New 3QuarksDaily column:
I have some very simple New Year’s resolutions, and some that require an entire column to spell out. One example of the latter is that I want to make a subtle but meaningful change in how I talk to my (middle and high school) math students about proofs.
First, I need to be open about the fact that talking about proof in mathematics comes with an especially strong impostor syndrome: as a secondary school teacher, who am I to talk about the nature and limits of deductive reasoning in a discipline of which I have barely scratched the surface? I know high school proofs of high school mathematical concepts; I am vaguely aware that people much cleverer than I have tried to reduce all mathematical claims to analytical (logical) truths, or at least to a limited set of axioms; and I believe that after having mentioned this, I have to name-drop Gödel as the person who has supposedly put a stop to these projects, even though I have never studied his incompleteness theorem and doubt I would be able accurately to judge its relevance and meaning. That’s about it.
More here.