What is the Study of Mathematics?

[jostpuur]

The title What is Mathematics?, and the question in the original post

What is Mathematics the study of?

are in fact different questions. It could be clearer if you make it clear which one of these you are trying to answer. My post #49 dealt with the first one, and #50 with the second one.

 

[Holocene]

Mathematics is more than just a language; it describes some general truths.

Take for example the ratio between the circumference of a sphere, and its diameter. That ratio is ALWAYS the same, regarless of the size of the sphere. It doesn't matter if it's an object the size of a glass marble, or an object the size of a star.

The ratio is ALWAYS the same, regardless of the size of the object.

 

[JoeDawg]

Mathematics is more than just a language; it describes some general truths.

Mathematics IS a language that describes general relations.

A circle is a circle, by definition. Its a generalization based on experience.
We say something is not a circle when it contradicts, or expands on, the definition of a circle.
Mathematics allows us to describe a circle very precisely.
A square is not a circle, by definition, these two definitions conflict.
A sphere is not a circle, by defintion, a sphere expands on the definition into 3 dimensions.

The definition of a circle comes about because we live in a certain type of spacetime and can perceive certain dimensions. Its a generalization, the fact we can apply this generalization to many observed things is a function of the fact its a generalization. The definition is always true, because we have defined it precisely that way.

 

[oldman]

Mathematics IS a language ...

While I agree with you as far as this, there seems to be some confusion in the replies to the question raised in the OP, namely "What is Mathematics the study of?"

This may be because other disciplines mentioned in the OP, like mechanics and biology, study aspects of the "real" world (if this indeed exists --- as the evidence of our senses suggests it does) --- whereas mathematics involves the study of properties of an abstract entity, which some assume is a structure that exists in the Platonic world, fully formed, waiting to be discovered by any creatures capable of doing so.

Others, like myself, believe that mathematics is an ephemeral construct like all languages --- whether they be invented by human beings, as with Zulu, Latin and English, or by birds, who use various twitterings for communications that must seem pretty important to them.

There is much scope for confusion here. Perhaps it would be useful to consider how
subjects like mechanics, biology and mathematics arose -- their provenance, as with works of art, so to speak --- and especially what kind of animals use them and why.

 

[yhp266]

Mathematics is what mathematicians do.

this definition is useless and also wrong. It seems to imply mathematics is a human construct.

 

[Hootenanny]

this definition is useless and also wrong. It seems to imply mathematics is a human construct.

If mathematics is not a human construct, a framework/formalism constructed by humans to solve problems, then what is it?

 

[yhp266]

My definition of mathematics is that it is merely an abstraction of ideas

My personal view is that mathematics is permanent outside of our existence.

 

[Noone]

Math is a dictator that tell's logicaly how each line must effect another line, hence every number is a line, 2=ll 1=l and in which ways can those lines effect each one another, in every way shape and form through a fixed logical dictation.

So math is the studie of how line's effect one another in everyway shape and form, bound by a logical dictation of how they must effect each one another in everyway shape and form.

Its like a lang, used like a tool, a true gift to have and use, for that of which you need or seek.

 

[al-mahed]

perhaps one can say that math is a system such that there is no exceptions ( a particular process leads to a particular result any time) and when the "rules" are followed there is no absurd conclusions according to these rules

 

[oldman]

perhaps one can say that math is a system such that there is no exceptions ( a particular process leads to a particular result any time) and when the "rules" are followed there is no absurd conclusions according to these rules

You're confusing maths with "reality" here, I think. Maths is an abstract language --- and it's constructive to give examples, rather than just express an opinion.

The simplest example of this abstract language involves the counting numbers we all use. They are an abstraction and their arithmetic is another. The language of maths is used to quantiatively describe "reality" -- (the "reality" of your "particular process", al-mahed?).

Another quite simple example most of us are familiar with is the description: "exponential increase" , where we talk of the rate of increase of something (population for example) being proportional (another abstract math concept) to the value of that something (yet another abstract math concept).

Or, to be more succint, we write down an abstraction; a differential equation, namely (with N for quantity and t for time) dN/dt proportional to N, and then solve it -- as N proportional to (the mysterious number) e raised to a power proportional to t.

One should appreciate that this sort of abstract gobbledygook, used with physics, proves --- from an evolutionary point of view --- to be the supremely useful lever that has enablied us to infest this planet with billions of individuals. Maths is one heck of an important language!

By the way, an "abstraction" is just another human concept, too. I'll bet dogs find smells both as abstract and as useful as we find, say, the counting numbers --- and that smells stimulate their doggy imaginations as much as abstractions do ours!

 

[Pythagorean]

Humans are pattern-seeking creatures. They tend to see patterns where there are not any (in numerous ways). Psychologists have long documented this phenomena. There are a series of optical proofs that one can find, Philosopher Daniel Dennet has a lecture on youtube where he displays these test:

http://youtube.com/watch?v=wIdxbJyvfNw&feature=related

This is proof of our ability to see optical patterns where there aren't any.

Mathematics, logic, and religion (to a certain extent) are the same property of pattern-seeking on a different level than the optical example above. We tend to seek symmetry and patterns even in the morals we create ("treat others how you want to be treated").

Without qualitatively assigning experiential properties to math, it really has nothing to do with reality. We show in the physical sciences that things can behave "like" a certain function in mathematics, but that is a metaphor, and not a sort of mystical sign that mathematics is inherent in the universe. Mathematics must be used like quilt material to best describe all aspects of reality, and it must be described with experiential, qualitative attachments.

There is no absolute math that can describe everything as it evolves in time... that, so far has only been within the capabilities of reality itself.

 

[oldman]

Humans are pattern-seeking creatures. ...Without qualitatively assigning experiential properties to math, it really has nothing to do with reality. We show in the physical sciences that things can behave "like" a certain function in mathematics, but that is a metaphor, and not a sort of mystical sign that mathematics is inherent in the universe. Mathematics must be used like quilt material to best describe all aspects of reality, and it must be described with experiential, qualitative attachments.

There is no absolute math that can describe everything as it evolves in time... that, so far has only been within the capabilities of reality itself.

You put it very clearly. All I'd add is that as well as pattern-seeking, we spend a lot of time pattern-describing. It's very helpful for evolutionary success! Thanks, from your (approximate) antipodes.

 

[Air]

The study of the measurement, properties, and relationships of quantities and sets, using numbers and symbols.

...So basically the study using calculations?

 

[musicor]

who am i?

Oh Math, so deep and beautyfull lady... i will not talk about math as i think that term is contaminated with dozens of thousands years of fascination and misconception.
lets talk about thought. Math is founded on logic and logic is founded on thought. Without the identity principle, trueness and falseness are the same and there is no possible logic, as everything becomes the same thing and nothing becomes all. But the reality is not founded above any concept, but on perception, no matter who perceives, a photon or a human being, an idea or a concrete brick, everything changes its state when perceive something else. reality is founded on the mutual influence of the beings (or things if you prefer) i.e. all that exists, if exists out of itself, communicate. and if that thing has a memory, i.e. perceives the time i.e. follow the changes of its internal states, that thing is able to distinguish between at least 2 different perceivments and can be used to do logic, math etc... But and the reality behind all that mechanical stuff? even the more abstract idea has a kind of mechanic, turning a human being not more than a dog or any other physical system. The internal simulacrum used to model (describe) the reality is as fake as the simulated reality itself, and some times appear the same.
But and the absolute reality? we feel something else, or not?
yes, and that is the real reality, the feelings space. Feeling is the universal language, not Math.
thought, and logic, and math, and concrete jungles are made of feelings.
maybe i am too stupid for that forum, but i am not too stupid for the love embrace with the final reality, that's the way i feel.
PS. Oldman, are you the oldman Mc from FICS?

 

[oldman]

Oldman, are you the oldman Mc from FICS?

No, I'm not.