For better or worse, we are creatures of habit. The experiences we have had make an imprint on us, coloring our perceptions. Sometimes wisdom emerges from those experiences, but we may also pick up some wrongheaded notions along the way. When it comes to mathematics, we may approach a given problem with preconceived ideas as to what the correct answer should be. Although intuition can be valuable at times, it can also mislead us. Simple mathematical thinking, however, can often clarify things. The following anecdote shows what can happen when our intuition leads us astray.
A Joke
A mathematician, a physicist, and an engineer are trying to prove that all odd numbers are prime.
The mathematician says, “3 is odd, 3 is prime. 5 is odd, 5 is prime. 7 is odd, 7 is prime. By induction, all odd numbers are prime.”
The physicist says, “3 is odd, 3 is prime. 5 is odd, 5 is prime. 7 is odd, 7 is prime. 9 is odd, 9 is not prime. An experimental error. 11 is odd, 11 is prime. 13 is odd, 13 is prime, etc.”
