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First, I am not sure Functional Analysis is as obscure as some other areas. But, second, this just shows, once again, that one ought never to use "clearly," "obviously" etc in proofs.

It is the same principle as writing programs so they are easier for the next programmer to read. That person may be you.



I don't read maths papers, but in CS papers too, words like "clearly" and "obviously" etc. serve as red flags to me that screams "hand-waving or big gaps coming up".

Often it's understandable short-cuts, but often it also turns out that the author has left out very substantial chunks of knowledge, or sometimes clearly don't understand why they got the results they did.

In CS papers there's an additional red flag: Maths. Outside of a few maths heavy areas of CS where it is justified, if a CS paper is full of equations, it's a good sign they'll have glossed over a lot of essential information, such as parameters that often turns out to be essential to be able to replicate their results. Not always, but often enough for me to be vary.

I'm guessing it is because in the instances that include pseudo-code or working code, it is instantly obvious that something is missing, both to the author and to reviewers, but when it's obscured in equations it takes more effort to identify the same flaw because so many steps are often legitimately left out because of conventions that it's non-trivial for someone not steeped in the same notation to determine which bits should be defined and which bits are not necessary. I'm sure most of the time it's not intentional. But taking that shortcut seems to make it a lot easier to forget which additional information is actually necessary. And the irony is that I've seen plenty of example where the equations have taken up just as much space as pseudo-code or even working-but-naive implementations would have taken.


Wait, let me get this straight. It's a red flag when a computer science paper has math in it? Computer science (in the asymptotic limit) is math. And the papers ideally should read like math papers. Otherwise it's not CS.


it also leads to proof by intimidation which often masks errors.




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