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The context is that of a conference, Problems of Cosmical Aerodynamics, held in Paris, France, on August 16–19, 1949. It was organized at the initiative of the newly founded IUTAM and of the IAU. It gathered fifty-two scientists, among which there were thirty-four astronomers and eighteen physicists or fluid mechanicists. The chairs were J. M. Burgers for IUTAM and H. C. van de Hulst for IAU. Among the participants were W. Heisenberg, J. H. Oort, E. Schatzman, T. von Karman, C. F. von Weizsacker and, of course, J. von Neumann. G. I. Taylor could not attend the conference because of sickness. The conference was managed in a rather informal style, the program being decided during the first day, a little bit like our Oberwolfach workshops. Discussion sessions happened every day in the afternoon. I wish to comment here on the session chaired by von Neumann, devoted to the Existence and uniqueness or multiplicity of solutions of the aerodynamical equations. The records of the discussion are reprinted in this issue after these comments. They are taken from pp. 75–85 of the conference proceedings, published by the Central Air Documents Office, Dayton (Ohio), 1951. Instead of a discussion, the session was actually a long monologue by von Neumann, after which he apologize(s) for having taken up so much of the limited time. He then answers the questions of a handful of scientists. The session ends with a comment by Burgers about the consequences of this discussion for astronomical problems. In order to make the context as clear as possible, it is necessary to recall that during WWII, von Neumann had been involved in the Manhattan Project, dedicated to the construction of the American nuclear bomb, while Heisenberg led the German nuclear weapon program, to which Weizsacker collaborated. This was the origin of their common, though independent, interest in fluid mechanics and shock waves. However, the 1949 conference had a peaceful target, and the conversations remained courteous. In addition, Germany was no longer a threat, thus it became meaningful to involve German scientists in such a conference. The

Von Neumann’s comments about existence and uniqueness for the initial-boundary value problem in gas dynamics