My job is part fancy technical writer, part creative tester of software. I was looking over a book I found on testing and debugging and it has the following joke:
A Mathematician, a Physicist and an Engineer are all told "all odd numbers are prime".
Mathematician: This is silly. 9 is a non-prime odd number.
Physicist: 3 is prime, 5 is prime, 7 is prime, 9 is experimental error, 11 is prime, 13 is prime, 15 is experimental error, 17 is prime, 19 is prime. The empirical evidence is overwhelming.
Engineer: 3 is prime, 5 is prime, 7 is prime, 9 is a good approximation, 11 is prime...
The conclusion of the text?
Avoid the physicist's error: not trying the right value
Avoid the engineer's error: trying the right value, but not noticing the contradiction
Be smart like the mathematician: finding the right counter example, with minimum wasted efforts, that contradicts the statement
That's my job apparently... being smart like the mathematician.
More "9 is a prime" responses are here.
As an aside, the REAL response of the mathematician was: 3 is prime, 5 is prime, and 7 is prime. By induction, all the odd integers are prime.