Lesson 1

Let's recall where we are. We realized that a proof is not just what is written in a book after the word “theorem”. A proof can be understood much more broadly: it is any string accepted by a certain verifying algorithm. After that, we discussed that in different situations, we naturally want the proof to be relatively short. In any case, up to this point, we understood a proof as something static, a string that a person or a computer checks. However, a proof can also be interactive—and this happens already in real life! For example, in math circles, students explain their solutions to problems while answering questions, and in court, the accused proves their innocence by answering the judge's questions.