They didn't know the trapezoidal rule.
The point is that the "because the investigators were unable to cite an unpublished work, I submitted it for publication at their request" justification doesn't make much sense. She could have just explained to them that no citation was needed for something so trivial.
I can see how if you were unaware, and several colleagues in your field were unaware, it might be good to include some kind of external information about the thing. I can also see why you might not want to link to Wikipedia.
I do think writing a medical article about it for people to link to is silly. Surely if you wanted a citation, you could just cite a math textbook.
Aren't many Nobel Prizes in Economics done like that? Take some well-known math/physics formula, rename variables to make them represent some economic quantities, name the resulting formula after oneself, publish, get the prize?
You cannot trivialize this step. Most people's job in data analysis is basically this. Figuring out what quantity fits where in the formula _is_ the research.
edit: To make it clear, it would have been fine if here model explained something using trapezoidal formula. But she seems to be claiming the formula, not a model.
She didn't name it after herself, the users did:
> collegues ... began using it and addressed it as "Tai's formula"
As is typically the way with eponymous scientific works, people citing the work add the author's name e.g. Maxwell's equations or Higgs' boson. The author doesn't typically declare "I have discovered X, which I shall call ${self.name}"
[1] (PDF link https://math.berkeley.edu/~ehallman/math1B/TaisMethod.pdf
I don't think this rule applies here, because the paper introducing "Tai's rule" calls it "Tai's rule" rather than others citing it. As if Higgs called it Higgs' boson in his paper.
At best, a distinction without a practical difference.
> Three formulas have been developed by Alder (3), Vecchio et al. (4), and Wolever et al. (5) to calculate the total area under a curve
[3] Alder I: A New Look at Geometry. New York, The John Day Company, 1966.
This book is in turn available in archive.org:
https://archive.org/details/B-001-001-934/page/n269/mode/2up
So basically the author in question didn't even bother to read the relevant part of the book she referenced, and also misunderstood the explanation of the Area and Integral chapter as something that Irving Alder developed.
I didn't bother looking up the other two references to help preserve my sanity.
https://kconrad.math.uconn.edu/math1132s20/handouts/taicomme...
Mary Tai herself also replied and explained the background to the paper a bit more:
> While a doctoral candidate working on my dissertation at Columbia University in 1981, I needed to calculate total area under a curve. During a session with my statistical advisor, and after examining several alternative methods, I worked out the model in front of him. The concept behind it is obviously common sense, and one does not have to consult the trapezoid rule to figure it out. [...]
> Why I call it Tai's model. I never thought of publishing the model as a great discovery or accomplishment; it was not published until 14 years later, in 1994. Because of its accuracy and easy application, many collegues at the Obesity Research Center of St Luke's-Roosvelt Hospital Center and Columbia University began using it and addressed it as "Tai's formula" to distinguish it from others. Later, because the investigators were unable to cite an unpublished work, I submitted it for publication at their request. Therefore, my name was rubber-stamped on the model before its publication. [...]