Quote of the Week...from E.T. Bell

 'Obvious' is the most dangerous word in mathematics.                E.T. Bell

I'm not sure what mathematician E.T. Bell exactly meant here by the word "obvious", but when I read this quote earlier this week on the BrainyQuote website it brought to my mind a pet peeve regarding how this field is often taught in schools.  It's more annoying than dangerous when a teacher is rambling through an obtuse presentation at the front of a class and decides to pepper his or her lesson with "of course this" and "obviously that"...if it were all so obvious, we poor students wouldn't need you up front to explain it to us!  Here's another "mathematics" quote I read from the same site, by the late economist Paul Samuelson: "My belief is that nothing can be expressed by mathematics that cannot be expressed by careful use of literary terms".  This quote seems to fly in the face of how we're accustomed to perceive mathematical concepts, in a more two-or-higher-dimensional presentation instead of with ordinary language.  Have you ever heard or read a purely verbal, literary exposition of a mathematical course or even lesson?  I haven't, but I wonder whether the capacity to accurately verbalize mathematical concepts shouldn't be a valuable, sought-after skill for mathematicians as well as mathematics teachers.  Wouldn't it be great, instead of tuning in on the radio to political hacks like Rush Limbaugh, Michael Savage or Mark Levin, you had a station with a talk show whose host spoke Math...has it even ever been done before?  What if society educated people to be able to speak out detailed principles in mathematics and technology in ordinary conversational language with one another...I might find the listening experience akin to discerning meaning from a foreign language I only have rudimentary knowledge of, but I also know that many of us process our thoughts out verbally and such an added component to our communications would doubtless raise the educational and reasoning levels of our general population, knowing such abilities existed and were attainable.  Maybe if some of us achieved a verbal proficiency in math we also could cockily ramble on like everything in it was "obvious", although the opposite effect may instead be the result.  I think Bell may have meant his quote to stress that every step in a mathematical progression of reasoning has to be rigorously attended to and that carelessly glossing over a point as being "obvious" could well unravel the entire solution or theory being examined.  So the upshot of all this is that when anyone is engaged in the sometimes torturous endeavor of mathematical discussion it would be better to just preemptively omit that pesky word from their vocabulary...