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.

**Update**

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.

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