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Define......."Mathematics"

Posted on 2004-10-15
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What will be the precise definition of "Mathematics". Like Physics is the study of matter, Statistics is the study of chances. One of mine friend says Math is the study of numbers but I am not agree with her as Math is more than numbers but how can I define it in one or two lines.
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Question by:hyynes
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by:ozo
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by:minichicken
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Quite a good definition of Mathematics: http://www.wordiq.com/definition/Mathematics

Glossary of Mathematics: http://www.mathematicallycorrect.com/glossary.htm
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by:avizit
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by:nicholassolutions
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try http://www.m-w.com and type in mathematics for a concise definition.  Also see the following google link for a bunch of definitions:
http://www.google.com/search?hl=en&lr=&q=define%3A+mathematics
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by:mal4mac
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Mathematics is not just about numbers, e.g. topology involves shapes and mathematical logic involves  logic. Definitions of mathematics (if that is possible) have involved many major philosophers in decades of work, often resulting in very different definitions. I suggest you read a few books by top mathematicians with a philosophical inclination. A good place to start is Roger Penrose's incredible new book "The Road to Reality" which considers mathematical truths to exist in an ideal world of Platonic Forms (although I diasagree with this view, he produces some great arguments for it which are fun to argue against). Check out:

http://www.321books.co.uk/reviews/the-road-to-reality-by-roger-penrose.htm

By the way, physics is not just the study of matter it is also the study of energy (and the origins of matter and energy).

All these subjects are far too complex to produce precise definitions in a few lines. And, to be honest, I don't think a precise definition is possible. It is fun trying though.  Goedels theorem shows that, even in mathematics, there are truths that cannot be proven. So if you can't be precise in mathematics how can you be precise in English language definitions?
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by:avizit
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Actually its not even the question of definitions ..

all the different sciences are not there in isolation , amost always one branch of science will intrude ionto another .. like mathematics poking its nose in physics , biology , physics getting inside chemistry etc . so a clear demarcation is anyway not really clear :)
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by:rjkimble
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From MathWorld:

Mathematics is a broad-ranging field of study in which the properties and interactions of idealized objects are examined. Whereas mathematics began merely as a calculational tool for computation and tabulation of quantities, it has blossomed into an extremely rich and diverse set of tools, terminologies, and approaches which range from the purely abstract to the utilitarian.

Bertrand Russell Eric Weisstein's World of Biography once whimsically defined mathematics as "The subject in which we never know what we are talking about nor whether what we are saying is true" (Bergamini 1969).

The MathWorld page: http://mathworld.wolfram.com/Mathematics.html
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tidda earned 50 total points
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From Webster's Revised Unabridged Dictionary (1913) :

  Mathematics \Math`e*mat"ics\, n. [F. math['e]matiques, pl., L.
     mathematica, sing., Gr. ? (sc. ?) science. See Mathematic,
     and -ics.]
     That science, or class of sciences, which treats of the exact
     relations existing between quantities or magnitudes, and of
     the methods by which, in accordance with these relations,
     quantities sought are deducible from other quantities known
     or supposed; the science of spatial and quantitative
     relations.
 
     Note: Mathematics embraces three departments, namely: 1.
           Arithmetic. 2. Geometry, including Trigonometry
           and Conic Sections. 3. Analysis, in which letters
           are used, including Algebra, Analytical Geometry,
           and Calculus. Each of these divisions is divided into
           pure or abstract, which considers magnitude or quantity
           abstractly, without relation to matter; and mixed or
           applied, which treats of magnitude as subsisting in
           material bodies, and is consequently interwoven with
           physical considerations.


From WordNet (r) 2.0 :

  mathematics
       n : a science (or group of related sciences) dealing with the
           logic of quantity and shape and arrangement [syn: math,
            maths]
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by:List244
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The study of the measurement, properties, and relationships of quantities and sets, using numbers and symbols. -Dictionary
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by:Mangolata
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I would describe it as:

The study of the measurement, properties, and relationships of quantities and sets, using numbers and symbols.
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by:nathanhudson13
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The science of structure, order, and relation that has evolved from elemental practices of counting, measuring, and describing the shapes of objects. It deals with logical reasoning and quantitative calculation
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by:nathanhudson13
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The relationship and properties of quantities, through the use of numbers
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by:nathanhudson13
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a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement
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by:nathanhudson13
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The science that deals with numbers, quantities, shapes, patterns measurement, and the concepts related to them, and their relationships. Includes arithmetic, algebra, geometry, trigonometry, calculus, etc.
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by:nathanhudson13
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the list goes on...

Different people have different interpretations of what maths truly is...

Try building a time machine, going back in time, and asking Archimedes, Euclid and Pythagoras. They are more likely to give you the explanation you require althought i believe thats probably a task in itself;o)
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by:mal4mac
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Pythagoras is likely to give you an answer involving "number mysticism" that would be totally unacceptable to anyone but the most extreme "new age" mystifier. And that from someone who led a school that gave us one of the most rock solid theorems in mathematics. Funny old world. Interesting that Euclid's Elements has remained the touchstone for mathematical truth for so long, and the time machine for Euclid is available from Dover:

http://www.321books.co.uk/reviews/elements-euclid.htm


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by:frugle
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42.
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by:rjkimble
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The nature of mathematics has changed quite a bit over the last century. Those classic definitions are fairly useless these days. For one thing, the collapse of old style mathematics brought on by the various paradoxes (Russel, Richard, ....) of the early twentieth century forced mathematicians to figure out exactly what they were doing and to make mathematics much more precise. In one very real sense, mathematics is now the study of logic and sets. However, that definition doesn't really tell you very much.

Some good references:

http://plato.stanford.edu/entries/russell-paradox/
http://mathworld.wolfram.com/RussellsAntinomy.html
http://mathworld.wolfram.com/RichardsParadox.html
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by:Andrea Ercolino
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Mathematics is the study of what to human beings appears as meaningful structured properties and relations.
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by:ghatlodia
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i would say mathematics is to find certainity and if not then to find nearest approximation to the assumed certainity for particular object, process or anything in this universe.
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by:rjkimble
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I think the best approach to finding the definition of mathematics is to ask mathematicians -- after all, they're the ones who study it.
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by:hyynes
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No doubt that all the links are useful for me  but I have limited points to end up this question.
Hope friends not mind

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by:Andrea Ercolino
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rjkimble,
I like Maths and maybe I'm a mathematician myself (BTW, what makes one a mathematician?)... and I was really surprised when I saw that my short def was very similar to the one you transcribed from wolfram!!
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by:rjkimble
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A mathematician is somebody who studies mathematics. How's that for a nicely circular definition? :-)

I think you need to be exposed to a broad range of mathematical study before you can classify yourself as a mathematician. A typical science major in a U.S. university will study calculus, differential equations, and a couple more courses, mainly aimed at numerical computations (e.g., probability and statistics, engineering math, ....). However, mathematicians study far more diverse areas, such as logic, set theory, algebra, optimization, analysis, geometry, topology, and so on. In my opinion, you don't truly appreciate the breadth of mathematical study until you have taken the equivalent of a mathematics major at the baccalaureate level.

For the record, I have a Ph.D. myself (as I note in my member profile). Theoretical physicists come pretty close to being mathematicians themselves, although they tend to specialize in the more computational areas. In particular, particle physicists and cosmologists tend to be very adept at mathematics and to use highly abstract mathematics in their work. I don't know about the backgrounds of the other experts who post here regularly, but I have seen quite a lot of good stuff posted by a number of them.

I also think there's a particular mindset that separates mathematicians from other scientists. I have worked with physicists, and I have a B.S. in physics myself. The way they tend to look at things differs from the way that mathematicians tend to look at things. One such difference is this: suppose we have an equation, say m*d(dx/dt)/dt + K*x = 0. The physicist will tend to think about what m, x, t, and K mean (mass, position, time, and spring constant in this example), and these concepts will frame the way he or she tackles the solution. The mathematician will tend to look at the equation as a collection of symbols and not bother himself/herself about what they mean exactly. If the equation doesn't describe something "real," the physicist will generally not find it particularly interesting. On the other hand, the mathematician doesn't really care if it corresponds to anything real. That's just a small illustration of my take on the differences in mindset.

And that's my two cents. Hope this helps.
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by:Andrea Ercolino
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During my years at the university I studied calculus, differential equations, and numerical computations (e.g., probability and statistics, engineering math, ....) and logic, set theory, algebra, optimization, analysis, geometry, and something more but almost no topology. :-(
I have a degree in IT engineering.

But I like the circular def, in fact I'm not a mathematician because I don't study Maths. :-)
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by:mal4mac
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Well worth two cents Dr Kimble! I've just read Gleick's biography of Richard Feynman which outlines the reasons that Feynman became a physicist even though he was one of the most (if not the most) talented mathematics students MIT had ever seen. Basically it was for the reasons you give, he wanted the variables to "mean something".
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