Nontrivially fillable gaps in published proofs of major theorems
In my experience, Linus&#x27;s law [1] is false in scientific research. There&#x27;s a popular view that peer review is a strong filter that allows other researchers to have confidence that a claim is correct. My guess is that this might contribute to Linus&#x27;s law being false, because many researchers actually do seem to think &quot;it&#x27;s been checked, so it must be okay, I don&#x27;t need to check anything myself&quot;. Or, perhaps, people don&#x27;t do much checking in the first place.<p>My view is that peer review is a fairly low (and random) bar to pass that doesn&#x27;t necessarily say much about the validity of a work. More people should check things more carefully.<p>Recently I got reviews for a paper I wrote back, and a reviewer was skeptical of one claim I made because (paraphrasing) &quot;If this were true, that would mean all previous researchers were wrong.&quot; They&#x27;re exaggerating as it would only mean many researchers were wrong; I think some were skeptical of this for a long but kept quiet about it. But the idea that &quot;everyone seemed to accept it, therefore you are probably wrong&quot; independent of any arguments made seems popular, despite it being obviously fallacious. I have some arguments. The reviewer should engage with those arguments rather than make some appeal to popularity. Edit: To be clear, what I was claiming here would overturn something dating back to the 1930s that last received a well-accepted revision about 40 years ago.<p>[1] <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Linus's_law" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Linus's_law</a>