April, 19-23.

From April 19 until April 23 dr. Tinne Hoff Kjeldsen will be the guest of the mathematics department of Nijmegen University. During her stay in the Netherlands she will give two lectures in several places. Both talks will be on the history of Nonlinear Programming (abstracts below). The talks are planned as follows.

April 21, 10:30-11:30. Nijmegen University, Department of Mathematics Staff Colloquium. Room CK N4.

April 22, 15:00-16:00. Utrecht University, Institute for History and Philosophy of Science. Staff Colloquium.

April 23, 16:00-17:00. Amsterdam Free University (VU), Department of Mathematics Staff Colloquium.

It was the so-called

The beginning of the mathematical theory of nonlinear programming can be dated back to the important paper

The following is the summary of the thesis by dr. Tinne Hoff Kjeldsen. The thesis itself in in Danish. Title:

The present dissertation is about the history of nonlinear programming. It is divided into two parts of which the first can be considered as the history of the development of nonlinear programming and the second part as a contribution to the aspect of multiple discovery in the history of mathematics.

In the first part an overall picture of the emergence and establishment of nonlinear programming as a mathematical field for research is presented. The history of George B. Dantzig's development of linear programming after the second world war and the military influence on this development is treated. Based on this and on analysis of the work in linear and nonlinear programming of Harold W. Kuhn and Albert W. Tucker it is argued, that the emergence of the duality theorem in linear programming changed the scientific state of affairs of linear programming, from being a mathematical model for a concrete, practical problem within The U.S. Airforce to become a mathematical interesting research area. It is further argued that this change, in combination with the financial support from

In the second part of the thesis the aspect of multiple discovery of the Kuhn-Tucker theorem in nonlinear programming is analysed. This aspect turns up in the history of nonlinear programming, because it is stated in the secondary literature, that the Kuhn-Tucker theorem was independently discovered by Ostrogradsky and Farkas at the end of the nineteenth century in connection with inequality constrained equilibrium in mechanics, and in modern time by W. Karush in 1939 and F. John in 1948. Based on historical analyses of the works of Ostrogradsky and Farkas, I conclude, that their results can be seen as versions of the Kuhn-Tucker theorem only if there work is interpreted within a frame work of modern physics. Today the Kuhn-Tucker theorem is ascribed also to Karush and partly to John. The historical facts is that Karush's work was a master's thesis, that were never published, Johns work was first rejected by the Duke Mathematics Journal, but then got published in a collection of essays for Courant's 60th birthday. My purpose of including this aspect of multiple discovery was to understand, why a mathematical result at a specific time, and in a specific context, can generate a new mathematical research area, while a similar result, developed almost at the same time but in a different context, did not cause any reaction. My analysis of the work of Karush, John, Kuhn and Tucker and the contexts they appeared in, give rise to the conclusion, that the technical context -and in some cases also the sociological context- had significant influence on the importance of the different results.