Arthur Cayley (1821-1895) was a pioneer of invariant theory and among the first to work out the details of the characteristic equation for 3x3 matrices in general. The Cayley-Hamilton theorem is given on page 24 of "A memoir on the theory of matrices" [1], and quickly followed by the great sensibility of an old-style mathematician: "I have not thought it necessary to undertake the labour of a formal proof of the theorem in the general case of a matrix of any degree." ( though nowadays we automate the next few cases on a computer ) Coefficients of the characteristic equation are homogeneous polynomials in the matrix elements, and may be obtained by summing over matrix minor determinants. The characteristic equation itself holds for any similar matrix, thus we may construct a zero sum for every coefficient by subtracting the most general polynomial from a polynomial in a set of distinct variables, with all off-diagonal symbols set to zero. If the dimension of the matrix is N, then we obtain N distinct polynomials z_i, such that z_i = 0. Over field K, the null ring RZ=K[[z_1,z_2,...,z_N]] is a subring of R = K[[a,b,...,L1,L2...,L_N]] with lowercase alphabet for generic matrix elements and L_i for eigenvalues. Two expressions p1 and p2 from R are equivalent whenever a third expression p3 from RZ exists such that p1 + p3 = p2. Without the normalizing factors in the denominator, the squared elements of the eigenvectors are obtained from the diagonal of projector matrices, also guaranteed to exist as corollary to the Cayley-Hamilton theorem. The real problem with Terence Tao's proposal to obtain "Eigenvectors from Eigenvalues" is that it engages in revisionist history. The authors expect to find proof an old, fundamental results in a post-Hilbert language that didn't exist during the days of Cayley and Hamilton, when the question of finding "Eigenvectors from Eigenvalues" was originally settled. Were the old masters alive today, we think that they would be more impressed with the performance of modern computer algebra systems, which easily find and prove identities within well-defined polynomial rings. Some applause is deserved by subsequent authors for finding particularly nice polynomials in R; however, the amount of success needs to be gauged relative to other theorems in the field. In our perspective, a "theorem" of the sort "p1 + p3 = p2", is not really that great compared to the discovery of the null ring KZ and the original proof of the Cayley-Hamilton theorem. In fact, infinitely many equivalent functions p2 are guaranteed to exist as a corollary. In our opinion, that is how they should be viewed. All the preceding text was written as notes for an article titled "Inside the quantum bikeshed", which planned to discuss Parkinson's law of triviality, as it often manifests in the sciences. However, Predrag C. convinced me that it would be rude and inconsiderate to write such an article. Counterpoint: If instead, we were living in a world of science fiction, and suffering from hard-scrabble existence after the fall of the empire, of course we would : * * demand the return of the Beskar Iron to its rightful owners! * * --Brad [1] https://royalsocietypublishing.org/doi/pdf/10.1098/rstl.1858.0002