Economists used to communicate without using any math at all. They relied on clear thinking and plain English. A fantastic example of this is Ronald Coase’s 1937 essay on the nature of the firm.
Economists should still rely on clear thinking and present their thoughts and research findings using plain English. No matter how technical, all good communication should strive for clarity.
In general, scientific, technical and business communication contains far too much jargon and obfuscation. We readers are often blinded by obscure notation and professional jargon when a few clear well-written paragraphs would suffice.
All that noted, there is an important role for using mathematics to communicate in economics. Quantitative analysis allows us to extend and explore in ways that English alone simply cannot.
Modeling and simulation, for example, can give us insights that would otherwise not be possible without providing a quantitative interpretation. These tools rely on a clear English language elucidation as their foundation.