Citing a rare paper by von Neumann: Various techniques used in connection with random digits

By | July 18, 2019

John von Neumann wrote a marvelous paper in 1951 about random variate generation, which is widely cited in the literature. Here is the BibTeX for those who are here for the citation:

@incollection{vonNeumann1951,
title     = {Various Techniques Used in Connection with Random Digits},
author    = {von Neumann, John},
booktitle = {Monte Carlo Method},
editor    = {Householder, A.~S. and Forsythe, G.~E. and Germond, H.~H.},
series    = {National Bureau of Standards Applied Mathematics Series},
volume    = {12},
chapter   = {13},
pages     = {36--38},
year      = {1951},
publisher = {US Government Printing Office},
address   = {Washington, DC},
}

The main challenge with this paper is citing it correctly (needless to say, the BibTeX citation given by Google Scholar is fully incorrect). Some people have posted questions on StackExchange about how exactly to find this paper. Librarians I have asked also had a hard time pinpointing the exact citation (and had more fun tracking this down than I had expected), because the work is cited inconsistently in the literature. For example:

INFORMS biographical profile of John von Neumann:

Von Neumann J. (1951) Various techniques used in connection with random digits. Journal of Research of the National Bureau of Standards, 3: 36-38.

Von Neumann’s Rejection Technique Reexamined, J. A. Grzesik:

J. VON NEUMANN, Various Techniques Used in Connection with Random Digits, Applied Mathematics Series 12, National Bureau of Standards, Washington, DC, 1951, pp. 36-38.

John von Neumann : collected works. vol. 5 : design of computers, theory of automata and numerical analysis:

Various Techniques Used in Connection with Random Digits. Chapter 13 of Proceedings of Symposium on Monte Carlo Method held June-July 1949 in Los Angeles. J. Res. Nat. Bur. Stand. Appl. Math. Series, 12:36-38

von Neumann’s comparison method for random sampling from the normal and other distributions, George E. Forsythe:

John von Neumann, “Various techniques used in connection with random digits, in Monte Carlo Method, Appl. Math. Series, vol. 12, U. S. Nat. Bureau of Standards, 1951, pp. 36-38 (Summary written by George E. Forsythe)

A source file of the document itself (which somehow mentions pages 36-38 in the citation, but contains pages 768-770 in the document itself):

J. Res. Nat. Bur. Stand. Appl. Math. Series 3, 36-38 (1951)

Another source file. This document shows page numbers 36–38 and is titled “13. Various Techniques …” which cross-checks with the mention of Chapter 13 from the Collected Works citation.

These citations are clearly inconsistent. They describe publication venues as some combination of J. R. NBS, an edited book called Monte Carlo Method, and/or a volume in the NBS Applied Mathematics Series. They also mix volume numbers 3 and 12 for each of these patterns. The page numbers 36–38 strangely agree for different candidate venues. The Journal of Research of NIST archives do not contain the paper…

It turns out that NIST Special Publication 730 has a detailed summary of the original symposium at which the paper was presented and where it was ultimately published (the following is from pp. 13-14):

The “Symposium on the Monte Carlo Method” was jointly sponsored by the Rand Corporation and the Institute for Numerical Analysis with the cooperation of the Oak Ridge National Laboratory. The committee on arrangements consisted of J. H. Curtiss, H. H. Germond, A. S. Householder, C. C. Hurd, and R. P. Peterson. The Symposium was held on June 29, 30, and July 1, 1949.
The purposes of this Symposium were to interchange information concerning the usefulness of the method, to stimulate discussions relative to its limitations, and to indicate directions in which further theoretical research is needed. The program of the Symposium can be found in the Proceedings of this Symposium, published as NBS Applied Mathematics Series 12 in 1951, edited by A. S. Householder, G. E. Forsythe, and H. H. Germond. The title page and table of contents are reproduced in Appendix D.

Here is the title page and table of contents of the Monte Carlo Method edited volume. The full book is in the public domain and available here; digitized from the archives of Ohio State University. In addition to von Neuman’s paper, it has some fascinating content.

We can thus conclude that at least one correct way to cite the paper is as Ch. 13 of the Monte Carlo Method edited book, which was vol. 12 of the NBS Appl. Math. Series, as shown in the top of this page. I can’t seem to track down the paper in J. Res. Nat. Bur. Stand. which appears in several of the citations, and I very much doubt the journal contains the paper (either volume 12 or volume 3).

Unsurprisingly, the citation by George E. Forsythe, who edited the book in which the paper appeared and wrote the summary of von Neuman’s paper himself, has what seems to be the most accurate citation.

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