I am a lousy mathematician.  I can’t do algebra.  My eyes glaze over when asked to follow calculations on the board.  And I have a really bad memory.  These are just a few of my keys to success.

Because I have minimal facility with technical arguments I had to learn early on how to translate them into natural language so that I could understand them.  It takes a long time.  And quite often its just impossible to do.  In those cases I have to give up.

But when it works, I come away with a unique way of explaining things that are otherwise “left to the appendix.”  It makes for good seminars.  And it makes teaching time consuming but fun.

Best of all is that enough practice with this and it begins to pay off in research.  I can’t “figure things out” with a pen and pad in front of me.  Instead I start with an intuition, explain it to myself in a natural language, and see where that goes.  Progress usually means formalizing the intuition, seeing some implications on paper, and then retranslating those back, etc. (It helps when I have the talented co-authors I work with.)

I count this liability as a virtue because a) I have to find something to say I am good at, b) being able to explain things in plain language is a valuable skill which I am forced to acquire and c) I’d like to think that it acts as a mild fiddle-filter.  If I try hard and I can’t explain it convincingly it words, I am content to say that it must not be a compelling idea. (Not to say that silly ideas don’t nevertheless sometimes slip through the filter.)