**Two cases of mathematical secret from the Second World War: Abraham Wald and Alan Turing.**

*Though apparently technically related (according to Wikipedia), these two cases were actually independent of each other, and the mathematics used for very different purposes.*

Some fifty years ago, I read that Bellman optimization principle had
been kept a secret. It took me some time to sort this out, with the
help of the internet, as the information was not fully accurate. But
it was apparently almost true.

Actually, the mathematical technique kept secret was the related work
of **Abraham Wald** on **sequential analysis**.

Here is a (hopefully) more accurate version of the story, translated from the
French, from the page 145, in chapter 4 on Dynamic Programming of a Swiss
engineering book: Recherche opérationnelle pour ingénieurs, Volume 2
By Jean-François Hêche, Thomas M. Liebling, Dominique de Werra, PPUR
(Presses Polytechniques et Universitaires Romandes), 2003,ISBN: 2 88074 459 8.

Like most models and methods of Operations Resarch, Dynamic
Programming is, too, a by-product od the Second World War. It is
indeed during that conflict, with the concern of improving the
effectiveness of quality control in the production of ammunition, that
the American mathematician Abraham Wald proposes a new method that he
name *sequential analysis*. The main idea of his approach resides in
the replacement of traditionnal sampling with fixed size by a process
in which it is decided dynamycally whether the accumulated evidence is
sufficient, or whether, to the contrary, further test must be
performed. **This method being particularly efficient, it remains
classified as a military secret even after the war, and it is only in
1947 that it becomes awailable to the public.** Very soon afterwards,
at the Rand Corporation of California, independently from Wald, but
also in a military context, Richard Bellman becomes interested in
optimal control, and, more generally, in sequential optimization
problems. He originated the name *dynamic programming* and made the
methodology known in his reference work of 1957. It is in this book
that Bellman proposes his *optimality principle* which states that any
shortest path is itself composed of shortest paths.

This is confirmed by looking in Wikipedia at the page on sequential
analysis, which lists other contributors, but has no reference to
Bellman principle. I do not know sequential analysis, and cannot
assess at this time whether it is appropriate to disconnect sequential
analysis from the later work of Bellman, as is done in wikipedia.

But this same wikipedia page raises another case of secrecy in mathematics,
concerning a similar approach used by **Alan Turing** in his cryptographic
work, which remained secret until the 1980s :

A similar approach was independently developed at the same time by
Alan Turing, as part of the Banburismus technique used at Bletchley
Park, to test hypotheses about whether different messages coded by
German Enigma machines should be connected and analysed together. **This
work remained secret until the early 1980s.**

*Boldface used in citations is mine, not from the original text.*