Thursday, June 28, 2012

'Trivial' trivialities

I am slowly coming to the conclusion that...mathematicians should really stop saying that things are 'trivial'.

As a cultural phenomena, it typically engenders some pretty bad actions--namely, continually negative self-talk and derision.  It is really more a source of punishment, although most people in mathematics, including myself, do it with good intentions by hoping that we are really conveying the message, "Don't worry, this isn't too bad."  If you constantly berate yourself and others that stuff is simple, then when you do find a beautiful--elegant--proof, it will initially be a source of great displeasure.

It also encourages fairly one-sided thinking.  I.e., the slick proofs are typically the proofs that show something in a few lines.  If someone mathematically matures with such proofs, and creating such proofs, they tend to think more like every other mathematician (i.e., it creates a lack of creativity), and the harder, longer proofs will be less frequently come by.

Think, for example, of Posa's Soup Proof.

That proof is absolutely trivial!  Why didn't the mathematical community do this?!  How could we be so stupid?!

^Tl;dr, the above is not helpful.

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