Is Mathematics an art or a science?

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High Stakes
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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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racheltriggs4
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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.
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username2130115
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(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).
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ChaoticButterfly
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I'd class it as a part of philosophy.
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username1539513
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(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
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username2151383
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mathematics is the art of self hatred
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EricPiphany
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An art and a philosophy.
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whydoidothis?
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Some of it is a branch of philosophy.
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Smaug123
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Why is the answer not "both"?
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Juichiro
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(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. 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.
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username2130115
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(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.
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Juichiro
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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.
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DaysOfOurUni
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(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.
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Smaug123
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(Original post by DaysOfOurUni)
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.
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.
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DaysOfOurUni
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(Original post by Smaug123)
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.
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.
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username1560589
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(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 can prove things using empirical evidence in maths(counterexample).

I don't really care what it's categorised as, it's maths.
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Absent Agent
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(Original post by morgan8002)
You can prove things using empirical evidence in maths(counterexample).

I don't really care what it's categorised as, it's maths.
Having a deep understanding of the discipline allows you to categorise it though.
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meediaabid
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I like to think of it as its own thing, neither an art or a science but sometimes the foundation of both
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Smaug123
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(Original post by DaysOfOurUni)
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.)
Ah, you're talking about A-level maths. I'm talking about graduate maths.
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DaysOfOurUni
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(Original post by Smaug123)
Ah, you're talking about A-level maths. I'm talking about graduate maths.
Nope, I'm talking about all maths :-)
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