How does a mathematician define Mathematics?

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The discussion revolves around defining mathematics and its essence. Initial definitions, including one from a dictionary, are critiqued for being overly simplistic. Participants express that mathematics is best understood through the actions of mathematicians rather than through rigid definitions. The conversation highlights the abstract nature of mathematics, emphasizing that it studies relationships and structures rather than concrete objects. There is a debate about whether a mathematician needs to define mathematics, with some arguing that questioning is essential for deeper understanding. The idea that definitions can be limiting is explored, with references to famous figures like Mozart and Einstein, who engaged with their fields without strict definitions. Participants also discuss the philosophical implications of defining mathematics and the importance of questioning in the pursuit of knowledge. The conversation touches on the complexity of mathematics, suggesting that it encompasses a wide range of topics and practices, making a singular definition challenging. Ultimately, the discussion underscores the value of dialogue and exploration in grasping the concept of mathematics rather than seeking definitive answers.
  • #31
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
 
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  • #32
moshek said:
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.
 
  • #33
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
 
  • #34
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
:smile:
 
  • #35
moshek said:
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.

moshek said:
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
: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.
 
  • #36
Lorentz hi:

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

Usually mathematician don't 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:
 
  • #37
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.
 
  • #38
I do think Mathematicians are hard to get around with if you're not playing their ballgame. But that's their own right.
 
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  • #39
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) !
 
  • #40
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
 
  • #41
moshek said:
Do you interest in a poem i wrote for mathematics ?

Yeah, I'm interested in your poem.
 
  • #42
Organic mathematics

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 don't find also anymore. i am afreid now that somone trow it away. I really want to share this poem with you.

Yours
Moshek
 
  • #43
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:
 
  • #44
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.
 
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  • #45
matt grime said:
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.

Lorentz said:
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:
 
  • #46
matt grime said:
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.

matt grime said:
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.
 
  • #47
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.
 
  • #48
matt grime said:
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.

matt grime said:
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.
 
  • #49
I think It is a same for this forum that someone decide to move your tread from mathematics ! I don't believe 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:
 
  • #50
Moshek what country are you from?
 
  • #51
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:
 
  • #53
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:
 
  • #54
  • #55
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 don't mind "Quantum number theory".


Yours
Moshek
:smile:
 

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