A bot crawled thousands of studies looking for simple math errors

dmd is a respected HNer, so it's inappropriate to question him.

Here's an example from my field, which I think is informative because it gives a concrete idea of how this plays out in a public arena.

tl;dr for this wall of text: 1) Authors A describes algorithm, 2) Author B publishes counter-example to show where #1 fails, 3) Authors A say it wasn't wrong, but that the author of #2 'misunderstood', and B should have contacted them first; and in any case here are the missing details, 4) Author B points out that paper #1 should have said those details were missing. 5) Authors C point out that authors A misunderstood many things in their own publications; authors A can't complain about others not contacting them first when they don't do it themselves.

"Canonical Numbering and Constitutional Symmetry" (1977), DOI: 10.1021/ci60010a014 describes an algorithm.

"Erroneous Claims Concerning the Perception of Topological Symmetry" (1978), DOI: 10.1021/ci60014a015 points out examples where the algorithm from the first paper, and from another paper, don't work.

The authors of the first paper followup with "On the Misinterpretation of Our Algorithm for the Perception of Constitutional Symmetry" (1979), DOI: 10.1021/ci60017a012 .

> A recent paper in this journal contained critical comments on two methods for the perception of topological symmetry. Carhart’s claim that our algorithm does not correctly perceive topological symmetry and fails with certain structures is the result of a misinterpretation of our algorithm.

> Unfortunately, the author did not contact us directly to help him clarify his misunderstanding. This failure is unusual and difficult to understand. Thus, it was not until we received the recent issue of this journal that we learned of this misinterpretation.

> In our paper we were particularly aiming at catching the interest of the organic chemist for the problems of uniquely numbering the atoms of a molecule. Therefore, we put particular emphasis on the criteria for determining priorities among atoms to enable the chemist to manually number the atoms of molecules according to our procedure. We restrained from giving all small details of the algorithm to keep the paper concise, working under the assumption that persons interested in the details would contact us directly. It is astonishing that Carhart at the point where we did not fully elaborate on the details works with the premise that we misconceived the problem. Initially one should rather assume that other people, too, understand a problem. Only if explicit errors are found should one digress from this conviction.

Carhart followed up with a letter to the editor, "Perception of Topological Symmetry" (1979) DOI: 10.1021/ci60017a600 :

> I am delighted to see that my critique’ appearing in this Journal has encouraged C. Jochum and J. Gasteiger to present previously unreported steps in their algorithm for the canonical numbering of chemical graphs. They refer to these steps as “small details”, but in fact they are the very essence of any routine which reliably finds unique numberings for, ...

> However, I did not misunderstand their previous article (unless lack of clairvoyance can be classed as misunderstanding); I simply took it at face value. My critical comments, and the counterexamples I presented, were completely appropriate in the context of that article. In contrast with their latest offering, Jochum and Gasteiger’s previous paper did not present a sound and accurate definition of constitutional symmetry, nor did it indicate in any way that crucial steps had been omitted. I am sympathetic with the problems of describing a complex algorithm in the limited space of a journal article, but if space limits the development of a fundamental concept, it is the responsibility of the author to say so, and to indicate that a reader must obtain additional information before he tries to implement the described procedure.

It ended with a letter from still other people writing another letter to the editor, "Canonical Numbering" (1979), DOI: 10.1021/ci60019a600 :

> We have been following with some interest the controversy appearing in this Journal regarding canonical numbering and various types of The first article by Jochum and Gasteiger contains a number of incorrect and misleading statements about both their work and the work of those who preceded them. ...

> Jochum and Gasteiger also strongly implied that they had a “simple” algorithm which gave complete partitioning, eliminating the need for a comparison step. Carhart correctly pointed out that this was not the case. Subsequent publication of the details of Jochum and Gasteiger’s indicated that it does contain a comparison step ...

> On a more general level Jochum and Gasteiger complain that Carhart did not contact them “directly to help him clarify his misunderstanding”. Yet it is obvious from the large number of misinterpretations and/or misrepresentations which appear in their work that they made no attempt to clarify their misunderstandings by discussing such matters with the original authors. Publishing last on a particular subject accords one considerable power, power that carries with it the responsibility to treat the preceding work with fairness and objectivity.

I used to hold this opinion, but my experience with academic research changed my mind. Much of the scientific knowledge we have is passed from generation to generation by mentoring. The amount of knowledge is so vast, and our means of searching the written literature for relevant facts so poor, that when I want to learn something or solve a specific problem there is no substitute for a discussion with an expert in the field.

The core problem is that human communication is very difficult. It becomes even more difficult when we try to communicate ideas without interaction, as we do when writing a book and expect someone to read and understand it. If I read a paper and I can't understand a sentence, it might take me days to figure out what's going on by myself, whereas asking an expert might yield an answer in less than an hour (sometimes minutes). The difference is really orders of magnitude.

There are whole fields that have effectively died because no one works on them any more. That knowledge doesn't live in anyone's mind. All the literature is there, but actually acquiring that knowledge by reading the literature is incredibly challenging and time consuming.

I have come to believe that the main purpose of hiring scientists in academia is to keep knowledge alive and have it passed on to future generations. Advancing research is of secondary importance. In fact I would say that most new research I see probably has no intrinsic value. I include my own research in this category. We have researchers solving esoteric problems of no value to anyone besides their own personal entertainment. Except, working on such research keeps our neurons firing and keeps knowledge alive. It is a well known phenomenon that taking a break from research very quickly leads to a sort of decay of memory. Our learned ideas and the connections between them wither away without constant reinforcement. In order to keep knowledge alive we have to engage in research, even if it seems pointless.

>I have come to believe that the main purpose of hiring scientists in academia is to keep knowledge alive and have it passed on to future generations.

Then these scientists should be devoted to producing textbooks and courses which can then be taught to non-research students. Yes, all knowledge about the scale of what a single individual knows (and keeps on their shelves, hard drives, etc) is embodied as communities and traditions, but we still get far greater redundancy of that knowledge from teaching it as undergraduate or master's-level coursework than from passing it down only via research mentoring.

If 25% of the population gets an undergraduate degree, 11% or so gets a postgraduate degree, and only about 1.7% get a PhD, then we need to be embodying society's knowledge among the larger cohorts for that knowledge to survive. We can't afford to live in a world where only 1.7% know how things work.

Anybody who objects to such an anodyne project that strenuously with such disingenuous arguments immediately makes me think they're hiding something.