Structuring Mathematical Proofs, a paper by Uri Leron

An interesting discussion on how to structure proofs.  I first noticed this paper in 1985.

Could we make proofs more human?  Proofs are generally terrifying, and the thought of having to go through them unpleasant.  The way they are commonly presented, they seem to be rigid and unresponsive to the readers queries, cold and take-it-or-leave-it stuff.  On the whole machine-like.

Turning to logicians is of no help.  Actually there are no logicians left; they have all taken to fabricating machines -- turing machines, generalized turing machines, and maybe 3-phase turing machines.

So, can we on our own do something to ease the situation, at least for the purposes of teaching?  Could we make proofs more `human', combining pleasure with learning?  Are there some general guidelines that we could follow in this endeavour?  Leron's suggestions might be of help.

A `tongue-in-cheek' slogan: Rigour dehumanizes, and absolute rigour dehumanizes absolutely'

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