Mathematics As An Art
Leroy Quet
science. I think of it, though, as an art. First, I use much
creativity when doing math, both when thinking up a math problem for
me to study and when actually solving that math problem. Second,
mathematics is beautiful, the beauty existing in both many proofs and
many results.
I suppose my attitude is colored by my attitude (similar to Hardy's
attitude) that I would prefer to do pure mathematics (or the other way
around).
What do some of you think about this?
Thanks,
Leroy Quet
Willse
I'd say that your partly right. Mathematics is not only a science, but also
the quantitative language of science. Mathematics also, however, has
definite inherent beauty, and also has a certain allowance for creativity
(and is therefore at least art-like, if not art).
Travis J. Willse
sal-...@geocities.com
Hugo van der Sanden
> Here's a philosophical topic. Mathematics is usually considered a
> science. I think of it, though, as an art.
I quite agree with you - maths seems to me to be of a very different
nature from what I perceive as 'science'. Firstly it seems to lack
any vestige of the 'scientific method' - that process of constructing
a theory, designing an experiment, performing the experiment, modifying
the theory to account for the results etc[1]. Secondly (though on a
related note), the purpose of science seems entirely different, in that
it seeks to construct abstract models that are efficient at predicting
real-life events to some accuracy[2], whereas maths (at least in any
branch pure enough to interest me) deals entirely with truth and not at
all with real life. (If _this_ is true, and we are allowed to use
_these_ rules, then _that_ is an indisputable consequence.)
Of course what I describe here is not 'the purpose of mathematics'
but 'my purpose in mathematics': the former is not a concept that I
imagine any three mathematicians would agree on. Nor, though, do I
imagine many scientists would agree with my characterisation of the
purpose of science - I am sure many if not most of them believe
themselves to be engaged in a search for truth rather than for a
mere 'useful model'.
I think it is relevant also to note the often cited correlation
between musical and mathematical ability in an individual; from my
perspective, it comes as no surprise.
Hugo
[1] The closest I've come to this in mathematics is when trying to
discern a formula for some sequence for which I have only a generating
function.
[2] Thus Newton's model of space-time is, in situations where its
accuracy is acceptable, more useful than Einstein's due to its
greater efficiency.
FGD
qqq...@hotbot.com (Leroy Quet) wrote:
> Here's a philosophical topic. Mathematics is usually considered a
> creativity when doing math, both when thinking up a math problem for
> me to study and when actually solving that math problem. Second,
> mathematics is beautiful, the beauty existing in both many proofs and
> many results.
> I suppose my attitude is colored by my attitude (similar to Hardy's
> attitude) that I would prefer to do pure mathematics (or the other way
> around).
> What do some of you think about this?
> Leroy Quet
A few comments, speaking as a mathematician and an artist. (In the more
or less classical sense of both words, and more or less successful in
both fields.)
I too think mathematics, at least the pure kind, is an art. I would
even go as far as saying that mathematics is the ultimate form of
poetry as it results from pure association of ideas, the words being
only accessory as they serve only for communication of these ideas. (Of
course, the aesthetic value of the words used is a bonus to any
beautiful mathematical statement.)
I don't think your argument using the creative aspect of mathematics to
prove it an artform is very strong. Surely, creativity is necessary for
any human activity to be an art, but it is not sufficient. Indeed, my
brother, who tends to the archives of a big investment firm, is very
creative in his work, but I don't think his work is art...
But not all the mathematics I have seen can be considered art. Take,
for example, the computer proof of the four color conjecture. By
itself, the four color conjecture is a nice association of ideas, but
the computer proof is not as it lacks the essential aspect of art: it
has to be communicable and communicated---art has no value unless it is
shared.
Many mathematicians, including myself, will agree with you in
considering mathematics as an art. But, so far, very few artists (in
the classical sense) seem to agree. In my experience, most have a very
bad opinion of mathematics and they are thus not ready to accept
mathematicians in their league. Of course, very few artists have a high
level of mathematical knowledge---which is the real problem.
From the historical point of view, mathematics has long been considered
an art. (I remember Plato saying something like this somewhere, maybe
in the Republic, I'd have to look it up.) And, as far as I know,
mathematics was the first science (in the sense of knowledge) to be
studied for its own sake. Note that art is the only form of human
activity which is done solely for its own sake, perhaps this is the
true characteristic of art.
Do you think all mathematicians are artists?
-- Frank
Sent via Deja.com http://www.deja.com/
Before you buy.
Bob Silverman
qqq...@hotbot.com (Leroy Quet) wrote:
> Here's a philosophical topic. Mathematics is usually considered a
> science. I think of it, though, as an art.
<snip>
> What do some of you think about this?
What I think is that you are simply bandying words about.
Define "art"
Define "science"
Now apply the definitions to the study of mathematics. I expect that
you will find that mathematics has elements of BOTH an "art" and
a "science" and that trying to place it in one or the other category
is a fruitless exercize.
--
Bob Silverman
"You can lead a horse's ass to knowledge, but you can't make him think"
d...@world.std.com
> Here's a philosophical topic. Mathematics is usually considered a
> science. I think of it, though, as an art.
it's not mathematical creativity, but mathematical aesthetics,
that leads us to call math an art. that is, in math the pursuit
of elegance is given a priority that is unusual in the other
sciences. on the other hand, what works against math's status
as an art-form is its exclusivity; usually, only specialists
can appreciate the kind of beauty that we seek. this exclusivity
is sometimes found in the visual arts and in music, but aesthetic
exclusivity always calls the definition of art into question:
"yes, but is it art?" "that's not music -- it's sounds ugly!"
in the same way, and for the same reason, calling math an art
necessarily inspires controversy. the popular definition of "art"
is something like: "beautiful stuff, created by talented people,
for the pleasure of all." but 2 out 3 ain't bad; i too think of
math as an art, as much as i think of it as a science and as a tool.
- don davis, boston
-
-
Herman Rubin
>Leroy-
>> Here's a philosophical topic. Mathematics is usually considered a science.
The question arises as to what constitutes a science. The original
meaning of the word, knowledge, certainly applies. But the current
use as knowledge about the "real" world does not.
>I think of it, though, as an art. First, I use much creativity when doing
>math, both when thinking up a math problem for me to study and when actually
>solving that math problem. Second, mathematics is beautiful, the beauty
>existing in both many proofs and
>> many results.
This also applies to the physical and biological sciences. The
popular view of the scientist as someone who fiddles around in
the lab and has nature provide the explanation is false; the
scientific contributions are made by creative people. As
Szent-Gyorgyi put it:
"Scientific research consists in seeing what everyone else has seen, but
thinking what no one else has thought"
Also, is there not beauty in the use of a small set of assumptions
to obtain many results about the behavior of many types of events?
I suppose my attitude is colored by my attitude (similar to
>Hardy's attitude) that I would prefer to do pure mathematics (or the other
>way around).
>> What do some of you think about this?
Hardy and some other modern mathematics are, I believe, an
aberration. I see no difference between pure and applied;
some mathematics has been applied, and some has not yet
been applied.
>I'd say that your partly right. Mathematics is not only a science, but also
>the quantitative language of science. Mathematics also, however, has
>definite inherent beauty, and also has a certain allowance for creativity
>(and is therefore at least art-like, if not art).
This is the point; mathematics is a language. It is a very
simple language, with a small strict grammar, and mainly a
defined vocabulary. Mathematical research is about the
grammatical properties. It is also the only language we
have in which precise statements can be made without very
lengthy circumlocutions, and as such, it is not only the
quantitative, but even the precise qualitative, language
for all forms of knowledge.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
hru...@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558
Richard A. Beldin, Ph.D.
An artist can be judged by the aesthetic appeal of his/her results.
A scientist can be judged by the openness and replicability of his/her
procedures.
Few of us would change our judgement of Picasso's Guernica, even if we
learned that a monkey had done the work. The value of the work speaks for
itself.
Nobody's theory, however beautiful, is valuable if it doesn't gibe with
empirical observations, properly documented.
Dick
Ken Pledger
> Here's a philosophical topic. Mathematics is usually considered a
> science. I think of it, though, as an art....
I believe it's neither. Mathematics is a unique human activity,
which doesn't fall under the umbrella of anything else.
It's sometimes compared with languages. Certainly a great deal of
science is expressed in mathematics rather than in any natural language
such as English. But that doesn't limit mathematics to being a science.
Also, mathematics can express very beautiful ideas just as English can
express poetry, but that doesn't restrict it to being an art. At a more
pedestrian level mathematics can express lists of instructions just as
English can express recipes. (Many people are aware of only this level.)
However, mathematics is not merely a language. It also includes the
literature written in that language. Much of it can't be translated into
English or anything else.
Mathematics is one of the greatest intellectual creations of
civilized humanity. There's nothing else like it. Certainly there's no
need for us to demean it by trying to squeeze it into a box labelled
"science" or "art" or "technique". Only the "mathematics" box is big
enough for it!
Ken Pledger.
Zeisel Helmut
>Here's a philosophical topic. Mathematics is usually considered a
>science. I think of it, though, as an art.
I would say, mathematics primarily is neither science nor art,
it is an epistemology.
While there is no agreement what mathematics is about,
there is an agreement
what mathematical truth and what a mathematical proofs are:
when you specify your premises and demonstrate how
you can derive your conclusion, you found a mathematical theorem,
a mathematical truth.
While mathematics can be helpful in other sciences,
it is clear that the epistemology that constitutes mathematics
is different from the epistemology used in science
(where experiments are an accepted proof).
Helmut
--
Leroy Quet
>Here's a philosophical topic. Mathematics is usually considered a
>science. I think of it, though, as an art. First, I use much
>creativity when doing math, both when thinking up a math problem for
>me to study and when actually solving that math problem. Second,
>mathematics is beautiful, the beauty existing in both many proofs and
>many results.
This is a response to a few of your responses to my origional post.
I think mathematics is indeed both an art and a science, as well as
being a language.
One thing more that makes me think of it as an art is the fact that
its "experiments" take place in the human mind.(Although, computers
are used these days.)
I think that some mathematics can be more an art, some more a science,
but which is which is a matter of taste. Likewise, some mathematicians
would consider themselves to be more of artists, some would consider
themselves to be more of scientists. All is to varying degrees and is
subjective.
Thanks,
Leroy Quet
Hop David
FGD wrote:
>
>
> Do you think all mathematicians are artists?
>
> -- Frank
>
> Sent via Deja.com http://www.deja.com/
> Before you buy.
IMO mathematicians are artists.
Very beautiful objects come from math: the circle and other conic sections,
regular polygons, Platonic solids, logarithmic spirals to name a few.
All human disciplines are influenced by the world around us. But
mathematics is the most abstract. A painter will be inspired by landscapes,
a musician by the sound of wind, water, traffic, the footfall of a horse. A
mathematicians looks inside. Math, more than other pursuits, comes from
imagination.
Many great artists were interested in math. Leonardo Da Vinci, Abrecht
Durer, and M. C. Escher are a few examples.
Isn't mathematics a search for truth and beauty?
Regards,
Hop
Hop David
FGD wrote:
> (snip)
>
> Do you think all mathematicians are artists?
>
> -- Frank
>
> Sent via Deja.com http://www.deja.com/
> Before you buy.
I don't think _all_ mathematicians are artists. But there are some painters
who exhibit in galleries who I don't think of as artists.
regards
Hop
FGD
FGD
hops...@tabletoptelephone.com wrote:
>
>
> FGD wrote:
>
> >
> >
> > Do you think all mathematicians are artists?
> >
> > -- Frank
> >
> > Sent via Deja.com http://www.deja.com/
> > Before you buy.
>
>
> Very beautiful objects come from math: the circle and other conic
> sections, regular polygons, Platonic solids, logarithmic spirals
> to name a few.
Desargues' theorem, Pascal's theorem, true beauty!
> All human disciplines are influenced by the world around us. But
> mathematics is the most abstract. A painter will be inspired by
> landscapes, a musician by the sound of wind, water, traffic, the
> footfall of a horse. A mathematicians looks inside. Math, more than
> other pursuits, comes from imagination.
>
> Many great artists were interested in math. Leonardo Da Vinci, Abrecht
> Durer, and M. C. Escher are a few examples.
>
> Isn't mathematics a search for truth and beauty?
I think so... But some may say that there is a difference between
searching truth and beauty and producing true beauty... To me, it is
still an open question whether mathematicians produce or discover
beautiful objects.
Fred Galvin
> I think so... But some may say that there is a difference between
> searching truth and beauty and producing true beauty... To me, it is
> still an open question whether mathematicians produce or discover
> beautiful objects.
Well, then it is "found art", isn't it?
Hop David
FGD wrote:
> (snip)
> > I don't think _all_ mathematicians are artists. But there are
> > some painters who exhibit in galleries who I don't think of
> > as artists.
>
> I agree: I don't think galleries are artists! ;-)
>
> -- Frank
>
> Sent via Deja.com http://www.deja.com/
> Before you buy.
Dagnab those purple people eaters. Maybe one day I'll learn how to write
good english.
hop