How does a mathematician define Mathematics?

[Lorentz]

I searched my dictionary and it said:

Science which deals with qualities of numbers and figures.

Is this the definition you would give or do you know a better one?

and How would you explain Mathematics to a layman?

 

[moshek]

Hi Lorentz :

Here is a very simple answer but amaybe difficult to understand:

Mathematics is what mathematician is doing!



If you want more explanation please let me know

Moshek

 

[moshek]

Mathematics is what mathematician are doing!



p.s sorry for my mistake in the answer i gave before !

 

[Chen]

I don't really think a mathematician wants to or needs to define mathematics.

 

[Loren Booda]

Mathematics is the symbolic representation of states or processes transformed through cognition.

 

[HallsofIvy]

I was going to say "Mathematicians don't define mathematics, they do it!" but I see that that has already been said!

If I really had to, I would be inclined to say "In all subjects, one has objects of study (mass, energy in physics; atoms, molecues in chemistry; etc.) and relations between those objects. In mathematics, one studies relationships in the abstract.

Another way of putting the same thing is to say that mathematical structures (groups, fields, vector spaces, etc.) are templates that essentially give all of the ways things can be related to one another. In applying mathematics to another field, one chooses a template and tries to fit the subject to that template.

 

[Lorentz]

Mathematics is what mathematician are doing!

Is that true? I wouldn't call myself a mathematician though I use maths all the time (by solving physics equations). So is what I'm doing not maths, am I a mathematician or is your definition incomplete?

 

[Lorentz]

I don't really think a mathematician wants to or needs to define mathematics.

Layman: Hi Chen, I hear you're Mathematician.
Chen: Yes, that's right.
Layman: Chen, what is Maths exactly?
Chen: I don't really think a mathematician wants to or needs to define mathematics.
Layman:

 

[matt grime]

If you're a mathematician you do maths, where does it say if you use maths you're a mathematician? As the old rule goes, if you need to ask then you don't need to know.


Besides, any mathematician can only describe what it is they do which is some part of mathematics.

 

[matt grime]

Ok, lorentz, define green, define music, define jazz. What makes you think it is necessary or even beneficial to ask a question just because you can.

Mathematics is the study of mathematical objects, and those are abstractions of physical objects and their models.

 

[Lorentz]

Ok, lorentz, define green, define music, define jazz. What makes you think it is necessary or even beneficial to ask a question just because you can.

I don't think we would have arrived at doing Maths if we didn't start questioning in the first place.

Mathematics is the study of mathematical objects, and those are abstractions of physical objects and their models.

Now was that so hard?

 

[matt grime]

But is that answer correct? It is glib, off the cuff, and not at all accurate, is it? It's the best I can do for someone who wants answers to unanswerable questions.

 

[ahrkron]

Now was that so hard?

No, since he only hid the question. You now would need to ask "what are mathematical objects".

The answer? what mathematicians study

 

[matt grime]

Damn, you spotted the trick...

 

[Lorentz]

But is that answer correct? It is glib, off the cuff, and not at all accurate, is it? It's the best I can do for someone who wants answers to unanswerable questions.

Yes, but what my dictionary said was even more off the cuff. Isn't it better for me to use your definition and try to understand what you meant by it?

 

[Chen]

I don't think we would have arrived at doing Maths if we didn't start questioning in the first place.

We arrived at this for asking questions that were meaningful and beneficial, rather than just any question that springs to mind.

 

[Lorentz]

No, since he only hid the question. You now would need to ask "what are mathematical objects".

The answer? what mathematicians study

Huh? didn't he say what Mathematical object are?

and those are abstractions of physical objects and their models.

 

[Lorentz]

We arrived at this for asking questions that were meaningful and beneficial, rather than just any question that springs to mind.

Isn't it more meaningful to know what you're doing rather then just doing it?

 

[Lorentz]

The important thing is not to stop questioning. (that's a qoute from Einstein)

I believe if you keep on questioning you'll reach a higher degree of understanding.

Maybe a misconception is that I'm asking for an answer, Well I ain't. I'm trying to discuss things so I can hear opinions which will help me grasp things better.

 

[matt grime]

But I didn't define what it meant for an object ot be physical or what a model of it is, or what it is that makes these things mathematical objects.

 

[Chen]

Isn't it more meaningful to know what you're doing rather then just doing it?

Sometimes yes, sometimes not. How is a precise defintion of "math" going to help us? Are there currently problems that cannot be solved because we have not a definition of "math"? Will we gain a deeper understanding of the universe once we know how to define "math"?

 

[matt grime]

Ask Mozart if he could define music, Lorentz. He didn't need a definition of it, he knew the rules of composition, and how to make it, that's sufficient. It was whatever we do that follows the rules that counts, and I don't mean that in a kowtowing way. These questions are easy to pose, impossible to answer and completely unnecessary.

 

[FZ+]

Lemme try!

Mathematics is the study of conceptual entities and their interactions within the framework of rules and templates produced as a formalism of a certain type of logic.

 

[Lorentz]

Ask Mozart if he could define music, Lorentz. He didn't need a definition of it, he knew the rules of composition, and how to make it, that's sufficient. It was whatever we do that follows the rules that counts, and I don't mean that in a kowtowing way. These questions are easy to pose, impossible to answer and completely unnecessary.

Maybe Mozart didn't need to define music. But he would have tried to explain music to someone who asked what it is.

I see where you're coming from. I completely agree that you don't have to know what Maths is to do Maths and it will even hold you back of doing Maths if you would keep asking yourself these questions. But besides your Maths framework there is a world needing to be explained. Why? Because we want to... actually we need to.. it's in the nature of the human being.
You say my questions don't have an answer, but does a question need an answer? I don't think so. What a question does need is questioning. If you don't question you'll be lost forever. A Mathematician isn't lost becuase he got his framework to rely on. But how did this framework got there in the first place?

A dictionary is full of definitions of words. Do these definitions truly grasp everything there is to know about these words? No, but it does give you a bit of a direction.

If you're talking about a dog and someone asks what a dog is, because he has never been told. You wouldn't say... well sorry but there's nothing I could say that will truly grasp everything there is to know about dogs. Of course your explanation won't be complete. And of course the person wouldn't have the same image of a dog like you have. But that doesn't mean you shouldn't try and show him the image even if your image is blurred and vague.

 

[Chen]

A question must lead to answers otherwise it is useless. Einstein could have sat and ask himself "Why is the speed of light constant" all day for the rest of his life, but it is the fact that he answered that question that made it meaningful.

 

[Lorentz]

A question must lead to answers otherwise it is useless. Einstein could have sat and ask himself "Why is the speed of light constant" all day for the rest of his life, but it is the fact that he answered that question that made it meaningful.

He didn't answer that question.

He questioned it and then came to a theory and NEVER to an answer.

 

[Chen]

Touche. Still, what do you expect us to gain by defining "mathematics"?

 

[moshek]

Lorentz:

I am sure that if you could ask Mozart
he could give you the definition
or if you like the explanation
to the most important and deep question
in the whole mathematics:

What is mathematics ?

Best
Moshek
:smile
:

 

[Lorentz]

Touche. Still, what do you expect us to gain by defining "mathematics"?

I don't expect you to gain much by it... as a Mathematician you surely have a picture of Mathematics in your head. And that picture might be a bit blurred, but it surely not as blurred as mine. So what I asked is to show me your picture so maybe I could refine my picture here and there. I'm satisfied with the replies I got, but I stumbled upon opinions that it isn't important to define Maths and that's something I don't agree with. A blurred picture is better then no picture at all (and remember you could always tell the person your picture is blurred... the thing is he will be happy with the blurred picture). The reason why I actually asked the question for a definition is because I'm writing a reader about Maths for pupils starting out with Maths. I didn't have a definition of Maths which I felt comfortable with so I asked you guys.

 

[Lorentz]

Lorentz:

I am sure that if you could ask Mozart
he could give you the definition
or if you like the explanation
to the most important and deep question
in the whole mathematics:

What is mathematics ?

Best
Moshek
:smile
:

Haha
and what would he answer?
or what would you answer for that matter?
I never got that "mathematics is what mathematicians do" explanation.

 

[moshek]

Lorentz:

Since Mozart have always the picture of his music he could have also a one big picture of the whole mathematics so he could describe it to you like Wittgenstein did as a Klein Bottle !

You see generally mathematician work only on a very local point in mathematic and they don't have the global picture .They can't see this picture also well you look on mathematics like this there is no more Logic !
the new center is the unity of mathematics { Hilbert vision }

Every symbol have it's duality of object and as operation that can meet again with this duality in the high 4 dimension.

If you see it you also see very clearly and strangly a solution to one of the 3 open problem that left form the famous list of Hilbert at 1900.

mathematics is not about some true outside the world ( Plato) and not about true in the world . The definition i wrote for you is the possitve interpatation to Goedel theorem !

Best
Moshek

 

[Lorentz]

Lorentz:

Since Mozart have always the picture of his music he could have also a one big picture of the whole mathematics so he could describe it to you like Wittgenstein did as a Klein Bottle !

You see generally mathematician work only on a very local point in mathematic and they don't have the global picture .They can't see this picture also well you look on mathematics like this there is no more Logic !
the new center is the unity of mathematics { Hilbert vision }

Every symbol have it's duality of object and as operation that can meet again with this duality in the high 4 dimension.

If you see it you also see very clearly and strangly a solution to one of the 3 open problem that left form the famous list of Hilbert at 1900.

mathematics is not about some true outside the world ( Plato) and not about true in the world . The definition i wrote for you is the possitve interpatation to Goedel theorem !

Best
Moshek

Thanks, that's of help.

I have to read carefully though as it's a bit beyond my scope, but I manage.

 

[moshek]

Very good !

Take your time Lorentz a day, a week, or eve a month or a year if you need it. But please don’t hesitate to ask me on any point since every word was chosen very carefully for you.

Best
Moshek

 

[moshek]

Lorentz:

Since the thread was located from some reason at Philosophy of mathematics I really wonder way and who did it ?

I want to add that if Einstein ( with his picture at the top of the forum) would not ask some philosophical question we were stack until today with Newton physics.

You ask at the beginning a very good question Lorentz

Moshek

 

[Lorentz]

Lorentz:

Since the thread was located from some reason at Philosophy of mathematics I really wonder way and who did it ?

Probably one of the moderators, but I'm not bothered about it. Though it's weird, because it's hard to get a definition of Maths out of a mathematician though at the same time they imply there is a strict definition by removing this from their forum.

I want to add that if Einstein ( with his picture at the top of the forum) would not ask some philosophical question we were stack until today with Newton physics.

You ask at the beginning a very good question Lorentz

Moshek

My point is: by questioning we won't get an answer (you'll only get a strict answer within a framework (which itself needs to be questioned)), but we will reach a higher understanding.