One is often drawn to offbeat mathematical ideas and how they could revolutionize mathematics or at least make maths more easy to learn.
Current examples are:
Of course, such innovation can be seen in a historical perspective where all math concepts were at some time radical (irrational numbers, logarithms or hyperbolic geometry).
Also, these innovations can be seen to reduce cognitive load (division in base 12 is easier), simplify notation (replace 2 \pi with \tau), enrich our vocabulary (sets + morphisms = category) or clarify important concepts (triangle geometry vs circle geometry).
But is it worth pursuing these ideas and their actual use in the classroom? Or do they just get in the way and we should just accept things for what they are?