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Tag: What is mathematics
Art and Mathematics
This post is actually one of the comments in my Mathematics is an Art post. I thought it would be a waste to just leave it in the comments section. It’s very informative and well written so I’m sharing it here. That way more people will have a chance to read it. It’s from the writer of one of my favorite blog Research in Practice, mr. benblumsmith. Here’s what he says about mathematics and art.
I want to add three defining characteristics (to me they are the defining characteristics) to the definition of art that you are constructing. I think all three help illuminate why math can be an art. I’m basing the choice of these characteristics on my own experience as a musician. Other artists might have other definitions, but actually I speculate that these are pretty commonly held as important characteristics of art.
1) Art is creative and expressive.
All the arts are about making things. Songs, paintings, plays, performances, etc. Crafts and industry are also about making things, but what distinguishes art is that the act of creation is an act of expression for the person doing the creating. Creating the painting, playing the sonata, singing the song, etc. are all ways of taking a part of yourself and giving it to others.
(Why math is creative and expressive: every time you figure out how to solve a problem you’ve never solved before, or how to prove a conjecture you have, you’ve made something new that expresses how your mind works to others.)
2) Art engages the imagination.
All the arts stimulate you to see, hear, feel things that aren’t part of the material world. You read a novel or see a movie and you imagine the world it creates. You hear a symphony and you may visualize all kinds of things, or you may just feel them. Either way, your mind and spirit are sent off in totally new directions.
(Why math engages the imagination: if not for math, would I ever have tried to visualize a 4-dimensional torus? The Riemann surface of the sine function? The real projective plane? The strange images in my head that I use to visualize concepts like exact sequences or field automorphisms?)
3) Art is driven by aesthetics.
Artists try to make their creations aesthetically captivating: beautiful, haunting, winsome, grotesque, tragic, delightful, etc.
(Why this applies to math: it’s different for every math person but we all have a sense of aesthetics – what makes math beautiful. For me and for many, a simple argument that proves a powerful result is elegant, for example Euclid’s proof of the infinitude of the primes. Even more beautiful is a theorem that describes a deep connection between apparently very different mathematical realms. For example the Pythagorean theorem as it connects “right anglyness” with “sum of sqaresiness,” the Fundamental theorem of Calculus as it connects “speed” with “area,” or Galois theory as it connects “groups” and “field extensions.”)
Two semi-classic pieces of writing on math as an art that you might find add to this conversation –
Paul Lockhart’s A Mathematician’s Lament.
G. H. Hardy’s A MathematiciansApology.
Both Lockhart and especially Hardy aggravate me (Lockhart with his blanket disdain for math educators and Hardy with his attitude that mathematical talent is an intrinsic attribute that declines with age), but both write eloquently and passionately about how math is a creative art.
Don’t forget to click the links he recommended. Very good read indeed.
Mathematics is an art
Whether we are conscious of it or not, the way we teach mathematics is very much influenced by what we conceive mathematics is and what is important knowing about it. As part of our Lesson Study project with a group mathematics teachers, I was tasked to share my thoughts about the nature of mathematics and its implications to its teaching and assessment.
I have always believed that mathematics should be experienced by the k-12 learners as both practical and theoretical, as a language, as a process of thinking and, as an art. Of these five, I have always felt the least confidence in speaking of mathematics as an art. Most of the times, my “mathematics is an art” becomes “there is art in mathematics”. The latter is much easier to discuss because teachers know this so there’s not much need for me to explain. What I do and I don’t know if I get away with it, is give beautiful examples. Here are two of them. Click image to get to the source.
Math Art | Love and Tensor Algebra via kwout
Where there is art, there is beauty. And what is the beauty of mathematics? In most cases, it’s in patterns. I would regale teachers with patterns in nature that mathematics could perfectly represent and capped my lecture with Galileo’s pronouncement that Mathematics is the language used by God to write the universe. With this, I could get away from mathematics as art to mathematics as language.
Then I came across this post titled What is an art? which defined art as a habit of thinking, doing, or making that demonstrate systematic discipline based on principles. The post described arts as about connections and that understanding the connections between things allows designers to accomplish their goals. It described art as based on principles and not just a series or procedures or methods; that there can be many methods inside an art … Finally, and I love this part, it said that art must be acquired as a habit, so that its practitioners become “unconsciously competent.” I thought the post could very well be speaking of teaching and learning of mathematics especially in its giving importance to making connection, open-ended problem solving, and the acquisition habits of mind which are favorite topics of mine when I’m invited to share my thoughts about mathematics teaching.
You may want to view this beautifully crafted video about mathematic in nature. Click link.