In a recent tutoring session, I told my student the following riddle:
A father is driving his son to a baseball game when they are involved in a car accident. The man is killed instantly; the boy is badly injured and taken to a nearby hospital for emergency surgery. While reviewing the case before surgery, the surgeon suddenly cries, “I can’t operate on him! That’s my son!” Who is the surgeon?
I used this simple riddle as an example of unexamined assumptions. One of the great contributions that math makes to a liberal arts education is teaching people how to examine assumptions and construct sound logical arguments. Learning how to write proofs can be frustrating at first, because it means learning to break down every hidden assumption, even the ones that seem pretty basic.
We use the commutative and associative properties of addition and multiplication every day; learning that they have names, and that they’re not necessarily a given in some systems, is so counter-intuitive that it’s hard to absorb. They don’t seem like things that need to be stated or counted among our assumptions. It’s hard to imagine that in some systems a times b doesn’t give you the same answer as b times a. It gets easier after you’ve seen a few examples; not necessarily simple, but easier.
Learning to find the hidden assumptions and then imagine alternatives in math prepares people to do the same thing in the world of human interactions. In human interactions, when cherished assumptions are challenged, and alternatives imagined, the assumptions often get defended as “facts of nature,” or “God’s law,” or “just the way it is.” But once people learn that hidden assumptions aren’t necessarily true, and once they see a few counterexamples, those arguments sound weaker and weaker.
That’s why a proposal to ban teachers from talking about homosexuality will ultimately backfire. The legislator sponsoring the bill claims that he’s trying to give teachers more time to teach core subjects, like math. People trying to defend their unexamined and unsupportable assumptions about human relationships would be better off trying to stop teachers from teaching math, because math is what teaches people to examine their assumptions, imagine alternatives, and recognize counterexamples.
This is why teaching keeps my hope alive, especially when my student was able to come up with three different possible answers to the riddle. It makes me hopeful that it will get easier to imagine that a boy has two fathers or that women, even mothers, can be surgeons.