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Is mathematics a science?

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Jitro
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12 Nov 2012, 9:02 pm

Some people say that it is. Others say that it is not.



Fnord
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12 Nov 2012, 9:48 pm

Is English England?

No, English is the language of England.

In a similar way, mathematics is the language of science.


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Jitro
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12 Nov 2012, 9:55 pm

Fnord wrote:
Is English England?

No, English is the language of England.

In a similar way, mathematics is the language of science.


Mathematics is not a language in the linguistic sense.



Fnord
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12 Nov 2012, 10:00 pm

It is when you know and understand what the symbols mean.


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Kurgan
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12 Nov 2012, 10:06 pm

Math is actually far more intuitive (and universal) than any language. Take a look at the treacherous spelling in the English language (eg. how the "a" in "atom" is pronounced in a different manner than the "a" in "art"). Now take a look at how orderly math is; the same arithmetic rules are valid everywhere, from our own Earth to the core of a neutron star to the farthest galaxies.



Last edited by Kurgan on 12 Nov 2012, 10:10 pm, edited 1 time in total.

Fnord
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12 Nov 2012, 10:09 pm

Kurgan wrote:
Math is actually far more intuitive (and universal) than any language. Take a look at the treacherous spelling in the English language (eg. how the "a" in "atom" is pronounced in a different manner than the "a" in "art"); now take a look at how orderly and universal math is.

Ampere's Law ...

Image

Have you ever seen anything expressed more eloquently (Outside of Shakespeare or Dante)?


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Jono
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13 Nov 2012, 2:10 am

Mathematics has been called a "science" mostly due to the original definition of the word, which just means a field of knowledge, however it is not a science in the empirical sense as it does not use the scientific method. Although there is such a thing as experimental mathematics, rigorous mathematical proofs are still considered more important to mathematics than demonstrations, still differentiating it from science in the Popperian sense. However, mathematics is also the only field of knowledge that can develop without empirical investigation, mainly because it deals with abstract concepts and their logical consequences, not with the outside world (unless for some reason you decide to include philosophy, that is).



ruveyn
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13 Nov 2012, 8:59 am

Fnord wrote:
Kurgan wrote:
Math is actually far more intuitive (and universal) than any language. Take a look at the treacherous spelling in the English language (eg. how the "a" in "atom" is pronounced in a different manner than the "a" in "art"); now take a look at how orderly and universal math is.

Ampere's Law ...

Image

Have you ever seen anything expressed more eloquently (Outside of Shakespeare or Dante)?


Yes. The covariant version of Maxwells equations is even prettier.

Maxwell was a capital G genius for coming up with the displacement current (the second term on the right). He did it on a priori principle grounds of conserving charge and not having a current coming from Nothing. It was not a common empirical fix at all, because at the time there was no empirical reason for asserting the existence of the displacement current. It was purely mathematical, but it turned out also to be right.

ruveyn



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13 Nov 2012, 11:18 am

Jitro wrote:
Fnord wrote:
Is English England?

No, English is the language of England.

In a similar way, mathematics is the language of science.


Mathematics is not a language in the linguistic sense.
Yes, it is :/


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Jitro
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13 Nov 2012, 11:40 am

Vexcalibur wrote:
Jitro wrote:
Fnord wrote:
Is English England?

No, English is the language of England.

In a similar way, mathematics is the language of science.


Mathematics is not a language in the linguistic sense.
Yes, it is :/


No it's not. It doesn't have words nor grammar. The mathematical concepts have to be expressed the English language (or some other language).



Vexcalibur
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13 Nov 2012, 11:43 am

Jitro wrote:
Vexcalibur wrote:
Jitro wrote:
Fnord wrote:
Is English England?

No, English is the language of England.

In a similar way, mathematics is the language of science.


Mathematics is not a language in the linguistic sense.
Yes, it is :/


No it's not. It doesn't have words nor grammar. The mathematical concepts have to be expressed the English language (or some other language).
It has words and grammar.


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ruveyn
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13 Nov 2012, 11:54 am

Vexcalibur wrote:
Jitro wrote:
Vexcalibur wrote:
Jitro wrote:
Fnord wrote:
Is English England?

No, English is the language of England.

In a similar way, mathematics is the language of science.


Mathematics is not a language in the linguistic sense.
Yes, it is :/


No it's not. It doesn't have words nor grammar. The mathematical concepts have to be expressed the English language (or some other language).
It has words and grammar.


But is not susceptible to empirical falsification. The objects of a mathematical theory do not exist in the physical universe outside our skin. They live in our heads.

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ScrewyWabbit
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13 Nov 2012, 12:48 pm

Math is simply a tool to quantify and measure the universe around us. As such, it provides a framework for other sciences, but it is not a science itself, just an area of knowledge and understanding, I'd say.



Fnord
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13 Nov 2012, 3:27 pm

Vexcalibur wrote:
Jitro wrote:
Vexcalibur wrote:
Jitro wrote:
Fnord wrote:
Is English England? No, English is the language of England. In a similar way, mathematics is the language of science.
Mathematics is not a language in the linguistic sense.
Yes, it is :/
No it's not. It doesn't have words nor grammar. The mathematical concepts have to be expressed the English language (or some other language).
It has words and grammar.

Words are symbols that represent concepts. Mathematical symbols represent concepts.

Numerals and constants can be nouns or adjectives.

Variables are the pronouns.

Operators (+, -, x, /, et cetera) are the verbs and adverbs.

Formulas are sentences.

Algorithms are paragraphs.

It's all so simple, once you know and understand the language.


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ruveyn
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13 Nov 2012, 5:11 pm

ScrewyWabbit wrote:
Math is simply a tool to quantify and measure the universe around us. As such, it provides a framework for other sciences, but it is not a science itself, just an area of knowledge and understanding, I'd say.


Pure abstract mathematics that is done for its own sake rather than for another task, has become an art form. Remarkably, some of the abstract art has later become useful in science. For Example, Reimann's analysis of tensors and higher dimensional spaces and their curvature became the main weapon for Einstein and his theory of gravitation. Also Group Theory, invented by Galois later became the heart and center of physical theories of symmetry.

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slave
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15 Nov 2012, 9:10 pm

Jono wrote:
Mathematics has been called a "science" mostly due to the original definition of the word, which just means a field of knowledge, however it is not a science in the empirical sense as it does not use the scientific method. Although there is such a thing as experimental mathematics, rigorous mathematical proofs are still considered more important to mathematics than demonstrations, still differentiating it from science in the Popperian sense. However, mathematics is also the only field of knowledge that can develop without empirical investigation, mainly because it deals with abstract concepts and their logical consequences, not with the outside world (unless for some reason you decide to include philosophy, that is).


Hmmm..... :scratch: