While ideas are undoubtedly more important than mere notations, the power of a good notation cannot be over-stated: gresham.ac.uk/lectures-and-events/notation-patterns-and-new-discoveries
As an example of this, in the mid-1980's a notation was developed for juggling tricks. It was found when using this notation that there were hitherto unexpected connections between existing tricks, and emerging patterns in the notation suggested the existence of new, previously unknown tricks. These in turn led to new ways of thinking about, teaching, and learning existing tricks, as well as providing new material on which to build.
The transcript and downloadable versions of the lecture are available from the Gresham College website: gresham.ac.uk/lectures-and-events/notation-patterns-and-new-discoveries
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