Rediscovery of calculus in 1994: what should have happened to that paper? There's a well-known paper in academic circles that features a rediscovery of the trapezoidal rule for numerical integration by a medical researcher:


  “A Mathematical Model for the Determination of Total Area Under Glucose Tolerance and Other Metabolic Curves”, Mary M. Tai, Diabetes Care, 1994, 17, 152–154.


I think the paper's only figure says it all:

               

You can find comments on many blogs about it, most of them along the lines of “turns out calculus was invented in 1994”. I think it truly is a bit sad that the paper made it past the researcher, her immediate colleagues and friends, a Yale professor of electrical engineering who is thanked for “his expert review”, and most importantly reviewers, without someone giving the author a hint.

In my opinion, the most optimistic view is to see it as an educational paper: the method is not new, but that particular medical community didn't know about it, so it was worth publishing. However, that is not what the paper states: the author clearly presents the method as new and names it after her.



Okay, I think I have explained the context. My question is: after that peer-review failure was exposed, what should have happened to the paper? What happened is that the same journal published a series of comments on the paper, and a reply by the author to the comments. Was that the correct/ethical way of handling the issue, as an editor? Or should the paper have been retracted?
Online publishing, at the face of it, should be giving editors some room for maneuver. In this case, they could append the online version of the paper with an editorial note like


  EDITORIAL NOTE: Citing this paper as "Tai's method" is strongly discouraged, as the method is actually known under the name of trapezoidal rule. See also Comments for further explanations.


The academic community affected by this rediscovery should have taken actions accordingly, and editors in other journals should have made sure that citations to the paper are only given if something other than the trapezoidal rule is being discussed. 

John Paul II apologized for a number of misdoings by the Catholic Church. The editors should've apologized to their research community for committing this peer review failure. It's OK to be wrong from time to time; science moves by rectifying things that come into contradiction with other bits of knowledge. However it's not OK to withhold knowing that you are wrong and insisting on it.