This talk, like every single scientific seminar I can recall attending but one [1], was given in a slideshow program like PowerPoint. The first half of the talk consisted of an overview of Bell's theorem, quantum non-locality, historical interpretations of polarization, etc. The corresponding slides complemented the speaker's words; they were full of illustrations, sentences, and diagrams that helped to convey his message. The second half discussed recent theoretical research by the presenter. The slides contained a lot of mathematics. To explain the math, he would often make statements like,
"From this equation we can see..."or
"It's clear that these two equations reveal..."
After the talk I was struck by how clear and easy to follow the first half was, while the second half was completely lost on me. His statements above were not true! The reason for this is, I believe, not my lack of familiarity with the material but because equations are not always good means to communicate ideas.
The strengths of mathematics are that they are unambiguous and succinct. Additionally, in terms an engineer might understand, they compress and encode ideas. The downside is that during a talk the listeners must uncompress these ideas to understand them, which takes time and distracts from the speaker's message. Additionally, if the audience doesn't have the background required to make sense of the equations, they can't even decode them to begin with.
Equations are most useful when they're easy to understand and when the speaker absolutely cannot allow for any ambiguity in their message. However, since the purpose of a talk is to transfer information to the audience, the speaker must consider more efficient tools, like illustrations and words. More than likely, if an idea can't be represented in words, then it's not a good idea.
[1] The exception was given by a physics Nobel laureate using transparencies and an overhead projector.
