Funny Children's Stories

Proof

Yesterday, in math class, we were learning what a proof is. Our math teacher said that in mathematics people do not just say things. In mathematics everything must be rigorous. The most important thing in mathematics is proof. And she would tell us what it is.

I had already heard about proofs from different people, but no one could explain it clearly. Only once someone told me that a proof is when someone proves something.

So yesterday I was very happy when I heard that our teacher was going to explain everything to us. And the math teacher told us once again that proof is the most important thing in mathematics. She then added that a proof is when someone proves something. And that if the word “Proof” was written in math books and in textbooks on mathematics, it would then be followed by the actual proof. The teacher also said that everything should be proven rigorously. And that in mathematics no mumble-jumble was allowed.

Then the teacher asked us whether everything was clear or not. And many of us began to nod their heads “yes, all is clear.” Then the teacher asked me what I understood about proof. Honestly speaking, I understood nothing. But I answered that a proof is when someone said that a proof would be provided or wrote the word “Proof.” Afterwards, the proof would be written.

The teacher asked me, “Is that all?”

I replied that I did not know when it would end, this proof thing.

And the teacher said that I did not understand the most important thing of all, that the proof should be rigorous. If it is not rigorous, then it is not really a proof at all. And again, she asked me whether I understood that or not.

While I was thinking about my answer, someone else in the class raised his hand and asked the teacher how one could know whether the proof was strict or not. The teacher switched her attention to him and said that he did not listen to her at all. And that probably no one was listening to her. After that she repeated everything from the very beginning. But as she was repeating all the same things, I again did not understand anything.

But when the teacher asked everyone, “Is this clear?” all of us together answered, “Clear.”

Then the teacher unexpectedly praised me and said that I had posed a very important question. When she praised me, I at first thought she was making fun of me. But it turned out that she was actually quite serious.

She said that mathematicians came up with a way to understand when the proof was completed. In such cases, they would say “which was to be proved.” And she said she hoped that from that moment on I too would only provide rigorous proofs and, at the end, would say “which was to be proved.” And asked me, “Okay?”

And I replied, “Yes, sure.” And I thought to myself, yeah, sure. Right away, I will start to say “which was to be proved.” Even without it, I was already teased enough in our yard for my good grades in school.*

It was a good thing that Anton recently stood up for me. He said that he saw nothing wrong with getting fives in school. And just as things were getting better for me in our yard, our math teacher came up with that.

And for the rest of the day, I kept thinking about how terrible it would be if at school I ever said “which was to be proved.”

And tonight I had a dream that I had already had a few times before. I had a dream that I was “it” in Twelve Sticks. And one of us ran up from behind me and broke up all the sticks. It happens every time I have this dream. But this time, the one who broke up all the sticks walked right up to me very closely, made a terrible grimace, and said, “Which was to be proved.”