Pros and cons of including mathematical equations in presentation slides

You are starting from the wrong point if you are asking the question of whether to use formulas in isolation.

When you write a presentation, a paper, a proposal, an expose, or anything else, here are two questions you should ask yourself:

• Who is my audience? What is their prior knowledge? Why are they there and what are their motivations for attending/reading? What do they want to take away from you provide them with?

• What is my own motivation? Do I want to teach them something new? Do I want to illustrate how smart I am? Do I want to give an overview of a field that everyone in the audience should understand, or do I want to impress a few key people?

If you have answers to these questions, then (and only then) should you start writing. You will find that, maybe unsurprisingly, the question of whether to use formulas will have different answers depending on your audience and what you want to achieve. If you are giving a job talk and you want to provide depth to your talk, then formulas are probably a fine approach. If you are giving a department colloquium that should have broad appeal to grad students and professors alike, then maybe using words instead of formulas is the better approach.

The point is: It all depends -- on the audience and what you want to achieve.

Ultimately, it boils down to a question why people do presentations. In your text I see two reasons:

• presentation is the way to explain your research and results to others;
• presentation is the way to show other how complex is your research and how difficult was it to obtain and understand the results.

People who are mostly inspired by the latter tend to show how much they know about the subject.

People who have mostly the first motivation think about how much their audience will learn about the subject.

I personally believe that the success of the presentation (or a class) is measured not by how much you told, but how much the audience received from you. So I side with your approach — keep long formulas to papers and only use short equations and a lot of visuals in your slides.

I teach in a mathematical field (statistics) and I always encourage my students to minimise equations in their presentations, and never present equations that they are not going to go through and explain clearly to the audience. Sometimes basic equations showing your model form are useful, but sometimes you can give an explanation without the aid of mathematics. In any case, you should only show equations if they assist the audience in understanding your work, and if you are willing to take time in your presentation to go through each equation and explain it.

Including mathematical equations in a presentation solely to "show the complexity of the research" (i.e., show off) is academic masturbation. It bamboozles the audience for the purpose of aggrandising the speaker. Don't do it --- push back on their suggestion to the contrary.