## Doing Mathematics on the ENIAC. Von Neumann’s and Lehmer’s different visions

Citations: | 2 - 0 self |

### BibTeX

@MISC{Mol_doingmathematics,

author = {Liesbeth De Mol},

title = {Doing Mathematics on the ENIAC. Von Neumann’s and Lehmer’s different visions },

year = {}

}

### OpenURL

### Abstract

In this paper we will study the impact of the computer on mathematics and its practice from a historical point of view. We will look at what kind of mathematical problems were implemented on early electronic computing machines and how these implementations were perceived. By doing so, we want to stress that the computer was in fact, from its very beginning, conceived as a mathematical instrument per se, thus situating the contemporary usage of the computer in mathematics in its proper historical background. We will focus on the work by two computer pioneers: Derrick H. Lehmer and John von Neumann. They were both involved with the ENIAC and had strong opinions about how these new machines might influence (theoretical and applied) mathematics.

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Citation Context ...lementing the new approach is an interesting story, suffice it to say that Johnny’s wife, Klari, and I designed the new controls in about two months and completed the implementation in a fortnight.” (=-=[33]-=-, p. 128). 9suggested to prepare “a preliminary computational model of a thermonuclear reaction for the ENIAC.” As is recounted by Metropolis [33, p. 126]: For a whole host of reaons [von Neumann] ha... |

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Citation Context ...terest in weather prediction. The available mechanical computers at that time however were not fast enough to his idea, so he thought about building an electronic computer using vacuum tubes (See e.g.=-=[32]-=-). In 1941, Mauchly met Presper J. Eckert at the Moore School at Penn University. Eckert “was willing and agreeable to talk about the possibility of electronic computers [...] Nobody else really wante... |

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Citation Context ...d thus had to devote its “official” time to military computations. At the time von Neumann got involved with the ENIAC, he was already a consultant to Los Alamos. It was he who first 6 Neukom’s paper =-=[35]-=- gives a detailed description of “the ENIAC’s second life”. It should also be noted here that while the usual account on the rewiring of the ENIAC is that von Neumann suggested the idea and Clippinger... |

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Citation Context ...ng a statistical measure of the randomness of distribution of the digits [...] The computations for e were finished in July 1949, those for π during LaborDay weekend, in September 1949. 8 In [34] and =-=[36]-=- set-up and results are 8 As was the case for several more theoretical computations done on the ENIAC, these were all done outside the “official time”, during holidays. As Reitwiesner [36] explains, f... |

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Citation Context ...project, and with “real” computing. In this context von Neumann’s logical background would prove very useful. It was not his interest in logic, however, that triggered his interest in the subject. In =-=[39]-=-, Ulam explains why von Neumann got interested in computers (pp. 93–94): It must have been in 1938 that I first had discussions with von Neumann about problems in mathematical physics, and the first I... |

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Citation Context ...able random numbers, sequences that are nowadays known as pseudo-random. 3.2 Are π and e random? Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin. =-=[42]-=- Von Neumann’s interest in the statistical properties of numbers like π and e should, most probably, be understood in the context of the use of the Monte Carlo method on the ENIAC. In 1949 he suggeste... |