Any areas in maths thats hand wavy? Is so where?
Any area of math must be firmly grounded in order to be an area of math.
On the other hand, a "popularized" account of any area of math will probably need to be "hand wavy" not to be intelligible to the general public. It is not a matter of the "area" but of the depth to which an individual wants to study the area.
Many important areas of math begin handwavy and are only later made rigorous. For example, Fourier series were scoffed by mainstream mathematicians when Fourier first thought of them because he handwaved a few things.
Euler's big breakthrough at age 29 was the solution of the Basel problem... except his "proof" by "factoring" sin(x)/x wasnt made rigorous until much later!
This is the natural way new areas of math are developed.
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