Why are many mathematics talks incomprehensible?
Something about our field has been bothering me for a while: Overall, we mathematicians do a relatively poor job of presenting our research to a general audience (here is Doron Zeilberger’s comment on the subject). There are certainly some spectacular expositors in the field. But overall, we could do much better in presenting our work. This is a problem both of training and practice.
I work at the intersection of mathematics and biology. Over the years, I have been on a number of thesis committees for graduate students in both fields. Graduate training in the two disciplines is quite different. Importantly, students of mathematics are not trained as extensively to give presentations, or write in an accessible way. There are a few differences in the way we do things that could be responsible:
Mathematicians spend a lot less time preparing graduate students to present their research. Most biologists require students to give talks regularly during lab meetings, and at conferences. Many graduate biology programs require graduate students to give oral progress reports annually or twice a year. Although things are changing, this does not seem to be the norm in mathematics.
We also put less emphasis on writing. Publishing one or two peer-reviewed paper is frequently a requirement for a PhD in biology. Moreover, students often have to submit a thesis proposal, or a mock grant proposal as part of their qualifying exams. The writing is critically reviewed – I have been on committees where students had to rewrite their proposal several times before it was accepted. For many students in mathematics the thesis is the first, and sometimes only, original piece of scientific writing they will produce.
The reason for the differences may be that good presentations are much more important in biology. Even a mediocre talk will raise eyebrows, and it can kill your chances of getting a job. And a poorly written grant will not be funded, no matter how good the ideas. In biology there is a high overlap between people that do excellent research and give excellent presentations. Less so in mathematics. The cynical reply here is that these are just better salesman and get more funding, and hence run bigger and more productive labs. But perhaps these are simply the people who view the presentation of their research as an integral part of their work.
I don’t mean to say that we need to emulate biologists in every way. I see plenty of problems in graduate education in biology – graduate students frequently get no programming experience, and little teaching experience. They most certainly do not learn enough math and statistics.
However, with the current situation in academia, only a handful of PhD students will find academic jobs. Mathematics students entering industry will have learned the persistence and concentrated effort necessary to do research. Many will learn how to program. These are invaluable skills. However, the ability to write well and present ideas clearly is also indispensable. Shouldn’t we do a better job in teaching our students these skills?
Things are getting better. For instance, the students in our SIAM chapter at my university (University of Houston) have organized a student paper presentation event. Participation was strong, and I was impressed with the presentations. Paper exchanges, where students read and comment on each other’s writing have also been helpful. There are numerous other ways in which we can help our students and postdocs become better communicators. And I think we should consider this an essential part of their training.