How and how much do the notations and diagrams influence
our understanding of mathematical
concepts?
This question was stimulated by the MathOverflow questions Thinking and Explaining and Suggestions for good notation.
[Math] How and how much do the notations and diagrams influence our understanding of mathematical concepts
big-listbig-picturenotationsoft-question
Best Answer
To support the last remark of Donu Arapura, the following anecdote might be helpful: The late Beno Eckmann, one of the key players of the early developments in algebraic topology in the 40ies and 50ies, was asked to explain, why the revolution in algebraic topology happened in the 50ies. You can find his answer in his "Mathematical Miniatures". In short, he explains that the idea to represent a function by an arrow, and a composition of functions by a diagram was completely unknown until the late 1940ies (!!!), when Leray introduced this notation. There seems to be no doubt that even the formulation of modern algebraic topology would have been impossible without the idea of an arrow and/or a diagram!