missing pieces

I am currently taking a course in mathematically modeling prions, viruses, and bacteria.  It turned out to be a very small seminar averaging 4-5 students per class, but it has been fascinating because the instructor's wife - also a mathematician - is attending the class, as is another female faculty member.  (These are, incidentally, the first two female professors that I have interacted with during my time in the math department.  Also incidentally, it is hilarious and adorable to watch this elderly couple squabble over whether what is written on the board makes sense.)

Gender and marital relationship aside, what intrigues me is watching very experienced mathematicians argue, critique, and frequently interrupt to make clear that they are confused by the lecture.  I am frequently confused and lost, but nevertheless I am usually hesitant to interrupt because I assume it is my lack of mathematical background that is the problem, not the lecturer.  As such it would take more than fifteen seconds, say, to catch me up on the calculus of variations, asymptotic expansions, perturbation theory, or whatever area of mathematics or physics I do not know.  But as often as not it is a simple mistake, omitted symbol, or other minor problem that is confusing not only me but also everyone else in the room.  So one of the huge bonuses of the class is watching the experienced mathematicians interact with the lecturer.

In addition to the three faculty that attend, there is a single other student in the course.  He has a background in pure mathematics - but absolutely no biology.  I have a background in biology and medicine, including the short course on microbiology from medical school, but a fairly limited background in mathematics.  So it's interesting that while he generally has no idea what we are modeling - to the degree that he didn't know what a virus was (a bit of genetic material, either RNA or DNA, surrounded by either a membrane, protein capsid, or both) - I usually have very little idea how we are modeling it.  After class the other day, I gave him a quick sketch of how HIV infects cells and how that process differed from, say, that of a bacteriophage.  In return, he gave me an outline of the assumptions being made in the model - which I didn't even recognize were assumptions or a whole area of physics!

So therein lies the fundamental difficulty not only in doing research but in sharing one's results: the biologists who would care about and be able to critique them can't understand what is being said, while those able to understand models have no idea what is being modeled (with a few rare exceptions).  And while mathematical biologists do end up learning the biology of their areas, they may or may not know anything about other areas of biology.

Specifically, I've noticed that the math and physics students usually don't have a very good notion of the biological systems being modeled, nor whether the model in question does a good job of capturing the essential elements  of the system.  A major problem, at least in the mathematical biology courses I have taken, is that they tend to be much more likely to take the behavior of the mathematical model as accurately representative of the biology itself.  On the other hand biologists tend to zone out as soon as an equation appears, because the mathematicians are speaking in a foreign language with very foreign concepts and tools.  And personally, I have a pretty good grasp of the importance of others' models, a very basic ability to critique them based on their correspondence with biology, and plenty of biological questions - but not enough mathematical and computational tools to tackle them.

Maybe in another decade?