A New Pictorial Mathematical Language

  Over the past thirty years or so, there has been a movement to design proofs without words because sometimes a single picture conveys so much more than two or three paragraphs trying to explain the same thing.

When teaching mathematics, we are told to provide both written and visual information on the same topic so that students have a better chance of understanding the concept.

Since 1975, The Mathematical Association of America has had a column devoted to showing proofs of things without words.  So they use pictures and diagrams to show the proof since sometimes the picture is much clearer.  This article has a lovely multi-part explanation of the idea behind it in easy to understand pieces.

In 2017, three men from Harvard developed a 3-dimensional pictorial language called quon which can be used from math to physics and more.  The language is designed to transmit complex amounts of information in simple pictorial designs.  Although it was created to convey quantum information but in the meantime, it lead to the discovery of results in other areas of mathematics.

This new language uses images to convey the same information in the usual algebraic equations plus a bit more.  It visualizes the concept via a picture which allows people to "see" the concept rather than relying on written equations.  It also allows mathematicians and physicists to share the same frame of view when looking at the same equation rather than interpreting it differently.

Originally, the language operated in two dimensions but recently has expanded into a third dimension so  it can be swiveled, deformed or viewed in different ways, which leads to the creation of equations.  They discovered this language works well in expressing Pauli matrices, an intricate part of quantum information protocols. 

These three men have continued their work to expand the use of the quon language in other sectors of mathematics.  This language shows the promise of allowing mathematicians to experience new insights into all sorts of mathematics from Algebra to Fourier analysis, statistical physics to string theory. 

Furthermore, it is believed that this particular language may be the basis of a new field of study.  In addition, other people are beginning to use quon to prove some extremely complex equations using simple pictorial representations.

Imagine a way to express complexity in just a few three dimensional pictures.  So cool.  Let me know what you think, I'd love to hear.  Have a great day.