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When are two proofs essentially the same? (2007)
A couple of years ago I spoke at a conference about mathematics that brought together philosophers, psychologists and mathematicians. The proceedings of the conference will appear fairly soon—…
It is an interesting challenge to try to be as precise as possible about these words, but I found that even the seemingly more basic question, “When are two proofs the same?” was pretty hard to answer satisfactorily. You may have general comments to make, but I’d also be very interested to hear of your favourite examples of different-seeming proofs that turn out, on closer examination, to be based on the same underlying idea (whatever that means). Having said that, I once put that to Terence Tao in a conversation and he immediately adopted a more general perspective from which one could regard the two arguments as different ways of carrying out the same essential programme.
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