Advisor does not acknowledge their paper to be wrong, what to do?

Question

This is a follow-up to my previous question: (Advisor's paper fundamentally flawed, what do I do?).

My advisor and another student collaborated on a paper. After reading it carefully myself, I've come to the conclusion that the approach, method, and analysis are all fundamentally flawed and the main result is plain wrong. A main result of the paper is a mathematical theorem. The paper was published in a peer-reviewed venue.

I've asked for clarification, which the authors (including my advisor) were not able to give. I've then pointed out the mistakes and errors in the approach and analysis, and gave counter examples that invalidate the main result. My advisor seem to agree with the errors during one of our meetings, but as far as I can tell no further actions were taken on the authors side. I then did not bring this up as I did not feel that was a good idea, since my advisor said I should "move forward instead of find mistakes in the past". However several months later my advisor is still endorsing the paper, and after I pointed out the errors again I received no reply.

So my questions are:

1. What should I do regarding this paper? Should I let this slide, or is there some higher authority I should report this?

2. What should I do moving forward with my Ph.D. studies? Does this event indicate the incompetency of my advisor? I know a suggestion might be switch advisors, but I've already tried working with several faculty members and the experiences are all none-the-better, and this has already taken a huge amount of time and I'm already several years into the program.

Answer 1

1. No, there is no higher authority. The academic knowledge system is specifically designed to be dependent on the individual and the distributed community judgement of a piece of work, and not a single authority. If the work is flawed, the community will come to know this in time. If you want to accelerate this, write a paper setting out your objections and let the community decide. But don't do this while your advisor is still your advisor.

2. All academics will have published work in their past that has flaws in it, it is just in the nature of scholarship. In more empirical studies all work is wrong. Its not a case of if someone will find flaws, or contradict it, but a case of how long our work remains the best currently available approximation to the truth. Some people will recognise the flaws in their work. Many won't. Get used it it - its how academia is.

Unless your advisor is insisting that you build directly and inescapably on work you believe to be wrong (or won't let you explore the exceptions or counter examples), then just let it go.

Answer 2

Yes, your advisor's attitude says something on their competence and honesty. Yes, there is a difference between works that are correct (at least technically) and works that are "plain wrong". And yes, everyone makes mistakes, but there is a difference between researchers who correct their mistakes, and people who always "move forward" without making reliable contributions to science.

Regarding the flawed paper, you should probably do nothing. There are so many wrong papers out there that it is a waste of time trying to correct them, except those that attract much attention and follow-ups. Most papers quickly fall into oblivion anyway.

Regarding your PhD studies, this is a tricky question. There are many options, depending on the particulars. Formally switching advisors may not be needed for distancing yourself from your advisor scientifically.