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
:smile:

[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: :confused:

[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 :smile:

[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 :smile:

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"? :smile:

[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"? :smile:

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 dont 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 dont 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 begining a very good question Lorentz

Moshek
:smile:

[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 begining a very good question Lorentz

Moshek
:smile:

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.

[moshek]

Lorentz hi:

I agree with you that real open discussion about your question can bring to high understanding about mathematics.

Usually mathematician dont like this question because it bother them very much acording the way the got there respect. Don’t you think it is ridicules situation.

Well ,Instead of you i was bother way the moderator who work for this forum
that use Einstein picture move your tread withotle telling you way the did it ?

maybe someone from them can explain it now here ?


Best
Moshek
:smile:

[Lorentz]

They didn't tell me, they just moved it. But as I said I'm not bothered.

In my opinion the only justifiable reason to move a topic is if a topic isn't being discussed (e.g. because people in the specific forum ain't interested). This certainly was not the case as the Mathematicians even came to this forum to finish the discussion.

There's no specific place for any topic (as it's merely a question of classification which isn't strictly set). I chose the Maths forum which was reasonable, I think.

[Lorentz]

I do think Mathematicians are hard to get around with if you're not playing their ballgame. But that's their own right.

[moshek]

Lorentz:

Yes your thread was respond very nicely were you decide to locate it
so i hope it will be back to mathematics in the very soon.

Can one of the moderate here can give the explanation to Lorentz ?


Do you interest in a poem i wrote for mathematics ?


Best
Moshek

By the way : I respect real philosophy as the high level of the spirit even more than mathematics which i am quite familiar ( i think) !

[moshek]

I do think Mathematicians are hard to get around with if you're not playing their ballgame. But that's their own right.
Lorentz


-----------------------------------------------------------------

This is very very Sad if you have real respect to mathematics.

Moshek

[Lorentz]

Do you interest in a poem i wrote for mathematics ?

Yeah, I'm interested in your poem.

[moshek]

Dear Lorentz :

I am really sorry to tell you that i just look and don't find my poem "For mathematics" that i locate in Mathematics forum under the thread "Organic mathematics" that i dont find also anymore. i am afreid now that somone trow it away. I really want to share this poem with you.

Yours
Moshek

[Lorentz]

I found it for you! :smile:


For Mathematics

The current big-band
His here real Glory.
Milky way is around us.
A solar system was created.

Everything is a number
Said Pythagoras
While he could hear
The music of the spheres.

But so many water
Cover the head of Hipasus
After he discovery
The secret of irrationality.


Maybe Euclids hide the story
For the protecting the axiom
Of the parallels
To establish his own mathematics.

While Newton calculate
The end of the world
Leibniz with the monads believed
A unify language must exist.

Goethe could see here
With the generic type
But he just did not
like or know mathematics

Hilbert was staying
So misunderstood
With his list of 23 problems
and the organic unity.


A.Connes with
Noncomutativs geometry
100 to Hilbert end with
some new understanding.

M.Athiya for his Index
And K theory
Talk about here
As some Enigma.

I Stuart with his vision
Share her flexibility
In his Epilog
The nature of numbers

Wittgenstein say
We should be Aliens
To see here in
The bottle of Klein.


From the top mountain
Of the Rieman hypothesis
We can see the real mount Analog
And Hear its’ sixth symphony. ’


Einstein did a real
First step of a child
When he ask how we
measure a length.

Only if we could See again
The world Like children
We will count again
Now from the beginning 1. 2. 3.


Moshe Klein 4.4.04


You put a smile on my face, thanks for your poem. :cool:

[matt grime]

Here's a simple reason why your thread might have been moved:

has any post in this thread added to the understanding of how to practise mathematics?

No, not in the slightest.

It is a question about mathematics, not about something in mathematics, which appears to be the primary function of the maths forum.


I can tell you what mathematics is. To do so I would need to list every thing that has been done in mathematics. The word mathematics is a label to signify all that knowledge, and perhaps where it will lead. There is no short way of explaining it, just as there is no short explanation of what an animal is, as opposed to a plant.

Some people will tell you that Quantum mechanics is part of physics, some that it is mathematics. In many ways the boundaries are artificial and personal.

Pure maths is the study of the methods of solution, applied is the study of the solution.

Inside those two distinctions are various subdivision: Fluids, Quantum Mechanics, Mathematical Physics, Solid State....
Then there are the pure subjects, Analysis, Logic, Algebra, Topology, Geometry, Combinatorics. Even inside those divisions are divisions and overlaps - topology and geometry use algebra, but aren't themselves algebraic, hence the terms algebraic geometry.

The reason why there isn't an answer is not because there is some problem with the philosophical, but that there are such diverse related topics (oxymoron, admittedly) that they defy categorification into nice simple words. And if you think there ought to be a short answer then you're a fool to yourself.

As to the Mozart reference.

He would be able to explain what his music is by talking about scales, structure, form, key, but would he have been able to give a definition that would allow you to recognize hip hop or bhangra as a form of music? Would preclude things that weren't in the western keys, why the restriction to discrete frequencies? The answer is that the subject is its practice to each person.

There are no nice answers, and if there were it wouldn't be worth studying.

[Lorentz]

Here's a simple reason why your thread might have been moved:

has any post in this thread added to the understanding of how to practise mathematics?

No, not in the slightest.

It is a question about mathematics, not about something in mathematics, which appears to be the primary function of the maths forum.


In my opinion the only justifiable reason to move a topic is if a topic isn't being discussed (e.g. because people in the specific forum ain't interested). This certainly was not the case as the Mathematicians even came to this forum to finish the discussion.


Hmmm... seems I couldn't care less. :rolleyes:

[Lorentz]

I can tell you what mathematics is. To do so I would need to list every thing that has been done in mathematics. The word mathematics is a label to signify all that knowledge, and perhaps where it will lead. There is no short way of explaining it, just as there is no short explanation of what an animal is, as opposed to a plant.

Some people will tell you that Quantum mechanics is part of physics, some that it is mathematics. In many ways the boundaries are artificial and personal.

Pure maths is the study of the methods of solution, applied is the study of the solution.

Inside those two distinctions are various subdivision: Fluids, Quantum Mechanics, Mathematical Physics, Solid State....
Then there are the pure subjects, Analysis, Logic, Algebra, Topology, Geometry, Combinatorics. Even inside those divisions are divisions and overlaps - topology and geometry use algebra, but aren't themselves algebraic, hence the terms algebraic geometry.

The reason why there isn't an answer is not because there is some problem with the philosophical, but that there are such diverse related topics (oxymoron, admittedly) that they defy categorification into nice simple words. And if you think there ought to be a short answer then you're a fool to yourself.

As to the Mozart reference.

He would be able to explain what his music is by talking about scales, structure, form, key, but would he have been able to give a definition that would allow you to recognize hip hop or bhangra as a form of music? Would preclude things that weren't in the western keys, why the restriction to discrete frequencies? The answer is that the subject is its practice to each person.

There are no nice answers, and if there were it wouldn't be worth studying.

Thanks for another usefull contribution, though it seems you still can't see where I'm coming from.


And if you think there ought to be a short answer then you're a fool to yourself.


I never said it had to be short and I certainly didn't ask for an answer.

[matt grime]

I think I've offered two interpretations to your question, the metaphysical and the physical. If you think that I do not see where you're coming from rephrase the question, however you should bear in mind that to me you've got a non-well formed question. You did ask how does a mathematician define mathematics didn't you? if you didn't want an answer then why ask it? The theme running through your replies is that you appear to think that mathematics is deficient because there isn't an answer.

[Lorentz]

I think I've offered two interpretations to your question, the metaphysical and the physical. If you think that I do not see where you're coming from rephrase the question, however you should bear in mind that to me you've got a non-well formed question. You did ask how does a mathematician define mathematics didn't you? if you didn't want an answer then why ask it?


Maybe I did ask the wrong question, but what I really wanted to ask should have been clear by now. You can't hang me up on every word I say.

The theme running through your replies is that you appear to think that mathematics is deficient because there isn't an answer.

I think you've seen ghosts. I don't think mathematics is deficient. And for the zillionth time... I'm not interested in an answer.

[moshek]

I think It is a same for this forum that someone decide to move your tread from mathematics !!! I dont belive that matt did it to you. well you ask a beautiful question very natural like the eye of innocent child
Very good you don't except to an answer but to dialog around it.
Thank you very much for potting my poem "For mathematics"
in this thread I am sorry for my mistakes in English and that i thought someone put it away from this forum. I quote there some of the leader of the mathematical world today. I have already English editing to this poem and i will put it there soon.

You make me to smile also.

Yours
Moshek
:smile:

[Lorentz]

Moshek what country are you from?

[moshek]

Lorentz:

Please sent me privet e-mail to gan_adam@netvision.net.il
and i will be glad to answer to your question.

I just put the edit poem in "Organic mathematics"
please look on it there.

Yours
Moshek
:smile:

[Organic]

Dear Lorentz,

How does a mathematician define Mathematics?

I researching this question for about 20 years, you can find it here:

http://www.geocities.com/complementarytheory/CATpage.html

Yours,

Organic

[moshek]

Organic:

Please tell me what is the connection between the way you defined mathematics to the science attitude of Goethe since he did not respect so much mathematics { as far as i know} ?

Thank you

Moshek
:smile:

[Organic]

Hi Moshek,

As much as I know, by Goethe, our cognition's abilities to develop some theory, cannot be ignored.

My point of view of the Natural number is based on this idea, for example:

http://www.geocities.com/complementarytheory/count.pdf

[moshek]

Hi Organic:

As far as i know Goethe all his life were dedicate to unify the contradiction in all aspect of life so it may fit your new concept of number. Goethe was not recognize as a sciences despite the fact that he contribute a lot to it. He was recognize ( until today...) as a great poet. so you may change it now with your significant work i named if you dont mind "Quantum number theory".


Yours
Moshek
:smile: