No abstract

This article expands on Curry's work on how to implement the problem of inverse interpolation on the ENIAC (1946) and his subsequent work on developing a theory of program composition (1948-1950). It is shown that Curry's hands-on experience with the ENIAC on the one side and his acquaintance with systems of formal logic on the other, were conductive to conceive a compact "notation for program construction"which in turn would be instrumental to a mechanical synthesis of programs. Since Curry's systematic programming technique pronounces a critique of the Goldstine-von Neumann style of coding, his "calculus of program composition"not only anticipates automatic programming but also proposes explicit hardware optimisations largely unperceived by computer history until Backus' famous ACM Turing Award lecture (1977). The cohesion of these findings asks for an integrative historiographical approach. An appendix gives, for the first time, a full description of Curry's arithmetic compiler. * This paper is a contribution to the ENIAC NOMOI project.

No abstract

At the beginning of the 18th century, several mathematicians noted regularities in the decimal expansions of common fractions. Rules of thumb were set up, but it was only from 1760 onwards that the first attempts to try to establish a coherent theory of periodic decimal fractions appeared. J.H. Lambert was the first to devote two essays to the topic, but his colleagues at the Berlin Academy, J. III Bernoulli and J.L. Lagrange, also spent time on the problem. Apart from the theoretical side of the question, the applications (factoring, irrationality proofs and computational advantages) as well as the tabulation of decimal periods aroused considerable interest, especially among Lambert's correspondents, C.F. Hindenburg and I. Wolfram. Finally in 1797-1801 the young C.F. Gauss, informed of these developments, based the whole theory on firm number-theoretic foundations, thereby solving most of the open problems left by the mathematicians before him.

International audienc