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I'm thinking of art in the traditional sense as visual, musical or literary.

Mathematics certainly requires technique, and hence one can say craftmanship. But whereas the production of an art (at least in the traditional sense) is a unique art object, this doesn't seem to hold for mathematics. Can Newtons Principia, for example, be considered an art object; or Einsteins papers?

Also, an art immediately impacts the emotion, senses & imagination in a way that mathematics doesn't. Of course mathematicians talk about the aesthetic charm of a particular idea or the beauty of a certain theory - but this seems reserved for the cognoscenti, the composer. It doesn't have an audience in the same way say that a composers music can.

But can there be a melancholic mathematics, a joyful algebra? Nietszche of course talked about a gay science - but my reading is that this is not the same thing what I'm talking of here.

  • "art immediately impacts the emotion, senses & imagination in a way that mathematics doesn't". I disagree with this sentiment, although mathematics often requires an uncommon and often large background knowledge to enjoy, so does much of art. For instance, modern art is considered art, but much of it evokes no thoughts or feeling unless you know how to look at and think about the art-work. I know that I've been moved by beautiful proofs (not my own) much more than most of the music I've heard. Also, an artifact is not necessary for art: think of dance or other performance arts. – Artem Kaznatcheev Oct 15 '13 at 21:49
  • I'm not really sure this type of question ("Is X art?") is fit for this site. In principle, anything can be art to someone. Can mathematics be art? Of course, I'm sure someone could find it so. If your question is, "Is it intrinsically art?" then is not the answer simply then a matter of definition? – stoicfury Oct 17 '13 at 8:39
  • @stoicfury, I think there is at least one definitively negative philosophical answer to this question (and your "of course" is misplaced, because to answer positively is to adopt a particular philosophically laden presupposition about what it is that mathematicians are doing), so I'll respectfully disagree. – Paul Ross Oct 17 '13 at 9:47
  • I think that the answer to this boils down to precisely what art is. – Baby Dragon Oct 19 '13 at 5:25
  • there is art in math, but math as a whole is not art. – CognisMantis Nov 19 '14 at 17:39
5

Mathematics isn't art. Only art is primarily focused on emotional expression or evocation. All other things that might evoke strong emotions and feelings as a secondary objective or byproduct (an algorithm, a hand made musical instrument, a mathematical solution) aren't art. Even though we might call them "works of art" that's a superlative and technically incorrect, they're something else first and emotionally expressive second.

A meal can be art if the focus is on emotional response. A painting can be not-art if it's more purposefully messaged (propaganda or advertising). The boundaries are of course vague as so much art could be considered religious propaganda (no disparagement intended here). And of course a urinal can be art. But mathematics is almost always purposed into the not-art category. I suppose it could be repurposed as art (like the urinal), or it's possible that mathematics could be performed as art, but this would be the rare case, or maybe an art form that has yet to really be developed.

Obviously I'm putting a fairly rigid definition on art, but if not constrained this way anything can be art. The anything-can-be-art viewpoint might be useful in some ways, but then what would artists do?

  • If only art is primarily focused on emotional expression or evocation, would you claim that all art is primarily focused on emotional expression or evocation? Consider the pieces of Escher that I presented above, and others of his works; or many modernist pieces. Do these seem to have the provocation/expression of emotion, or of thought and ideas, as their motivating principle? I agree that not everything is in practise art; but I think that your definition is much too restrictive, and furthermore it's not clear why art (as with 'game', pace Wittgenstein) should even have a definition. – Niel de Beaudrap Oct 17 '13 at 6:45
  • @NieldeBeaudrap - yes, my definition is too restrictive. Thoughts and ideas are definitely part of the currency of art. But IMO the definition can't be open to any kind of communication, a stop sign isn't art (until it's repurposed as art). I guess my position is that art can't be utilitarian. Of Mice and Men is art, Advanced Photoshop isn't art, but there's no clear line. – obelia Oct 18 '13 at 18:11
  • I largely agree; I don't see a urinal as art, but a provocation to the art establishment, which then became enshrined as a symbol; whereas renaissance art took Christianty & Classical culture as a subject - contemporary art seems to take philosophy as a subject. – Mozibur Ullah Apr 25 '14 at 20:31
  • @de Beaudrap: Modernist art (& Escher), if we take the full spectrum of art (all times & geographies), is minor; the general picture I see, appears to be emotion directed to an other, human or sacred (heroes/nature/god/gods). Obelias definition agrees with Deleuze/Badiou - where its primary sense is affective. – Mozibur Ullah Apr 25 '14 at 20:38
  • 1
    From the point of view that mathematics explores our shared intuition and not some objective world, and that the feeling of clarity and harmony we get from logic is an emotion, and not something entirely different, your argument here breaks down. The ultimate aim of mathematics is to evoke that feeling, and not to provide a basis for science. The latter is just a natural side effect because only emotionally satisfying logic can really be used on the world, (otherwise it is just too much work). – jobermark Feb 18 '16 at 17:37
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You are asking a question with a bit of subtlety here. How much of mathematics consists of mathematical writing — that is, general attempts by the author to convey an idea (if only to themselves in the future)? And of course, what do you mean by art?

Can Newtons Principia, for example, be considered an art object; or Einsteins papers?

Undoubtedly yes, particularly in the case of Einstein's work. His famed Gedankenexperiments, and the logical consequences thereof, are the subject of this work of art; his prose is the execution — which are the more excellent because they don't involve heavy mathematics; his use of simple algebra to tackle the subject of what we call special relativity is routinely extolled by physics educators, and amounts to an appraisal of artistic technique used to convey an important subject. That the subject is important intellectually and instrumentally rather than grasping at human emotion directly is, to me, beside the point. Furthermore, as an afficionado of clear communication, I would rate the clarity of the prose as nearly matching Bertrand Russell, another great mathematician and (quite independently but more importantly in this case) explicator, whose prose is a pleasure to read because he makes approaching subtle distinctions nearly effortless through his precise but flowing style.

I am less directly familiar with Newton's Principia as a body of text, and perhaps a modern appraisal would find it wanting somewhat in style; as medieval artists today might be criticized anachronistically for their lack of use of perspective (for realistic geometric representation, not only being unavailable to them, was perhaps not their intent either). Newton uses a lot more argumentation using Euclidean axiomatic constructions than any modern approach would ever use; but of course, Newton invented most of the tools we would use today to convey the subject, and was secretive enough not to use them in his own treatise on natural philosophy. We might construe Newton's work as an exercise in constraint as a body of art treating its proper subject, but it is a body of art that would be extremely challenging to most who tried to appreciate it.

But these are the works of masters, and besides are mostly full of prose. You probably mean to ask whether we are meant to interpret the formal symbolic treatment of the mathematics as poetry. Calling it "poetry" is a bit much, perhaps; but it does get across that I mean a style of writing which is in sharp distinction from representing anything like normal speech. Indeed, writing a piece of mathematics involves a lot of precise repetitive acts and carefully judged movements in particular directions, so that if one must describe an analogue to mathematics in another creative field, it would be perhaps more appropriate to compare it to dancing, and in particular ballet. Certainly I am struck by the extent to which a mathematical development can be graceful and flows smoothly — or clumsily fails to do so.

If mathematics is an art, is it a representational art? Absolutely, yes. Even the most abstract mathematics is grasping at notions of relationships and structure; extremely technical formulations of ideas that perhaps only a philosopher would love, except in those cases that physicists or other scientists discover them in their subject. Or, of course, a brilliant artist such as M.C. Escher, who without mathematical training intuited tilings of the hyperbolic plane in such works as Angels and Demons:

"Angels and Demons", M. C. Escher.

This is not to say that a mathematical idea is art because an artist could convey it visually: this is to say that an idea could be apprehended independently by mathematicians and visual artists, and presented in different forms, where the medium of the visual artist is the one better suited for a popular audience.

Yes, mathematics is an art, and every calculation in math class is analogous to a study of how to express or exercise some idea. If it is a little recondite, can we not say the same for contemporary art, or atonal music? If the subject or the expression is a little recherche, perhaps this puts mathematics in good company (or perhaps one might say in practise that it puts the other pieces of difficult to appreciate art in good company). But undoubtedly mathematics has many of the features of an art whose purpose is to explore an idea. Back of the envelope calculations are hasty sketches; we even call them "proof sketches", though the sketch is not of the proof but of the idea that the proof itself is meant to convey, just as a sketch is developed upon in portraiture.

If the art objects of mathematics are not as unique, it is merely because the techniques of mathematics are easy enough to grasp, for enough others, that it is an art uniquely amenable to forgery — except that we don't think in terms of forgery, because as an art the priority of mathematics is not so much unique expression as elegant expression (can you forge the art of a dancer?). This is in part because we use the representations we create to try to better grasp at a difficult subject; and as far as pride and professionalism are concerned, first expression is what most people obsess over (as with other works of art as distinct from their forgeries).

As for the final question — can there be a melancholic mathematics, a joyful algebra? — though economics may be called a "dismal science" (where the latter part of the term is perhaps an unsupported allegation), I don't think this is the point. Does Excher's Angels and Demons have an emotional impact? Perhaps if one is strongly religious; but what of his other works, such as Metamorphosis II?

"Metamorphosis II", M.C. Escher

What emotion does this provoke? From personal experience, and that of many I've known, there are perhaps only two clear emotions that it provokes, which may or may not be distinct: intrigue and wonder. The audience may be narrow in which mathematics provokes such responses, but this is exactly why many people are drawn to it: for whatever reason, many are transfixed by the ability of mathematics to express relationships. While there may not be many artists such as Escher who provoke such an immediate but relatively abtracted intellectual appreciation (he's no Van Gogh or Michelangelo, after all: one mounts an Escher on the wall for different surface reasons than one does Starry Night), at least in Escher we can see that there is precedent in the visual arts, by a non-mathematician, of someone whose work provokes a very similar response — and anecdotally, in a very similar collection of people — the same general response as mathematics.

Thus I would say that mathematics is an art; and that if you insist that it is not an art, that there is then no sharp dividing line between art and mathematics, as one can gradually and subtly shift between the two subjects much as Escher shifted between the forms in his own art.

6

The connection between mathematics and art goes back thousands of years. Mathematics has been used in the design of Gothic cathedrals, Rose windows, oriental rugs, mosaics and tilings. Geometric forms were fundamental to the cubists and many abstract expressionists, and award-winning sculptors have used topology as the basis for their pieces. Dutch artist M.C. Escher represented infinity, Möbius bands, tessellations, deformations, reflections, Platonic solids, spirals, symmetry, and the hyperbolic plane in his works.

Mathematicians and artists continue to create stunning works in all media and to explore the visualization of mathematics--origami, computer-generated landscapes, tesselations, fractals, anamorphic art, and more. AMS

One of the most commonly observed art created by mathematics is the various algorithms that organically create fractals and patterns for example. Consider Fractal Geometry.

Creation of natural objects normally the subject of artwork through a mathematical formula is just as artistic: enter image description here enter image description here enter image description here

Then you have abstract art: enter image description here enter image description here

So simply put, mathematics can indeed be art as well as the foundation for beauty, symmetry and organizational foundation of building or drawing in general.

  • Nice choice of pictures. I'd call this digital art - or computer assisted or algorithmically assisted art. Its not mathematics. I'm asking whether mathematics in-itself is an art rather it being the method to produce art (as above) or being the subject of art. That is can we consider the construction of measure theory, or the theory of integrals as an art object - or along these lines. – Mozibur Ullah Oct 15 '13 at 3:14
  • Indeed, this is art which has been produced with mathematics as a tool, as one would sculpt using a chisel or paint using a brush; or indeed because the subject is an abstract entity, perhaps one might say that it is art with a mathematical subject, as one might paint a snowflake (without implying that snowflakes are themselves art). – Niel de Beaudrap Oct 15 '13 at 8:28
2

The really tricky aspect of this question concerns the age-old problem of whether Mathematics is supposed to be a representation of something (say, relationships between things in the world on which we might establish some sort of predictive capacity) or whether its subject matter is privileged and ontologically substantial in its own right (as genuine objects in a fully reduced theory of science or as platonically distinct parts of reality that the mind is essentially linked to).

It seems like an important criterion for something to count as a form of art that it has intentional content (even if we do not take the artist's intent to be any part of the appropriate interpretation of art), or can be considered a depiction using a representational medium (this depiction need not be "of" anything in particular, or even be unambiguous or unequivocal). It would disqualify something from being art if it was a matter of bare existence. Plato's writings about foundational metaphysics and the forms may well count as works of art, and even a logical description of his theory might at a stretch be considered a work of art. On only one account would Plato's forms themselves, were they to exist, be considered works of art - Creationism. On any other interpretation, the forms would not be works, art or otherwise; they simply are, independent of any kind of intentionality, and this rules them out from any claim to constituting artistry.

Realist mathematicians aren't content to say that all there is to their subject matter is a collection of pieces of work in their proofs and theorems. On the Realist account, proofs and theorems are truthful because Mathematics is a factual discipline, and this needs to be so in order for its practice to be legitimate as a tool for other aspects of scientific analysis. As Frege remarked in his Basic Laws of Arithmetic, we invest our efforts in mathematics on a presumption of its unequivocal interpretation, and in order for this to be so,

... suppose one defined, for instance, the number zero, by saying: it is something which yields one when added to one... Only when we have proved that there exists at least and at most one object with the required property are we in a position to invest this object with the proper name `zero'. To create zero is consequently impossible. (p12)

A mathematical realist would then have to put their foot down and say that no, Mathematics is not an art. It can inspire art, and Mathematicians can be inspired by art to explore and theorise about previously uncharted areas of mathematics, but mathematics itself stands on its own; a body of facts to be represented by artists should they so wish.

  • So... you're saying that a realist would not say that mathematics is art, because like photography or really accurate portraiture, it's too representational? – Niel de Beaudrap Oct 17 '13 at 6:41
  • Niel, I think a realist would say that mathematics is not art because it's not representational, but rather a thing in itself. A photograph or portrait might be art (perhaps human inscriptions of proofs and theorems might be examples of this), but even if that were the case, you wouldn't say that the subject of the portrait or photo was art. The subject just exists. The realist doesn't create something new with proofs or theorems but simply uncovers mathematical facts, and written work doesn't change anything about what is mathematically true; merely what is known to be so. – Paul Ross Oct 17 '13 at 10:16
  • The representation in this case is the writing, i.e. "1+1=2" is a proposition which refers to a fact. Just as Magritte's painting of a pipe is not itself a pipe, instances of mathematical writing are not themselves mathematical facts, if one supposes that the writing refers to things which would in any case be True. – Niel de Beaudrap Oct 17 '13 at 12:37
  • Yes, that's right. But the mathematician isn't fundamentally engaged in the practice of writing or working with syntax, on a realist account. The writing is just how they communicate what they've been doing, rather like writing up a report after the fact. The work the realist mathematician does is conceptual/platonic/holistically-blobby-part-of-empiricist-science (delete as appropriate). Mathematics is what the writing tries to represent. The painting is not a pipe, and rather than treating Maths as the Painting, for realists, Mathematics is the Pipe, not art attempting to represent it. – Paul Ross Oct 17 '13 at 13:28
  • As a note, I am playing Devil's Advocate here, so any card-carrying mathematical realists would be very welcome to step in and correct me or amend my answer! – Paul Ross Oct 17 '13 at 13:39
1

Mathematics is not art. Art forms are accompanied with criticism, which discuss how to evaluate a piece of art, beauty and aesthetic of a piece of art and provides a framework to deepen our analysis of that piece of art. Art criticism influences and impacts upon the practice of art itself and has the ability to influence trends and patrons.

I contend that there is no criticism of mathematics, in the above senses. Neither the philosophy of mathematics or the ranking of journals serve as criticism. From this, I conclude that mathematics is not art.

1

Math in itself, the science in itself, the desire to inrerprete the world through pure numerical expressions and relationships, it is for sure a form of art... but the process of actually writting down a mathematical thought, its most likely not art... i say that because to me art is creativity: so any process that seeks to bring meaning to life, any process that seeks to create (meaning, life) is art.

  • Pedro, you may have a good point in here, but I would cite a canonical philosopher instead of your own opinion. Also, why would you say that it doesn't require creativity to express a formula or theorem in the most succinct way? Isn't that a similar process to expressing one's self in other domains? – James Kingsbery Nov 17 '14 at 19:09
  • Doesn't mathematics create meaning? Einstein, for instance, and the idea of 'relativity' which has crept (for better or worse) all the way into the world of modern art, the Beats, the Folks, the Civil Rights movement, the hippies, the politics of the New Left, the faith or 'anti-faith' of the New Theology? I could give examples, but I'll bet you have your own. – Darcy Davis Nov 19 '14 at 20:16
0

While Mathematics require creativity, it cannot be considered an art, simply because the result is always singular. There can be no creative alternative answer to any question (within the realm of logic), only a correct, a better or a worse answer. Therefore Mathematics also lack expression. You cannot find an answer "your way", you can only find a correct answer.

If you'd compare mathematics to painting, then there would be for any model only one correct way to draw it, and all painters would just vary in a degree of how exact they can copy that one perfect model. And even if that requires skill, talent and creativity to some degree, it cannot be considered art.

  • How can you say that mathematics requires 'creativity' and then you can only find a 'correct' answer? There are many ways to think about numbers, for example. – Mozibur Ullah Apr 27 '14 at 9:05
  • Creativity is required to find that one solution. Many problems were solved by people thinking out of the box. – TwoThe Apr 27 '14 at 10:24

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