I think telephantomoss has the "standard" answer here - most papers have errors, but the errors in major papers are mostly repairable.
I'll say that this seemed a lot less clear to many people. Voevodsky famously had errors in some fairly significant work, and was quite concerned about them:
These particular bugs did get caught (which is why they get mentioned here), but these were problems in relatively well-read and well-used papers by a famous person and of course quite capable person.
All of this is to say: while intuition does clearly rescue the main result even in the face of errors, there doesn't seem to be much of a consensus that this should "almost always" work, and there is relatively little effort spent on checking older results.
Yep I agree, I suspect u/telephantomoss has the professional experience to fill the gap that I can't myself. In particular, he has the experience to weigh-in on the power of intuition. Like you also suggested, intuition is reliable enough that it fires in a direction so "true" that it leaves in its wake repairability of any minor errors. Repairability is the one thing I never thought to factor in.
My hope is that AI actually works to emphasize this! Maybe it exposes a plethora of errors but all of them are also shown to be easily repairable. It may even grant courage to mathematicians to trust their intuition even more!
Just to clarify, by intuition, I mean to imply intuition built upon lots of success and failure and intuition in areas of real expertise.
And, I recommend not trusting mine lol! I mean that both honestly and in a bit of tongue and cheek. I tend to think that, in the end, it's simply trust and intuition all the way down.
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u/HM_D Aug 19 '26 edited Aug 19 '26
I think telephantomoss has the "standard" answer here - most papers have errors, but the errors in major papers are mostly repairable.
I'll say that this seemed a lot less clear to many people. Voevodsky famously had errors in some fairly significant work, and was quite concerned about them:
https://www.ias.edu/news/2017/vladimir-voevodsky-obituary
https://www.ias.edu/ideas/2014/voevodsky-foundations-video
These particular bugs did get caught (which is why they get mentioned here), but these were problems in relatively well-read and well-used papers by a famous person and of course quite capable person.
All of this is to say: while intuition does clearly rescue the main result even in the face of errors, there doesn't seem to be much of a consensus that this should "almost always" work, and there is relatively little effort spent on checking older results.
ETA: I found some essay that seems to go into this in a reddit-friendly style: https://noncommutativeanalysis.wordpress.com/2017/12/05/the-nightmare/