A complete reconstruction of Lehmer’s ENIAC set-up for computing the exponents of p modulo two is given. This program served as an early test program for the ENIAC (1946). The reconstruction illustrates the difficulties of early programmers to find a way between a man operated and a machine operated computation. These difficulties concern both the content level (the algorithm) and the formal level (the logic of sequencing operations).

The aspects of Erhard Weigel's Analysis Aristotelica ex Euclide restituta that foreshadowed and helped form some characteristics of symbolic logic are highlighted: first, the idea of a pure form of a logical syllogism or of a mathematical proof and, second, a tentative arithmetisation of some aspects of logic. Also, Weigel's emphasis on the role of symbols and figures in the process of mathematical proof is discussed.

A history of writing the history of computing is presented in its relationship to the history of mathematics. As with many historiographies, the initial history of computing was very much an internalistic history. In the late 1970s, the field became more serious and started looking at the histories of mathematics and technology for (methodological) inspiration. Whereas the history of mathematics was initially quite influential, it is the history of technology (in its U.S. form) that has become the dominant framework for (...) doing history of computing since the 1990s. (shrink)

ArgumentJohann Heinrich Lambert (1728–1777) developed a very detailed theory of science and experiment. Using Lambert's hygrometric studies, this article provides an introduction to Lambert's theory and its practice. Of special interest is his well-founded theory on the emergence and definition of concepts and his neat eye for heuristics that should ultimately lead to a mathematization of physical phenomena. His use of visualizations in this context is especially remarkable.

In response to the so-called ‘software crisis’ of the late 1960s, many approaches were proposed to turn software engineering and programming into more systematic disciplines, to turn an art into a science. This paper studies one popular example often used in these proposals, the computation of a list of primes, to discuss some salient features of the proposed programming paradigms. It also looks at the actual implementation in the early 1970s of the prime program on a time-sharing system and on (...) a complex scientific computer. Confronting theory with practice uncovers what the programming paradigms fail to grasp: the interaction with the user and the interaction with the machine. (shrink)

C.F Gauss’s computational work in number theory attracted renewed interest in the twentieth century due to, on the one hand, the edition of Gauss’s Werke, and, on the other hand, the birth of the digital electronic computer. The involvement of the U.S. American mathematicians Derrick Henry Lehmer and Daniel Shanks with Gauss’s work is analysed, especially their continuation of work on topics as arccotangents, factors of n2 + a2, composition of binary quadratic forms. In general, this strand in Gauss’s reception (...) is part of a more general phenomenon, i.e. the influence of the computer on mathematics and one of its effects, the reappraisal of mathematical exploration. (shrink)

A complete reconstruction of Lehmer’s ENIAC set-up for computing the exponents of p modulo two is given. This program served as an early test program for the ENIAC (1946). The reconstruction illustrates the difficulties of early programmers to find a way between a man operated and a machine operated computation. These difficulties concern both the content level (the algorithm) and the formal level (the logic of sequencing operations).

After the First World War mathematics and the organisation of ballistic computations at Aberdeen Proving Ground changed considerably. This was the basis for the development of a number of computing aids that were constructed and used during the years 1920 to 1950. This article looks how the computational organisation forms and changes the instruments of calculation. After the differential analyzer relay-based machines were built by Bell Labs and, finally, the ENIAC, one of the first electronic computers, was built, to satisfy (...) the need for computational power in ballistics during the second World War. (shrink)