A interactive proof system is like playing a game where you have to convince someone that you know the answer to a question. Imagine your friend gives you a math problem to solve, like "What is 2+2?".
In an interactive proof system, you would play the role of the person being asked the question, and your friend would play the role of the person asking the question. In this game, your friend would be trying to prove to you that they know the answer to the question, while you play the role of the skeptical judge.
In order to convince you that they know the answer, your friend would have to provide evidence, or "proof", that they know the answer. They might show you their math homework, or they might explain how they used their fingers to count to the answer.
As the judge, you would ask them questions to try and test their knowledge. You might ask them to explain how they got the answer, or you might ask them to solve a related problem to see if they really understand the underlying concept.
The interactive proof system is like a conversation between the person making the claim and the person trying to verify it, with each step building on the previous one. If your friend can successfully convince you that they really do know the answer to the question, then you would be satisfied that the proof is valid.
Interactive proof systems are used in computer science to verify mathematical theorems and other complex algorithms. Instead of using paper and pencil, the proof is presented as an interactive conversation between the person making the claim and the person checking it. This can help to ensure that the proof is accurate and trustworthy.