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Latest on abc Posted on April 3, 2020 by woit
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David Roberts says:
April 15, 2020 at 2:45 am
@W
gosh, thanks!
Suppose you take the same argument and present it in two different languages ? one, the standard categorical language, and two, Mochizuki’s language where distinct copies of an isomorphic object are relevant for colimits and other categorical constructions.
Assuming no other knowledge of what the argument actually is or how it is written, which language is more likely to conceal a subtle error in calculations or other mistake, and which language is more likely to make such mistakes easier to see?
This is tricky: it depends who’s reading it. Who are you envisaging seeing mistakes?
I can’t imagine (ignoring the fact this is IUT and tremendously baroque) that someone who’s had a decade of practice with their own idiosyncratic style of working would make mistakes more frequently that someone using the language of the majority, all things being equal, apart from the fact the latter person has more potential external checks and balances.
This latter point I think can’t be overemphasised. Andrew Wiles was still speaking the language of his community by the time he emerged with his (first attempt at a) proof of FLT, and even engaged the help of someone else to try to check the subtle parts of the argument before that. This hasn’t happened here…
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