This is a famous article in the mathematics community. While her results were known to humans for several hundred years she claimed they were not known to her. If this is correct then her derivation is an impressive feat but certainly not worthy of publication. According to [1] the paper still receives citations and some people refer to "Tai's model" instead of the Trapezoidal Rule.
You can read some comments to her article and her response in [2]. I think she should have acknowledged that her method is the Trapezoidal Rule. Maybe she has in the 20+ years since. I don't know.
The whole saga reminds me of a time that member of the biology department asked me, "Why does the Ti-83 calculate scientific notation wrong?" I asked what she meant. She gave me this example:
Calculate (3.75 x 10^23)/(9.34 x 10^(-5))
She enters the problem into the calculator to show me that it does indeed calculate the wrong value. She entered
3.75 x 10^23/9.34 x 10^(-5)
I had to explain to her that the order of operations was important.
Numerical methods like the one mentioned are basic stuff in mathematics. It's like someone claimed to have invented using derivatives in mathematical models. It's beyond eye-roll-inducing.
I'm not sure any more. I've once stumbled on a paper that claimed to solve the problem of balancing chemical reactions, where they tried to figure out in which proportion the compounds react. This is as simple as finding the null space of the corresponding matrix, and indeed the paper did more or less that, but it referenced a whole ream of other papers that all seemed to be trying to rediscover the same solution to a simple linear algebra problem. To this day I don't know if it was some kind elaborate joke or not.
Seems similar to what some of Machine Learning / AI has been doing: rediscovering stuff from statistics and giving it a new name and a new citation chain. Next big ML papers will be re-inventing causal analysis, endogeneity and structural models from fields where humans react to interventions, changing the model.
You can read some comments to her article and her response in [2]. I think she should have acknowledged that her method is the Trapezoidal Rule. Maybe she has in the 20+ years since. I don't know.
The whole saga reminds me of a time that member of the biology department asked me, "Why does the Ti-83 calculate scientific notation wrong?" I asked what she meant. She gave me this example:
Calculate (3.75 x 10^23)/(9.34 x 10^(-5))
She enters the problem into the calculator to show me that it does indeed calculate the wrong value. She entered
3.75 x 10^23/9.34 x 10^(-5)
I had to explain to her that the order of operations was important.
[1] http://johncanning.net/wp/?p=1863
[2] http://www.math.uconn.edu/~kconrad/math1132s14/handouts/taic...