## Lead by Counterexample

*March 30, 2011 at 3:03 pm* *
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A wonderful, handwritten sign hangs on the door to my friend’s office:

There is no way of falsifying, “Unicorns exist.”

This is a good example of the nature of mathematics. Although providing just one counterexample is proof that something is not true, the inability to provide a counterexample is not proof that something is true. Understanding this concept is fundamental to understanding mathematics. Perhaps this guy could use a refresher…

At a conference, a mathematician proves a theorem. A young woman in the audience interrupts him. “Excuse me, sir, but I believe that your proof must be wrong. I have found a counterexample to your theorem.”

“Not a problem,” the speaker replies. “I have another proof.”

Entry filed under: Uncategorized. Tags: example, postaweek2011, proof, unicorns.

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