Albert Einstein (1879-1955)
Autograph letter signed (with initials, 'A.E.') to Cornelius Lanczos, n.p., 24 February 1955
In German. One page, 281 x 217mm, in blue and black ink, including three scientific equations. Provenance: Sotheby's, 26 November 1980, lot 170.

'You should start from rigorous equations and only subsequently approximate the resulting equations': less than two months before his death, Einstein writes a critique of his old friend's latest paper. Einstein apologises for reading Lanczos's paper rather superficially, but nevertheless sends some observations. 'It seems somewhat dangerous to me to assume an approximate Lagrangian'. He provides a set of equations defining a symmetrical field, and points out that the first two parts are of the first order, but the last two of the second order. 'So you might think that you could limit yourself to the first two by approximating g^ik with η^ik. But if one sets the equivalent expression resulting from partial integration [he sets out the equation] then all terms are of the second order (which is more sensible). / That is why I think you should start from rigorous equations and only subsequently approximate the resulting equations. This way you are sure not to make any mistakes'. Further on, Einstein expresses doubt as to which set of field equations Lanczos is using as a starting point: 'If you set T_ik as 0 from the start, then it is very risky to assume freedom from singularity even within the areas of strong fields'. He goes on with several more critical notes, but again makes a disclaimer that his reading has been only superficial, as he is overburdened with scientific and other writings, 'And my 76 years are not made of cardboard either'. In a postscript, he adds some brief, but detailed, comments on Lanczos's The Variational Principles of Mechanics, published in 1949 and dedicated to Einstein, but which he has evidently only just read.