"A seemingly modest change of notation may suggest a radical shift in viewpoint. Any new notation may ask new questions." (Barry Mazur, "Imagining Numbers", 2003)
"Graphical design notations have been with us for a while [...] their primary value is in communication and understanding. A good diagram can often help communicate ideas about a design, particularly when you want to avoid a lot of details. Diagrams can also help you understand either a software system or a business process. As part of a team trying to figure out something, diagrams both help understanding and communicate that understanding throughout a team. Although they aren't, at least yet, a replacement for textual programming languages, they are a helpful assistant." (Martin Fowler," UML Distilled: A Brief Guide to the Standard Object Modeling", 2004)
"An essential feature of mathematics and statistics, particularly at a higher level, is the use of shorthand notation for a variety of concepts and measures. While this can be a strength in terms of providing conciseness and precision, statistical notation often proves to be an obstacle for learners in the early stages of learning." (Alan Graham, "Developing Thinking in Statistics", 2006)
"The notation is more important than the sound. Not the exactitude and success with which a notation notates a sound; but the musicalness of the notation in its notating." (Cornelius Cardew, 2006)
"Understand the data. What is given in the problem? Usually, a question talks about a number of objects which satisfy some special requirements. To understand the data, one needs to see how the objects and requirements react to each other. This is important in focusing attention on the proper techniques and notation to handle the problem." (Terence Tao, "Solving Mathematical Problems: A Personal Perspective", 2006)
"Write down what you know in the notation selected; draw a diagram. Putting everything down on paper helps in three ways: (a) you have an easy reference later on; (b) the paper is a good thing to stare at when you are stuck; (c) the physical act of writing down of what you know can trigger new inspirations and connections."
"But in mathematics there is a kind of threshold effect, an intellectual tipping point. If a student can just get over the first few humps, negotiate the notational peculiarities of the subject, and grasp that the best way to make progress is to understand the ideas, not just learn them by rote, he or she can sail off merrily down the highway, heading for ever more abstruse and challenging ideas, while an only slightly duller student gets stuck at the geometry of isosceles triangles." (Ian Stewart, "Why Beauty is Truth: A history of symmetry", 2007)
"Mathematical ideas like number can only be really 'seen' with the 'eyes of the mind' because that is how one 'sees' ideas. Think of a sheet of music which is important and useful but it is nowhere near as interesting, beautiful or powerful as the music it represents. One can appreciate music without reading the sheet of music. Similarly, mathematical notation and symbols on a blackboard are just like the sheet of music; they are important and useful but they are nowhere near as interesting, beautiful or powerful as the actual mathematics (ideas) they represent." (Fiacre 0 Cairbre, "The Importance of Being Beautiful in Mathematics", IMTA Newsletter 109, 2009)
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