Can you vouch for the validity of the results in papers that you cite and use in your own articles?
In April this year Blagojević, Cohen, Crabb, Lück and Ziegler posted a preprint on the arXiv (arXiv:2004.12350) writing in the abstract “This invalidates a paper by three of the present authors […] who used a claimed intermediate result from […]”. This, of course, got me interested and so I took a look at the introduction of that preprint.
The story is that there is an influential paper which was quoted and whose main result was used in quite a number of papers since then, but whose proof turned out to be incorrect (but apparently the main result itself is correct, as was proven now by these five authors). This was only noticed, because Blagojević, Lück and Ziegler used in their paper from 2016 not only the main result of the flawed paper, but also intermediate results that turned out to be actually wrong.
What bothers me the most here is the quite long list of papers that use the main result of the flawed paper apparently without noticing that the proof is wrong. I already had the general feeling that in mathematics too few people actually read in detail and therefore also check the validity of influential / seminal papers, or of papers that they essentially use in their own work. And the above told story reinforced this feeling in me.
I also admit my own guilt here: I think I have read less articles by other authors than I have written myself. Of course, I could talk my way out of this by saying that I don’t have a permanent position yet and therefore it is more important for me to write my own paper than to read other’s paper. But I have the feeling that this queue of excuses won’t stop when I finally get a permanent position.
So is there any reasonable way to change this, i.e., motivate more people to read other’s papers? Or am I completely wrong in my supposition, people are actually reading more than I suppose they do, and all this is actually no problem at all?