Couldn't resist quoting Conway (https://www.maths.ed.ac.uk/~v1ranick/books/dublin.pdf, p. 24) :

For nearly 50 years it has been supposed that the universality problem for quaternary integer-matrix forms had been solved by M. Willerding, who purported to list all such forms in 1948. However, the 15-theorem, which I proved with William Schneeberger in 1993, made it clear that Willerding’s work had been unusually defective. In his paper in these proceedings, Manjul Bhargava [https://www.maths.ed.ac.uk/~v1ranick/books/dublin.pdf, p. 27] gives a very simple proof of the 15-theorem, and derives the complete list of universal quaternaries. As he remarks, of the 204 such forms, Willerding’s purportedly complete list of 178 contains in fact only 168, because she missed 36 forms, listed 1 form twice, and listed 9 nonuniversal forms!