## Mathochism: Proof

One woman’s attempt to revisit the math that plagued her in school. But can determination make up for 25 years of math neglect?

In my other life as a theater critic, I’ve had the chance to review David Auburn’s play “Proof” twice. The show tells the story of a young woman named Catherine, who has devoted the last few years of her life to caring for her father, a brilliant math professor who was forced to retire when he got Alzheimer’s. Catherine is also a brilliant mathematician, but she left school to take care of her dad, and has become a bit of a recluse as a result. The show begins when her father dies, and the idea that he may have left a final mathematical proof that could change his field and his legacy among his papers drives much of the plot, including a conflict between Catherine and one of her father’s former graduate students.

As a math phobe who failed geometry the first time, I have only vague and unpleasant memories of proofs, even though I understand how central they are to mathematics in general. When I was in high school, they seemed inexplicable and complicated and torturous — why do I have to take the trouble to prove that angle is 90 degrees? Isn’t it obvious?

Today, Uchitel introduced us to proofs.

But before I elaborate on that, another confession: last week, when he assigned homework, he gave us problems from the section that introduces proofs. He hadn’t gone over that section, but wanted us to try it out anyway and see if we could make sense of it. I didn’t dare try. Yes, I am a math coward. Part of it has to do with long-ago bad memories, and part with shorter-term ones. And frankly, I just don’t want to become frustrated.

So yeah, I kind of suck that way.

But back to today’s lesson. A classmate had a question about a problem in the section I didn’t do. So far, this classmate is taking on the role of Befuddled Girl, often asking questions in an aggrieved tone of voice. Interestingly, I have not been befuddled so far (cowardly, sure!), but I was really glad she was the one who asked, because that led Uchitel to start explaining proofs.

He began by going over the rules of equations, the rules of inequalities and various definitions (for example, what is a complementary angle?). He also went back over some of the postulates we learned in class last week — so far, we have nine. (Reminder, must make flash cards. We are allowed to use them on the final.)

Once that was taken care of, we were ready to set up proofs, which come in two flavors; direct and indirect. Most of the proofs we are dealing with in the immediate future will be direct, which sounds like a relief. The proof set-up seems simple enough. You put the statements on one side, the reasons on the other.

As we started doing short proofs, first in algebraic, then in geometric form, I felt my panic subsiding. It was actually kind of fun, going from one step to the next to the next. Why have I always been so afraid of proofs? They make a lot of sense.

Now, I doubt grasping proofs will turn me into a brilliant mathematician. But I feel like I’ve taken a significant step in my math education by starting to enjoy them.

All text copyrighted by A.K. Whitney, and cannot be used without permission.

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