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Comment by dmh2000 | Hacker News Reader

dmh2000·

question: if a reviewer is given a proof to verify, then is it possible to simply step through each transformation and verify it, without really understanding the entirety? Or in cases such as this are there steps that are new or obtuse enough that there isn't a way to verify them without understanding the whole thing. Or, are there individual steps that require so much work that it is impractical to verify them?

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In practice, a proof contains many steps that are highly non-obvious unless you have a deep understanding of the subject. This is done not just for the sake of brevity, but also clarity. In a proof, there are a few key ideas you want to show. Around that, you need glue to convince the reader that your key ideas work, and save them from some the tedium and hard work of verifying that stuff.

A 1/4 page proof, when made as simple as you suggested, could easily bloom to 2 pages. At this point, your reader can no longer find those few key ideas, and is instead lost in the rigor.

If you write a proof in sufficient detail (which nobody does but is manifestly possible), it can be verified with no understanding at all. Indeed, it can be verified by ~300 lines of Python: http://us.metamath.org/downloads/mmverify.py

This process is very similar to analyzing the plot of a novel to the utmost detail: it depends not only on the "facts" but very much on the writing style (compare f.i. Joyce and H. James).

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