Applied mathematicians go to school and learn about math just like other mathematicians. There is no special treatment. We aren’t forced to take speech class and we aren’t taught to make a effective slide show. We fumble and trip our way through school and conferences to learn how to communicate with other mathematicians. We strive to explain our mathematics in the most rigorous and precise way possible. We use the language of mathematics to explain math.
Even if we have dreams of applying math elsewhere, we spend all of our time in a mathematics classroom talking to other mathematicians. What happens when we are finally put into a situation with a scientist or an engineer who doesn’t speak math? I’ll tell you. Total communication failure. You may have the same word that means two totally different things. You might think you mean different things but are actually in agreement! You can’t even agree if the variables are in a finite space or an infinite one when talking about the same model. How on earth can we begin to figure out how to communicate with them?
For much of my mathematics career I didn’t worry about the meaning of an equation I was trying to do something with. I accepted the equation as fact and moved onto the mathematics. This became an issue when I learned that I needed to speak with non-mathematicians about my equations. That’s right! I had to communicate my mathematical ideas without speaking in math. What did they know? What didn’t they know? What’s so obvious it’s trivial and what isn’t? This is a non-trivial problem. Oops, that was in math. Perhaps I should say- this is a tough problem!
There comes a time in every applied mathematician’s life when she has to learn that people do math without knowing what an L2 space is. It’s okay. Take a deep breath. This is survivable. Or so I’ve been told. I’m not good at it yet, but I started by comparing notes from the very beginning. I draw pictures and asked them how they would refer to that picture. (This had some fascinating results!) I found that I knew as much about their field’s vocabulary as they knew about mine. That helps. At least both parties are lost. So the next time you see a blank look on your colleagues face, it may not be because of your vast intellectual knowledge. Chances are good you just spoke math when you should have been trying for English.