How do you define mathematics? I took a watered-down physics class where you needed limited math skills. The teacher gave us all a sheet full of equations that he allowed us to use on the tests. I thought that that was ridiculous, but he said that he wasn't testing us on our memorization skills; he was testing us on our knowledge with using them. My friend and I never used those; we both knew calculus and we did the math on all of the physics problems and tests. With math, my friend and I managed to derive these formulas that he gave us. Because of this, I used to consider math to be a science. However, after reading this http://www.frihost.com/forums/vt-76771.html post, I realized that mathematics cannot be considered science. It does not follow the scientific method, and everything is proved in math. In science, nothing is proven. So since math cannot be considered a science, what can you define it as? Can you define it as a tool used in math? Or is math simply an art?
How do you define mathematics?
You can define it as a language, that's one way of looking at it. It's the language of science - all sciences use Math to express unambiguous concepts.
i would describe it as a way of seeing numbers and the relation between them like how we have love and hatred between human beings
Mathematics is for me a basic science. It is necessary to understand and proof other sciences. Someone who is missing the basics will never be able to have a clear view on other subjects. It will stay very hard to complete some courses or investigations. Also in real life it is necessary to have some basic knowledge, like getting control of the shoppingactivities.
| Georgeboy wrote: |
| Mathematics is for me a basic science. It is necessary to understand and proof other sciences. Someone who is missing the basics will never be able to have a clear view on other subjects. It will stay very hard to complete some courses or investigations. Also in real life it is necessary to have some basic knowledge, like getting control of the shoppingactivities. |
Defining math as a science is problematic since it doesn't follow the scientific method. It could equally well be defined as an 'art' - "skill in performance acquired by experience, study, or observation".
That's why I prefer to define math as a language.
You are, of course, correct to say that Math is a vital part of many subjects - all the sciences (including the social sciences) rely on a good understanding of basic math.
A subject / course which you dont like to study in your lifetime is nothing but Mathematics. And this is relative 
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| indianinworld wrote: |
| A subject / course which you dont like to study in your lifetime is nothing but Mathematics. And this is relative 8)
Keep Smiling - Keep Living !!!! _________________ as alwayZz - Cheers and Cherish indianinworld Visit me @ : http://www.sathish.frih.net |
A subject that you don't like to study? Wow, and all this time I thought that I'd taken math classes in my life... I guess I'm one of the weird people that love it.
Why bother typing a quote from a site. Just give the link like this:
http://www.math.ubc.ca/~scull/math230/whatismath.html
http://www.math.ubc.ca/~scull/math230/whatismath.html
I think the subject of Mathematics could be said to be quantity, pattern, and relationship.
I think the object of Mathematics is to formalize the description of these things, while making it possible to express very complicated ideas using very simple and sparse ideography.
Who remembers story problems from grade school?
Well interpreting from those stories to the abstract language of mathematics seems to be the essence of the whole thing to me.
Which is quicker and easier to express?
If Sally has five marbles, Johnny has twice as many marbles as sally, and Sue has 4 more marbles than Johnny's amount
Or...
X = 2*5 + 4
So... yeah.
Abstraction.
Consolidation.
Compression.
Of things that we already do every day... it's an efficiency thing.
Tell your mom I love her,
Uwe
I think the object of Mathematics is to formalize the description of these things, while making it possible to express very complicated ideas using very simple and sparse ideography.
Who remembers story problems from grade school?
Well interpreting from those stories to the abstract language of mathematics seems to be the essence of the whole thing to me.
Which is quicker and easier to express?
If Sally has five marbles, Johnny has twice as many marbles as sally, and Sue has 4 more marbles than Johnny's amount
Or...
X = 2*5 + 4
So... yeah.
Abstraction.
Consolidation.
Compression.
Of things that we already do every day... it's an efficiency thing.
Tell your mom I love her,
Uwe
I would say maths is a language as stated above.
But I would say it could be seen as a science when used for
computer programming.
It depends on what you see as the science in computing.
Is it the software or the physical surface chemistry.
But I would say it could be seen as a science when used for
computer programming.
It depends on what you see as the science in computing.
Is it the software or the physical surface chemistry.
Hey suddenly I have become a Language specialist. Try telling that to the admissions professsors at Oxford or Cambridge Unis a few years ago. Maths is not like the other "languages" you study. Maths is a tool to help you make sense of a problematic world around you. B is correct in saying that it is vital to helping to make sense of the scientific world. But it is a wide collection of quite disperate tools, particularly in Maths defined as "Pure", as opposed to "Applied". Even these two categories are quite wide and contain numerous branches dealing with abstract impossabilities in the real world which when combined do exist. Best definition is Science's "Tool" wether the science is Physics, Chemistry etc or the social sciences.
for me maths is always a very difficult subject.....all numbers revolves around my head.....i am very weak in maths......it always scared me....
In my opinion, maths is an tactical-base subject. It requires frequent practices and throughful understanding of it. I like mathematics since I was first taught on how to count. I still remember when I was 5, I have trouble to memorize the multiplication tables too and my mom just ask me sit there for a whole night so that I can memorize it well.
Mathematics.... have taught me that nothing in the world is throughly flat... there maybe only one solution in the question but you may take various of technique to calculate it out. That makes math fun.
Mathematics.... have taught me that nothing in the world is throughly flat... there maybe only one solution in the question but you may take various of technique to calculate it out. That makes math fun.
Maths are a science....what you have been defining as science are actually experimental sciences, only a sub-class of science which are limited to the dimensions for which they were defined, to the possibilities allowed by the physical world we are living in. That gives them this relative aspect of being controllable. Mathematics are a science, allowing you to put abstraction maske on pretty much all concepts that your mind can process, from philosophy and metaphysics (careful, philosophy is typically not a science because not always provable, just partly... this is a complex issue...) to the sciences we know in our every day life. Mathematics are the glue that bring all sciences together, you can use them for chemistry, physics, logics, computer csience, industrial engineering, finance... everything. To achieve thismathematics are composed of many unitary disciplines such as arithmetics, geometry, analysis, topology,....etc.
Is The True Science Or The Science Of Numbers.
Realy I Love math
Realy I Love math
| supjapscrapper wrote: |
| Maths are a science....what you have been defining as science are actually experimental sciences, only a sub-class of science which are limited to the dimensions for which they were defined, to the possibilities allowed by the physical world we are living in. That gives them this relative aspect of being controllable. Mathematics are a science, allowing you to put abstraction maske on pretty much all concepts that your mind can process, from philosophy and metaphysics (careful, philosophy is typically not a science because not always provable, just partly... this is a complex issue...) to the sciences we know in our every day life. Mathematics are the glue that bring all sciences together, you can use them for chemistry, physics, logics, computer csience, industrial engineering, finance... everything. To achieve thismathematics are composed of many unitary disciplines such as arithmetics, geometry, analysis, topology,....etc. |
But it can't be science. You don't use the scientific process or do any type of experimenting. I've been thinking about this a lot lately, and I've come to one solution. Math is an art.
Maths is the prescribed method for describing the real world. An example of this can be seen when we define the rate of speed an object falls to the ground from a certain height we include a 'constant' so that the product of the formula for calculating the speed of the falling object on impact is always the correct answer. We created a formula but don't understand fully why it works.
| Dlstreet wrote: |
| Is The True Science Or The Science Of Numbers.
Realy I Love math |
Well, math isn't just numbers. According to Wikipedia, it seems mathematicians like to call math as the subject of looking at patterns.
This is my way of defining math, using the idea of patterns: "math is about making patterns make sense, and thinking creatively about them."
| Afaceinthematrix wrote: |
| But it can't be science. You don't use the scientific process or do any type of experimenting. I've been thinking about this a lot lately, and I've come to one solution. Math is an art. |
Sure you use the scientific method, and you do experiments, too - you just don't do them on the natural world, you test theories with test cases.
The only difference between math and science is that science is dealing with the open physical universe and math is dealing with a closed logical universe. Otherwise they're identical, even down to speaking the same language.
There's no way math can be an art. It is far too rigorous, and entirely contrary to whimsical interpretations of its axioms. 1 + 1 does not equal 2 because it is pretty or aesthetically pleasing or because someone arbitrarily defines it to be so, it equals 2 because it must, no matter what anyone, anywhere, anyhow feels.
But the world is not black and white, and the antithesis of science is not art. Mathematics cannot be a science because it does not rely on observation of the universe (or on the universe at all), and it cannot be an art because it is strictly rigorous and axiomatically defined. So, it's something else. It doesn't have to be one or the other.
| nilsmo wrote: |
| This is my way of defining math, using the idea of patterns: "math is about making patterns make sense, and thinking creatively about them." |
Wouldn't that make a florist a mathematician, too? ^_^; Or someone who designs bathroom tiles?
| Indi wrote: |
|
Sure you use the scientific method, and you do experiments, too - you just don't do them on the natural world, you test theories with test cases. |
No, you don't do experiments or use a "scientific method." The only way in which you can do this would be trial in error, but that's not really math.... That's just trying to figure out an answer because of a lack of knowledge on how to correctly approach the problem.
| Indi wrote: |
|
There's no way math can be an art. It is far too rigorous, and entirely contrary to whimsical interpretations of its axioms. 1 + 1 does not equal 2 because it is pretty or aesthetically pleasing or because someone arbitrarily defines it to be so, it equals 2 because it must, no matter what anyone, anywhere, anyhow feels. |
I'm still convinced that math is an art. Many people look at "applied math" and see it's usefulness. Calculus is extremely useful in physics, for instance. I, however, see things extremely different. Most of the math I take now is abstract math - math that has absolutely no use in the "real world." Try proving that useless math. It gets even more useless. Why do I do this? Why do I spend hours and hours of my life studying this? I wondered this a lot until recently. One night I was working on a proof that I couldn't figure out. I started at 9 P.M. at night and finished at 6 A.M. in the morning (I can't sleep usually until I figure those types of things out). After I finished it, I looked down at my paper. I had many erase marks, scratch outs, and crumbled pieces of paper next to me. That's when it came to me. This is an art. This isn't a tool used in science (it's useless). This is a wonderful art that only a few people can find the beauty in. It doesn't matter how complicated it is. Chess is an extremely complicated game (I've spent hours of my life studying chess and various positions) yet many Grandmasters have considered it an art. What makes math any different?
| Afaceinthematrix wrote: |
| No, you don't do experiments or use a "scientific method." The only way in which you can do this would be trial in error, but that's not really math.... That's just trying to figure out an answer because of a lack of knowledge on how to correctly approach the problem. |
The scientific method is basically notice, theorize, test, repeat. The development of mathematical concepts works pretty much the same way. You notice something about something... let's say you notice that certain differential equations that are stable most of the time behave in a peculiar way for certain ranges of the parameters. You theorize that this is because of something else... let's say you suspect that that is because the solution is not continuous at those values. Then you check see if you're right... by attempting to show it by a proof.
Or, you know, you can look at it another way. Someone has already made a proof of something, and you think some part of it is screwy. So you do a test using test cases and find a case where the proof breaks down. And, when you do, you attempt to find out why. Etc.
The only reason it's not the actual scientific method is because it does not involve experimentation and observations of the natural universe - it deals with a "universe" that is an axiomatically defined, closed system of logic.
| Afaceinthematrix wrote: |
| I'm still convinced that math is an art. Many people look at "applied math" and see it's usefulness. Calculus is extremely useful in physics, for instance. I, however, see things extremely different. Most of the math I take now is abstract math - math that has absolutely no use in the "real world." Try proving that useless math. It gets even more useless. Why do I do this? Why do I spend hours and hours of my life studying this? I wondered this a lot until recently. One night I was working on a proof that I couldn't figure out. I started at 9 P.M. at night and finished at 6 A.M. in the morning (I can't sleep usually until I figure those types of things out). After I finished it, I looked down at my paper. I had many erase marks, scratch outs, and crumbled pieces of paper next to me. That's when it came to me. This is an art. This isn't a tool used in science (it's useless). This is a wonderful art that only a few people can find the beauty in. |
Oh, that's just a combination of lack of imagination (not seeing how it is useful) and lack of sleep (having a transcendental experience over a math proof).
It's useless, eh? You know, they once thought imaginary numbers were completely useless theoretical nonsense. Now they are fundamental in electronics, quantum physics, pretty much anything that deals with periodic functions. They also thought Lie groups and Riemann surfaces were just theoretical and would never have practical applications... and now they are fundamental in cutting edge physics. Not to mention Calabi-Yau math. In fact, i'd like to quote Brian Greene from The Elegant Universe (start of c. 6):
| Quote: |
| In 1968, a young theoretical physicist named Gabriele Veneziano was struggling to make sense of various experimentally observed properties of the strong nuclear force. Veneziano, then a research fellow at CERN, the European accelerator laboratory in Geneva, Switzerland, had worked on aspects of this problem for a number of years, until one day he came upon a striking revelation. Much to his surprise, he realized that an esoteric formula concocted for purely mathematical pursuits by the renowned Swiss mathematician Leonhard Euler - the so-called Euler beta-function - seemed to describe the numerous properties of strongly interacting particles in one fell swoop. |
| Afaceinthematrix wrote: |
| It doesn't matter how complicated it is. Chess is an extremely complicated game (I've spent hours of my life studying chess and various positions) yet many Grandmasters have considered it an art. What makes math any different? |
i have no idea. i don't recall saying that math was not art because it is complicated. i said that it was not art because it was universally objective and rigorously defined.
| Indi wrote: | ||
Wouldn't that make a florist a mathematician, too? ^_^; Or someone who designs bathroom tiles? |
By make sense of patterns I mean looking and thinking about "the core" of the patterns. ("The core" is a bit vague I know... who sees what I mean?) If a florist or tile designer is doing this then, sure, I'd call them mathematicians: I can actually see a florist making patterns of flowers, and seeing that they're a fibonacci sequence or something.
(But if they're just making their designs look pretty then it wouldn't make them a mathematician.)
mathematics is infinite. Mathematics is the science that studies the relationships between elements whether they are numbers, geometrical figures, groups...
Mathematics is the best of science. It is simple, Elegant yet powerful!
Mathematics is the best of science. It is simple, Elegant yet powerful!
| smurky182 wrote: |
| the relationships between elements |
Yup, that's what patterns would mean. It seems we have pretty much the same ideas here on defining mathematics.
| nilsmo wrote: | ||
Yup, that's what patterns would mean. It seems we have pretty much the same ideas here on defining mathematics. |
| Indi wrote: | ||
The scientific method is basically notice, theorize, test, repeat. The development of mathematical concepts works pretty much the same way. You notice something about something... let's say you notice that certain differential equations that are stable most of the time behave in a peculiar way for certain ranges of the parameters. You theorize that this is because of something else... let's say you suspect that that is because the solution is not continuous at those values. Then you check see if you're right... by attempting to show it by a proof. Or, you know, you can look at it another way. Someone has already made a proof of something, and you think some part of it is screwy. So you do a test using test cases and find a case where the proof breaks down. And, when you do, you attempt to find out why. Etc. The only reason it's not the actual scientific method is because it does not involve experimentation and observations of the natural universe - it deals with a "universe" that is an axiomatically defined, closed system of logic. |
The lack of experimentation is what makes it different from science. Experimentation is a key aspect of science.
| Indi wrote: | ||||
Oh, that's just a combination of lack of imagination (not seeing how it is useful) and lack of sleep (having a transcendental experience over a math proof). It's useless, eh? You know, they once thought imaginary numbers were completely useless theoretical nonsense. Now they are fundamental in electronics, quantum physics, pretty much anything that deals with periodic functions. They also thought Lie groups and Riemann surfaces were just theoretical and would never have practical applications... and now they are fundamental in cutting edge physics. Not to mention Calabi-Yau math. In fact, i'd like to quote Brian Greene from The Elegant Universe (start of c. 6):
|
A lot of math does have uses, but some of it does not. It's not a lack of imagination on my part; it's a lack of use of the math's part. Try proving that 1+1=2. Even little kids intuitively know that 1+1=2, so why would anyone waste time proving that? People with the love for the art of math would spend time proving that. Know one else will spend time proving that.
| Indi wrote: | ||
i have no idea. i don't recall saying that math was not art because it is complicated. i said that it was not art because it was universally objective and rigorously defined. |
Sorry, I misunderstood that last part. You said, "There's no way math can be an art. It is far too rigorous..." and I interpreted, incorrectly, that by "rigorous" you meant "complicated."
| Afaceinthematrix wrote: |
| The lack of experimentation is what makes it different from science. Experimentation is a key aspect of science. |
Experimentation is not the key aspect, observation is. Experimentation is just usually the best way to make observations of the physical universe. There are many cases where no experiments are done at all, just observations made - especially in cases where experimentation is simply impossible. The scientific method is observe-hypothesize-predict-observe (repeat). Experiments are just a convenient way to quickly and accurately make observations of specific predictions - if the prediction is that hot water will freeze faster than cold water outside, then you can either sit around and wait for a situation where you have two bodies of water at different temperatures sitting side-by-side and observe what happens... or you can make an experiment and observe it at your leisure while having better control over the variables.
In mathematics you don't have to deal with the vagaries of the physical universe, and it is much easier to make observations without the need for setting up controlled experiments. You can still run tests - if someone theorizes that one equation is another form of another, you can apply the scientific method directly: observe whether it works for standard values, hypothesize why it works, predict what cases it might fail under, and observe again. Proving things axiomatically is not the only way things are done in mathematics, it's just the preferred way (and if it were possible in science, it would be preferred there, too).
| Afaceinthematrix wrote: |
| A lot of math does have uses, but some of it does not. It's not a lack of imagination on my part; it's a lack of use of the math's part. Try proving that 1+1=2. Even little kids intuitively know that 1+1=2, so why would anyone waste time proving that? People with the love for the art of math would spend time proving that. Know one else will spend time proving that. |
Are you serious? ^_^; That's one of the most fundamental relationships in the universe. If mathematicians could show that 1 + 1 does not always equal 2, and give the conditions under which that is true, then you can bet your entire pay cheque that there will be theoretical physicists falling over each other to find a way to apply those fringe cases physically.
And, from the other point of view, if mathematics were not sure that 1 + 1 = 2, then physics could not apply it without caution. To put it another way, we know our understanding of physics is incomplete because we get mathematical singularities when we apply our known equations under certain conditions. Because of the efforts of mathematicians to prove things like 1 + 1 = 2, we are sure that the math is right, so our physics is wrong. If that were not the case, then how would we know that our physics was wrong? It might be right and the math is simply wrong. Those so-called "waste of time" proofs help enormously in theoretical physics.
(Incidentally... "even little kids know that..."? ^_^; Dude, there are a lot of things that humanity thought were blatantly obvious, beyond any rational questioning - things that "even little kids knew" to be true - that we now know are not true. For example, just a few short decades ago everyone knew that every event has a cause - "where there's smoke there's fire, where things or moving something must have set them in motion" etc. etc. - but now we no longer believe that. And why? Because that's what the equations showed - and because of the efforts to prove every part of mathematics completely, right down to 1 + 1 = 2, we knew the math was right, even if it contradicted our common sense... and what "little kids know".)
| Indi wrote: | ||||
Experimentation is not the key aspect, observation is. Experimentation is just usually the best way to make observations of the physical universe. There are many cases where no experiments are done at all, just observations made - especially in cases where experimentation is simply impossible. The scientific method is observe-hypothesize-predict-observe (repeat). Experiments are just a convenient way to quickly and accurately make observations of specific predictions - if the prediction is that hot water will freeze faster than cold water outside, then you can either sit around and wait for a situation where you have two bodies of water at different temperatures sitting side-by-side and observe what happens... or you can make an experiment and observe it at your leisure while having better control over the variables. In mathematics you don't have to deal with the vagaries of the physical universe, and it is much easier to make observations without the need for setting up controlled experiments. You can still run tests - if someone theorizes that one equation is another form of another, you can apply the scientific method directly: observe whether it works for standard values, hypothesize why it works, predict what cases it might fail under, and observe again. Proving things axiomatically is not the only way things are done in mathematics, it's just the preferred way (and if it were possible in science, it would be preferred there, too).
Are you serious? ^_^; That's one of the most fundamental relationships in the universe. If mathematicians could show that 1 + 1 does not always equal 2, and give the conditions under which that is true, then you can bet your entire pay cheque that there will be theoretical physicists falling over each other to find a way to apply those fringe cases physically. And, from the other point of view, if mathematics were not sure that 1 + 1 = 2, then physics could not apply it without caution. To put it another way, we know our understanding of physics is incomplete because we get mathematical singularities when we apply our known equations under certain conditions. Because of the efforts of mathematicians to prove things like 1 + 1 = 2, we are sure that the math is right, so our physics is wrong. If that were not the case, then how would we know that our physics was wrong? It might be right and the math is simply wrong. Those so-called "waste of time" proofs help enormously in theoretical physics. (Incidentally... "even little kids know that..."? ^_^; Dude, there are a lot of things that humanity thought were blatantly obvious, beyond any rational questioning - things that "even little kids knew" to be true - that we now know are not true. For example, just a few short decades ago everyone knew that every event has a cause - "where there's smoke there's fire, where things or moving something must have set them in motion" etc. etc. - but now we no longer believe that. And why? Because that's what the equations showed - and because of the efforts to prove every part of mathematics completely, right down to 1 + 1 = 2, we knew the math was right, even if it contradicted our common sense... and what "little kids know".) |
But to prove that 1+1=2 has become unnecessary because I believe that if 1+1 doesn't equal 2, then everything that we believe and understand would have failed a long time ago. Physics has already led to many discoveries and inventions that would not have been possible if our basic understanding of addition was incorrect.
The difference with little kids intuitively knowing something, and people in the past believing that they understand something that is wrong, is that 1+1=2 is something that has already shown to be true, and it doesn't really have to be taught to kids. Once they learn to count, most kids already have a since for addition.
I would define mathematics as the language connecting the metaphysical to the physical.
It is the expression of philosophical concepts which are abstract and inherently outside of the world that we have the ability to perceive although we are able to measure them by physical representation of value perceived by our consciousness.
I believe that this ability has been manifest throughout evolution but we had obviously only had use of creating a language for it, upon becoming self-conscious.
It is interesting to note that recent studies claim to have proven that many animals have a limited ability to count.
References:
Cognition, evolution, and behavior (pg.363)
By Sara J. Shettleworth
http://www.apa.org/monitor/apr99/math.html
It is the expression of philosophical concepts which are abstract and inherently outside of the world that we have the ability to perceive although we are able to measure them by physical representation of value perceived by our consciousness.
I believe that this ability has been manifest throughout evolution but we had obviously only had use of creating a language for it, upon becoming self-conscious.
It is interesting to note that recent studies claim to have proven that many animals have a limited ability to count.
References:
Cognition, evolution, and behavior (pg.363)
By Sara J. Shettleworth
http://www.apa.org/monitor/apr99/math.html
I wont compare math with science..
its like comparing a spoon and a plate..
Math is a way to represent a scientific fact..
its like comparing a spoon and a plate..
Math is a way to represent a scientific fact..
"Mathematics is the language God used to write the universe"
Galileo
It says it all really.
Galileo
It says it all really.
For me, Mathematics is a way to calculate things that happen around us. It’s also the link between English and Science. A lot of a things can be explain by Science, and proven by Mathematics.
But, once I learnt Additional Mathematics, it’s hell. I’m learning things that I have no idea how to apply in the real world.
But, once I learnt Additional Mathematics, it’s hell. I’m learning things that I have no idea how to apply in the real world.
Mathematics is a method of defining scientific concepts as they relate to the real world. Notice the occurrence of "constants" in mathematical formulae.
We don't have all the answers so we use the best tools we have to define theories and extrapolate from those.
We don't have all the answers so we use the best tools we have to define theories and extrapolate from those.
Here are some thoughts:
When folks like Euclid studied plane geometry, they produced facts (such as the fact that the sum of the angles of a triangle add up to 180 degrees & the theorem of Pythagoras) which are of great practical use.
However, Euclidean planes don't actually exist in the real world (as space is curved by gravity, according to Einstein's general relativity).
This doesn't make the Maths wrong - the point is that Euclidean planes are valid object of study in Maths even if they don't exist in reality.
So, despite appearances to the contrary, Maths actually studies abstract and not real concepts. This is a fundamental difference from Science. Science tries to describe the real world.
So what does Maths try to do? It tries to reach correct conclusions about (abstract) systems (such as Euclidean geometry). Starting from basic properties (called axioms) other properties are deduced in a logical fashion (using so called rules of deduction). A statement in Maths is true if it can be deduced in this way, and does not depend on any connection to the real world.
So in Maths one can study systems that are apparently different from perceived reality. A good example is Riemann's study of curved space in the 19th century. He undertook this as an academic "what if?" exercise. Then it turned out that space is curved, and so Einstein was able to apply his "nonsensical" geometry to the real world!
I think we can deduce from this that Maths is not a science. It is a language used by science, but is much more than just a language: it is essentially a language in which logical games are played. Sometimes the fruit of these games can be applied by science, but even if they can't , they're still valid Maths.
When folks like Euclid studied plane geometry, they produced facts (such as the fact that the sum of the angles of a triangle add up to 180 degrees & the theorem of Pythagoras) which are of great practical use.
However, Euclidean planes don't actually exist in the real world (as space is curved by gravity, according to Einstein's general relativity).
This doesn't make the Maths wrong - the point is that Euclidean planes are valid object of study in Maths even if they don't exist in reality.
So, despite appearances to the contrary, Maths actually studies abstract and not real concepts. This is a fundamental difference from Science. Science tries to describe the real world.
So what does Maths try to do? It tries to reach correct conclusions about (abstract) systems (such as Euclidean geometry). Starting from basic properties (called axioms) other properties are deduced in a logical fashion (using so called rules of deduction). A statement in Maths is true if it can be deduced in this way, and does not depend on any connection to the real world.
So in Maths one can study systems that are apparently different from perceived reality. A good example is Riemann's study of curved space in the 19th century. He undertook this as an academic "what if?" exercise. Then it turned out that space is curved, and so Einstein was able to apply his "nonsensical" geometry to the real world!
I think we can deduce from this that Maths is not a science. It is a language used by science, but is much more than just a language: it is essentially a language in which logical games are played. Sometimes the fruit of these games can be applied by science, but even if they can't , they're still valid Maths.
Mathematics is a language of defining the universe. It is a science of logic. Mathematics is the mother of all other sciences. There are so many other things that can be added here. But this is enough I suppose. Every study is directly or indirectly related to mathematics.
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