130115

Original post by Juichiro

5. It does not follow from your premise. Nor do you explain why it is "better" beyond "I think that definition is too narrow". Someone could come alone and say: hey, I think your definition is too narrow. In the religious sciences, we prove things by faith. Therefore, I think it is better to think of science as a field of systematic study which tries to prove hypothesises related to physical or abstract structures by inductive arguments (experimental observation), deductive arguments (mathematical proof) or faith (spiritual observation). And someone else could come and widen the definition and so on until the definition of science is so general that literally everything is a science. I don't see the point of trying to include maths in the category of science. You can't add it without changing the definition of science itself. That should be telling enough that maths does not belong there.

If science only includes the empirical subjects then you'd have to make an argument that mathematics is an art or mathematics is neither art or science. I think making an argument for the former would be difficult since when we think of art we think of subjective things like literature, religion, paintings etc; mathematics has lots of structure, mathematical proofs are objective and thus not falsifiable whereas literature and paintings are open to interpretation.

Reply 11

Juichiro

1. Technically, you could put anything you want inside the category of art since the definition of art itself is ambiguous enough. I would go for maths is neither art or science.

Reply 12

DaysOfOurUni

Original post by High Stakes

Science is usually a field of observation, whereby we can test and prove things using empirical evidence from experiments. This is not true for mathematics.

What do you guys think?

I've always believed Maths to be a language. I'm always curious when people are surprised by interesting patterns that emerge in nature and maths. We developed the language, it didn't have to be decimal so obviously there are going to be patterns!

I honestly think Maths should have the same classification as other language studies.

Reply 13

Smaug123

Original post by DaysOfOurUni

Some of maths certainly feels quite a lot like a science to me. I'm currently learning forcing, and it's like I've been handed a machine and I'm trying to work out how it works and what I can do with it. On the other hand, category theory feels more like the study of a language; combinatorics feels like a mixture of engineering and art.

Reply 14

DaysOfOurUni

Original post by Smaug123

Here's the thing: it sounds really complicated...but that's literally the only thing that makes people think it's scientific! It's still just a language. You still just have to memorise equations and calculations (/ grammar and vocabulary etc.)

I remember when I first saw computer programming languages like Python and Java and it all looked so complicated and then when I started 'translating', I realised how simple it was.

Reply 15

username1560589

Original post by High Stakes

Science is usually a field of observation, whereby we can test and prove things using empirical evidence from experiments. This is not true for mathematics.

What do you guys think?