# How does a mathematician define Mathematics?

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?

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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 Mathematics is what mathematician are doing!!!

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

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

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

HallsofIvy
Homework Helper
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.

moshek said:
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?

Chen said:
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
Homework Helper
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.

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matt grime
Homework Helper
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.

matt grime said:
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.

matt grime said:
Mathematics is the study of mathematical objects, and those are abstractions of physical objects and their models.
Now was that so hard?

matt grime
Homework Helper
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
Staff Emeritus
Gold Member
Lorentz said:
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
Homework Helper
Damn, you spotted the trick....

matt grime said:
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?

Lorentz said:
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.

ahrkron said:
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?

matt grime said:
and those are abstractions of physical objects and their models.

Chen said:
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?

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
Homework Helper
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.

Lorentz said:
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
Homework Helper
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.

matt grime said:
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.

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.