A requirement for clear speech is clear thinking. Very clear thinking is required to be a successful polymath in a technically challenging field.
In order to accomplish in a technical field, such as math, you need to think very "efficiently". It is possible to do this by spending so long coming up with a mental model of a specific area that your thoughts are efficient, but cannot necessarily be communicated to people except when their mental understanding is a reasonable match to your own.
However you cannot do this simultaneously in a great many areas. Therefore a polymath must find ways to construct models that are both simple and efficient. The underlying simplicity of their understanding then becomes evident in how clearly they can explain a precise understanding of whatever they are talking about.
The blog of the man himself: Always fun to read, and especially rewarding if you thought you were familiar with what he's discussing...