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Math Help - What is Math? (seriously)

  1. #1
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    What is Math? (seriously)

    Every person has taken math in school some time in their life. BUT, why donít we have a clear definition of Mathematics? What on earth are we studying? What kind of education puts you through 12 years of math and doesn't even explain to you what it is? Its funny/sad how we can't even define it in even a slightly coherent way. Which tells us a lot about how intelligent we and our teachers are.

    Doing a google search on "what math is" doesn't really help either.

    So I attempted to answer the question "what is math", and also since it is very close to science, I tried to explain "what is science", and compared them.

    what is math

    This forum is filled with people who know math and science, so I ask you to please view the video/article and criticize it as much as you can! your input is really valuable, thank you.
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  2. #2
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    Re: What is Math? (seriously)

    math=a biologist's worst nightmare
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    Re: What is Math? (seriously)

    Quote Originally Posted by CalculusAcademy View Post
    Every person has taken math in school some time in their life. BUT, why don’t we have a clear definition of Mathematics? What on earth are we studying? What kind of education puts you through 12 years of math and doesn't even explain to you what it is? Its funny/sad how we can't even define it in even a slightly coherent way. Which tells us a lot about how intelligent we and our teachers are.

    Doing a google search on "what math is" doesn't really help either.

    So I attempted to answer the question "what is math", and also since it is very close to science, I tried to explain "what is science", and compared them.

    what is math

    This forum is filled with people who know math and science, so I ask you to please view the video/article and criticize it as much as you can! your input is really valuable, thank you.
    You are assuming that every term in use must have a precise definition, but this is not obviously true (except possibly to Socrates and Plato but they were evidently wrong, try defining the term "tall building"). All that is really required is that you recognise an examplum when you see one. You cannot define "dog" but you learn to recognise one when you see it.

    If you insist on a definition; you could define Mathematics as the study of pattern and symmetry (in a formalised setting ....). But that won't really help you recognise mathematics when you see it without an awful lot of context.

    Also your post is not a question but click bait. You think you already know something of the answer and are posting here to boost your site's number of hits. Confirmed by the fact that you have not logged into MHF since posting your click bait, which of course makes you a spammer (according to the definition I have here).

    Also≤, your Einstein quote is an example of someone eminent in one field talking crap about another, Mathematics is not "independent of experience", it may be abstracted from experience but that is not the same thing as independence of/from experience. Which also nails the claim that mathematical propositions are a priori. If the space of experience did not appear to be a flat 3-manifold we would not have elementary geometry in the form that we do (we still might arrive at it as a limit in some sense derived from the space experience but that would be another story).


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    Last edited by zzephod; September 12th 2014 at 11:23 PM.
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    Re: What is Math? (seriously)

    Math is a field of study that should not be explored by all students, especially people who hate numbers.
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    Re: What is Math? (seriously)

    Quote Originally Posted by nycmath View Post
    Math is a field of study that should not be explored by all students, especially people who hate numbers.
    If you think maths is about numbers you are mistaken. It is about pattern and symmetry. Common arithmetic is largely about numbers but arithmetic is not mathematics. If you have been taught that it is about numbers (and nothing else) then you have been taught badly.
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    Re: What is Math? (seriously)

    First of all, thank you for your input.
    Sooo, lets say I am driving traffic into my website, that's not necessarily bad, I am not selling anything on the website, nor do I have ads in it, and the content is supposed to be educational.. I haven't been in the forum since I posted because school started and I got distracted, but here I am! taking notes on people's input..

    A) Can you explain why you can't have a precise definition? why is a "dog" undefinable? I mean just the fact that you can recognize a dog, doesn't that mean there is a definition of a dog, at least in your subconscious mind? I am confused, please explain this point to me.

    B) and why is math just patterns and symmetry? what about everything else? like numbers? do you have a reason for that?

    C) and finally, the quotes from different thinkers are just used for demonstration, it doesn't mean "if Plato/Einstein said it, it must be true!". Sorry if it seemed like that, I didn't intend it to be like that, the explanations after the quote are supposed to show why what I said is true/false...
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    Re: What is Math? (seriously)

    Quote Originally Posted by CalculusAcademy View Post
    First of all, thank you for your input.
    Sooo, lets say I am driving traffic into my website, that's not necessarily bad, I am not selling anything on the website, nor do I have ads in it, and the content is supposed to be educational.. I haven't been in the forum since I posted because school started and I got distracted, but here I am! taking notes on people's input..

    A) Can you explain why you can't have a precise definition? why is a "dog" undefinable? I mean just the fact that you can recognize a dog, doesn't that mean there is a definition of a dog, at least in your subconscious mind? I am confused, please explain this point to me.
    Would being able to recognise an instance of "dog" have been sufficient to convince Plato's Socrates that you knew the definition of "dog"? Do you think everyone would agree that this entity you recognise as a "dog" is in fact a "dog". The term "dog" is fuzzy at the edges and if you draw a boundary it is essentially arbitary and you will not get universal agreement with where you have placed it. So I would contend that there is no definition of "dog" that you can give, even if you can recognise an instance of "dog" when you see one. You learn from experence what the term "dog" refers to (most of the time) but there is no definition because a definition is precise but here the concept is not.

    B) and why is math just patterns and symmetry? what about everything else? like numbers? do you have a reason for that?
    Viewed in a certain light "number" may be related to pattern and symmetry. In fact number can be construed as a structure with translational symmetry. So when viewed in this light it is part of the subject matter of mathematics. There are other ways in which "number" displays symmetry and pattern ... But note the concepts "pattern" and "symmetry" are fuzzy just like that of "dog".

    Confining maths to number and those who do not hate it is being too restrictive. There was a joke in the department where I was an undergraduate that the only numbers seen by maths students were those of the exam questions.

    C) and finally, the quotes from different thinkers are just used for demonstration, it doesn't mean "if Plato/Einstein said it, it must be true!". Sorry if it seemed like that, I didn't intend it to be like that, the explanations after the quote are supposed to show why what I said is true/false...
    Unless the discussion is about what a particular author thought and the quote is to illustrate it, the use of quotes like this is an indirect appeal to authority.

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  8. #8
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    Re: What is Math? (seriously)

    I like to think of it this way:

    In every "study" we deal with specific objects and the relationships between them (In physics, the objects might be "mass" and "energy" or "distance" and "time", in chemistry, "elements" and "compounds", in history, "people" and "cultures"). In mathematic the objects we study are "relationships" in the abstract.

    (One of the most general, and so abstract, fields of mathematics is "category theory" in which we look at the "category of sets", "category of groups", "category of topological spaces", etc. The "objects" in such categories are sets, groups, topological spaces, etc. while the "morphism" are function, homomorphism, continuous functions, etc. from one of those objects to another. One of the remarkable results of "category theory" is that it is possible to do away with the "objects" entirely and define the category entirely in terms of the "morphism". In other word, it is relationships between the objects that are really important in mathematics.)
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    Re: What is Math? (seriously)

    A few points that I, as a non-mathematician, would like to elaborate on.

    (1) Any set of definitions ends up relying on some smaller set of undefined things.

    (2) There may be a very general and abstract definition of "mathematics" that is meaningful to mathematicians, but it will not be meaningful to students who have not studied any mathematical topics except the simplest.

    (3) Definitions (and the related device of typologies) frequently have fuzzy boundaries but nice clear centers. So there is no ambiguity in saying arithmetic, algebra, geometry, and calculus are part of mathematics. I would be hard pressed to define "language" in a rigorous way that would command virtually universal assent, but the absence of such a definition does not undercut the utility of teaching various languages to students. I do not need a general definition of language in order to justify the teaching of French or Japanese or Mandarin or Hindi.

    (4) It was said earlier that mathematics is broader than the study of numbers, which is true. But the study of numbers is one field within mathematics. The branches of mathematics that are mandated subjects of study involve numbers, which I consider incredibly useful mental constructs, and idealizations of the physical space in which we exist. Do you really believe it a serious question to suggest that there is no value in teaching people about these things because there may be no generally comprehensible definition that includes all the different fields comprising mathematics, including set theory, group theory, analysis, probability theory, number theory, etc., in addition to arithmetic, Euclidean geometry, elementary algebra, and calculus?
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    Re: What is Math? (seriously)

    Quote Originally Posted by zzephod View Post
    If you think maths is about numbers you are mistaken. It is about pattern and symmetry. Common arithmetic is largely about numbers but arithmetic is not mathematics. If you have been taught that it is about numbers (and nothing else) then you have been taught badly.
    Agreed with you completely. Maths is not all about numbers, it is about sets, symmetry and pattern.
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