What is a proof?
Or what constitutes a proof in a teaching context?
What’s the value of proof pedagogically?
Do proofs explain anything to students?
These are questions that I’ve been thinking about, and I was reminded about them today during a short discussion in the corridor. But it is too late to write about it tonight. What do you think? I’ll be back.
Being a theoretical physicist, proof does not come natural to me. We derive things. We work in models. We live in big frameworks of theory such as Quantum Mechanics and General Covariance and we try to construct new interesting models. We use mathematics and we trust mathematics.
But, as I have written elsewhere, I find mathematics deeper and basically more intriguing, than theoretical physics. And I do teach mathematics, and I enjoy its history and philosophy. So I struggle with proof.
In my teaching I explain mathematics. Lately I started to experiment with explicitly proving things. So I’ve had to come to grips with what constitutes a proof in a teaching context. This is my answer:
A proof is a logical argument that’s convincing to the audience.