Is the Mathematical World Real?

When I tell someone I am a mathematician, one of the most curious common reactions is: “I really liked math class because everything was either right or wrong. There is no ambiguity or doubt.” I always stutter in response. Math does not have a reputation for being everyone's favorite subject, and I hesitate to temper anyone's enthusiasm. But math is full of uncertainties—it just hides them well.Of course, I understand the point. If your teacher asks whether 7 is a prime number, the answer is definitively “yes.” By definition, a prime number is a whole number greater than 1 that is only divisible by itself and 1, such as 2, 3, 5, 7, 11, 13, and so on. Any math teacher, anywhere in the world, anytime in the past several thousand years, will mark you correct for stating that 7 is prime and incorrect for stating that 7 is not prime. Few other disciplines can achieve such incredible consensus. But if you ask 100 mathematicians what explains the truth of a mathematical statement, you will ge...