Math Languages

Why are YMLP’s Mathematician Laureates called artists? The background for this approach is influenced by the philosophers Nelson Goodman and Hannah Arendt. Goodman’s book, Languages of Art: An Approach to a Theory of Symbols, deals with aesthetics, which is a branch of philosophy that tries to understand creativity, the nature of beauty and taste, and the ways that art can instigate thinking, feeling, and action in others.

Goodman’s Influence on YMLP

Those familiar with the work of Nelson Goodman will recognize that the five attributes listed here are variations on his listing of properties or symptoms of when art is taking place. Rather than trying to decide whether we should call something “art” or not, Goodman helps us to recognize when art is “happening.” If you see a young person helping a group of people to do some or all of these things, they are acting together as artists:

  • Syntactic Density: the finest of differences (in the symbols employed) constitute a difference (among the symbols).
  • Semantic Density: there are symbols to refer to the finest differences in the world to which the symbols refer.
  • Relative Repleteness: comparatively many aspects of the symbols are significant.
  • Exemplification: When a symbol serves as a sample of properties it literally or metaphorically possesses.
  • Multiple & Complex Reference: Where a symbol performs several integrated and interactive referential functions (some direct and some mediated through other symbols).

The shift, for Goodman, is from the question, “What is art?”, to “When is art?” He accomplishes this through a shift from thinking of art as a kind of language or tool of
communication, to a kind of system of symbols. This changes the world of looking at and making art:

Language of Art

  • Symbol Systems
  • Resemblance
  • Representation
  • Denotation
  • Exemplification
  • Authenticity: autographic
  • Authenticity: allographic
  • Notation
  • Score, sketch, script, etc.

Mathematical Arts
Sometimes, Mathematician Laureates enact mathematics as dance. The dancer/choreographer mathematician is primarily concerned with:

  • Body – their materials are their own and others’ bodies; they isolate body parts in order to accomplish their goals.
  • Actions – they do things with and through their bodies.
  • Space – their actions are in relation to the place in which they find or put their bodies, and their work involves interaction with this place.
  • Time – the work has a beginning and end, rhythm, pulse, may or may not be free-flowing or determined, but nevertheless uses time as an element.
  • Energy – are they forceful, graceful, heavy, displaying bodies? Do things occur in time suddenly or smoothly? Delicately?

Sometimes Mathematicians Laureates enact mathematics as sculpture. The sculptor mathematician is primarily concerned with:

  • Line
  • Plane
  • Color
  • Value
  • Form
  • Space – both positive and negative
  • Subject
  • Theme
  • Balance – symmetrical or asymmetrical
  • Proportion or altered proportion
  • Emphasis
  • Rhythm and Repetition
  • Unity and Variety
  • Environmental
  • Installation
  • Additive or Subtractive
  • Assemblage
  • Casting
  • Representational, abstract or non-objective

Through the act of transporting, translating the into fiction, artists are able to keep alive concepts, thoughts, and ideas that have lost their presence in the world. Concepts and ideas that have become dubious can be re-examined through art. (Reference – Knott, 2013; p. 72)

The philosopher Hannah Arendt believed that the arts (and for us, mathematical practices are art!) hold particular promise for restoring connections to the world that have been severed by totalitarianism.

In particular, Arendt expressed four ways in which the (mathematical) arts can help us to unlearn some commonly held beliefs and notions of realilty:

  • laughter
  • translation
  • forgiveness
  • dramatization

And in this respect, it is common to find mathematician laureates using mathematics in one of these four ways. Their mathematical practices disrupt assumptions and perceptions, and help their communities to challenge them.

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