publications - How common is it for a paper to be wrong?

I am a student in computer science and I recently started working on my M.Sc. thesis. Now I am reading a 2011 paper with about 170 citations that was published in a well-known conference.

In part of the paper, the author briefly states the complexity of their algorithm (in just one line) and claims a complexity order that I believe is false. But I am really in doubt because I think if there was a problem with that paper, that should have been caught earlier by the editorial board.

I want to know, actually how common is it for such errors to be found in papers published in a well-known conferences?

Answer

I'll try to give a general answer from a non-CS perspective.

tl; dr: yes, there are errors out there. A lot of errors, clerical and not, even in oft-cited papers and books, from any field. It's inevitable: though they do their best to avoid errors, authors are human after all, and reviewers are humans too (I know, you never find a damn robot when you need one). Thus, whenever you read a paper, maintain critical thinking.

---

EXAMPLES

I'll start the too long section with an anecdote. When I was working at my master's thesis, some twenty years ago, I needed a result published in a much cited paper from a renowned author in the field of electromagnetics. At the time, (almost) young and inexperienced, I thought that papers were always absolutely right, especially when written by recognized authorities. To practice the technique of the paper, I decided to rederive the results: after a week spent redoing the calculations over and over again, I couldn't find the same final equation. I was able to discover the correct equation – the one I was finding – in a book published later by the same author. Indeed, it was a clerical error that absolutely didn't change anything in the paper, but it was annoying and taught me an important lesson: papers and books contain errors. And, of course, I later published papers with mistakes in equations (not for revenge!) [*].

After that first experience, I've discovered that you can find more fundamental errors, even in well known books and papers. I'll give you here a few examples, taken from different fields, to underline how broad the phenomenon is (in bold, the mistaken claim; within parentheses, the field):

1. (Classical mechanics) In Newtonian mechanics, the correct equation of motion in case of variable mass is F = dp/dt. This statement can be found in many classical books about newtonian mechanics, but it is plainly wrong, because that equation, when the mass is variable, is not invariant under Galilean transformations as it is expected in Newtonian mechanics (actually, the concept of variable mass in Newtonian mechanics can be misleading if not properly handled). For a deeper discussion see, e.g., Plastino (1990), Pinheiro (2004) and Spivak's book Physics for Mathematicians, Mechanics I. As a curiosity, that wrong equation is used by L. O. Chua in this speech (14:50 min) as an example to introduce the memristor.


2. (Circuit analysis) Superposition can't be applied directly to controlled sources. It was just a few years ago when I came across this statement for the first time, and I was stunned: hey, I've applied superposition to controlled sources since I was in high school, and I've always get the right result. How it possibly can't be used? In fact, it can be applied, the important thing is to apply it correctly, but there are really many professors (I have several examples from Italy and US) who don't understand this point and fail to notice that the proofs of several theorems in circuit analysis are actually based on the applicability of superposition to controlled sources. For more on this, see e.g. Damper (2010), Marshall Leach (2009) and Rathore et al. (2012).


3. (Thermodynamics) The Seebeck effect is a consequence of the contact potential. This false statement can be frequently read in technical books and application notes about thermocouples.

À propos of my own errors, a couple of weeks after having written this answer I discovered an error in an equation of a published conference paper which I co-authored. A fraction that should have been something like -A/B became B/A. Hey – I told one of the other authors – how could we possibly have written this? And how did it get past the reviewers? The fact is, that that equation was associated to a simple, well-known, example given in the introduction, an example so simple that probably neither us authors nor the reviewers gave a second look at the equation (of course, how can anyone write this wrongly?). I feel that many clerical errors like this one happen because of last-minute changes to notation: you have almost finished the paper and you realize that you could have employed a better notation... so, let's change it on the fly! And here is where certain errors sneak-in. Avoid last-minute changes, if you can.