In this passage, I shall illustrate some of the popular techniques for proving: All odd numbers are prime numbers. To this end, we will be visited (again) by the engineer, the physicist, and the mathematician.
Engineer: 3 is prime, 5 is prime, 7 is prime... therefore, all odd numbers are prime.
Physicist: 3 is prime, 5 is prime, 7 is prime, 9 isn't prime, discard as experimental error. 11 is prime, 13 is prime... therefore, all odd numbers are prime.
Mathematician: 3 is prime, 5 is prime, 7 is prime, 9 is prime, 11 is prime...