Sharing Joel David Hamkins’s “almost correct proofs” tweet with my son

I saw a really neat tweet from Joel David Hamkins this morning:

Or how about criticizing almost correct but subtly flawed proofs? From my book, Proof and the Art of Mathematics. #ProofandtheArt pic.twitter.com/rrJeSfE3Vh

— Joel David Hamkins (@JDHamkins) May 5, 2020

It seemed like a fun activity to try out with my younger son tonight – and like pretty much everything Hamkins shares, it was even better than I thought.

We started with the first problem and my son walked through a standard proof that the square root of 2 is irrational to make sure that he understood the problem:

Now we returned to the problem and he looked at each step carefully. He misses the error his first time through the proof, but catches it his second time through. This video is a great example of what a kid thinking about advanced ideas in math can look like:

The work on the first problem really helped him on the second problem. Here he was able to understand the false proof and find the error reasonably quickly. He also saw right from the beginning that the conclusion was correct even though the reasoning was wrong – I was happy that he noticed that feature of this problem:

This was a really fun project – it is really neat to see a kid thinking about proofs!