Mathematics and War

This talk will be an attempt at explaining connections between the military, science and technology in the 20th century. It will mostly deal with the United States since the 1930s and a few selected fields upon which the military influence has been particularly heavy, with "revolutionary" consequences, good or bad, for the evolution of civilian society everywhere.

Talk aims at tracing sources and discussing problems concerning the involvement of those participants in the multi-faceted relation of "mathematics and military/war" who considered themselves mathematicians. This includes the discussion of meeting places and ways of communication between mathematicians and the military (research councils, institutes, societies, journals), ideological positions of mathematicians as precondition for and generated by military work, and, not least, exemplary consideration of some epistemic transfer processes between mathematics and military applications.
Due to uneven historical sources the main emphasis is on comparisons between American, British and German work. Considerably less emphasis has to be given to France, Italy, Japan, and the Soviet Union, although it can be assumed that particularly Russian work in the field was well developed and effective in the war. Throughout the talk the problems of the establishment of "applied mathematics" as an academic subject and of internationalization of mathematics in the period considered (including migration and secrecy regulations) will be discussed as points of view of primary historical importance.

The German Enigma encoding machine and the contributions of famous cryptologists who broke it, are still topics which fascinate both scientists and the general public. After the monarchy of Kaiser Wilhelm II fell, the Weimar Republic came into being, and the idea of equipping the armed forces with encoding machine already found realisation in 1926. The German encoding machine, called Enigma, alarmed the general staffs of neighbouring countries, especially Poland and France. This work intends to describe the efforts of outstanding cryptoanalysts who solved the mystery of Enigma during the 30’s before the beginning of the war. Full reconstruction of the wiring and first deciphering results were already delivered to the British codebreakers at Bletchley Park by The Polish Cipher Bureau in August 1939. The military impact of the early studies of Enigma code breaking accomplished in Poland and the later investigations made by British cryptologists will be discussed.

The vast expansion of the US Navy in World War II and its increasing reliance on quickly emerging new technologies owed its success, in part, to the previously overlooked work of women. Much of this work was at the level of technician and mechanic, but there were also numbers of women with advanced educational and professional qualifications who held responsible positions during the war and who made high-level contributions in technical fields. While naval historians are increasingly interested in World War II technology, and historians in general are taking more account of the historical roles of women, no one is looking at these exceptional women who voluntarily set aside their professional lives to serve their country.
My talk focuses on the war work of two of these women: mathematicians Grace Murray Hopper (1906-1992) and Mina Spiegel Rees (1902-1997). Both were college professors until war service intervened. One joined the navy and the other remained a civilian but between 1943 and 1945 each held positions from which they influenced the U.S. Navy’s ability to wage a modern, science-dependent war. With a Ph.D. in mathematics from Yale University, Hopper taught at Vassar College in New York before joining the navy at the age of thirty-six. In June 1944, newly commissioned Lieutenant Hopper was sent to Harvard University's Computation Project, which had been taken over by the Bureau of Ships for the duration of the war. At Harvard the navy introduced Hopper to the emerging world of computing, pushing her into the new field which was to absorb the rest of her life. With no time for training she learned on the job how to program Harvard professor Howard Aiken’s Mark I computer, the first functional, large-scale, automatically sequenced, general-purpose, digital computer to be produced in America, and one of the few computers ready early enough to play a significant role in the war. The Mark I ran around the clock, churning out essential data for all sorts of ordnance projects, making complex calculations for navy guns, acoustic and magnetic mines, self-propelled rockets, and the atomic bomb. In addition to being one of only three programmers for the Mark I, and writing its first manual of operations, Hopper was instrumental in the development of its successors, the Mark II and the Mark III which were used by the navy after the war.
At the age of forty-one, Mina Rees, a Hunter College mathematician, was plucked from her quiet academic environment to help administer an unprecedented government-sponsored effort to organize scientific research for war. From 1943 to 1946, as Technical Aide to the Applied Mathematics Panel of the National Defense Research Committee, she oversaw contracts for navy and, to a lesser extent, for other military and civilian scientific projects involving extensive mathematical calculations. As assistant to Warren Weaver, the panel’s head, Rees was responsible for identifying significant projects and persuading suitable mathematicians to work on them, in the process directing funding involving millions of dollars of government money. Years later, Rees was recognized for her role in "deploying and sustaining" her country's mathematicians in the war effort.

In this talk I will focus on the significance of the Second World War for the rise and establishment of new disciplines in applied mathematics as well as for the renewed interest and growth in some related subjects in pure mathematics. The mathematical topics involved are mathematical programming, operations research, game theory, the theory of convexity, and the theory of systems of linear inequalities. Connections and interactions between different branches of mathematics on the one hand and between different kinds of driving forces in the development of mathematics on the other hand will be discussed. Special emphasis will be devoted to the significance of the interplay between practical problem solving and basic research in mathematics proper as a consequence of World War II and the post-war organization of science support in the USA.

Discovery of the Maximum Principle for the needs of optimal control and the subsequent development of optimization methods give a classical example of a mathematical theory, which initially emerged as an effective device for solving a purely engineering problem not amenable by existing mathematical methods, and eventually developed into a mathematical theory of major significance.
The Maximum Principle was discovered by L.S. Pontryagin in 1955 in an attempt to find a solution of a highly specific optimization problem related to the manoeuvres of an aircraft, formulated to him by two Air Force engineers.
I intend to briefly describe the history of this discovery, of which I was a witness and partially, together with Professor V. Boltyansky, a participant. We were both Prof. Pontryagins former post-graduates and at that time his young collaborators.

The practical need for and some general limitations of combat modelling will be mentioned.
Two traditional deterministic Lanchester laws will be presented, discussed (especially with regard to hidden assumptions) and criticised (traditionel Lanchester laws are quite often used far outside their field of validity). This goes for

My presentation will start with a presentation of the vital changes in warfare during the last decades. Mass armies are no more common tools for warfare. The big war has turned unusual, while limited (and controlled) use of military forces for political purpose still is in use. However the ability to maneuver and fight with weapons still remains a basic military skill and modeling of combat remains important for understanding war. A formulation of a basic problem for single weapon systems will be given and the effect of technology development are discussed in that context. Further comments will be given on problems in information processing in modern weapons and in Command, Control, Communication and Intelligence, where the technological changes are expected to be revolutionary. A short comment will also be given on transforming single weapons data to force characteristics, which is important for connecting analyses on low level with those on high level. I will also give some comments on Operations Other Than War and Asymmetric War - which are new challenges for military analysts as well as officers. Finally a critique will be given on the state of the art in military modeling.

In my contribution I will elaborate on facts, perceptions and allegations with regard to so called surgical strikes. What are the technical changes in modern weaponry? What are the professional and psychological approaches towards high tech arms? Political, legal, military and humanitarian aspects of the use of military force will be addressed in connection with "humanitarian intervention" and "fight against terrorism" before the background of NATO's aggression against Yugoslavia and war in Afghanistan.

The presentation will give a real-world based assessment of the developments in cyberwar, i.e. war in, on, and against data networks. Do we have to fear cyberterrorism or rather a new digital arms race between states. Finally, some implications on how to deal with arms control in this field will be discussed.

Alan M. Turing (1912-1954) was the chief scientific figure in the British communications war, personally responsible for the reading of Atlantic U-boat signals. As a result of this experience, he emerged in 1945 able to design a digital computer in the modern sense, as a practical version of the Universal Turing machine he had described as pure mathematics in 1936. In one sense, therefore, the war greatly accelerated the application of mathematical ideas. Yet Turing's chief mathematical collaborator, M. H. A. Newman, gave an entirely different assessment, presenting in entirely negative terms the loss to science caused by the war having interrupted Turing's career. This paper will examine both viewpoints, tracing the positive and negative influences of the war in Turing's theories of computation and artificial intelligence.

The purpose of this paper is to discuss the personal moral responsibility of scientists contributing to military research. A number of arguments defending the view that scientists do not carry any responsibility (or only a marginal responsibility) for the way in which their work is used are evaluated. It is argued that none of the arguments are convincing. Furthermore, some of the difficulties related to the ascription of moral responsibility to scientists are considered.

I shall address: 1. The revolution in the 17th century of the military, the state, and the rules of war and peace. 2. The application of mathematics to the art of warfare, political science and to law. 3. The 17th century’s conception of natural law as the science of really existing moral phenomena like physics as the science of real physical phenomena. 4. The Law of War and Peace by Grotius was the establishment of a new moral legal order on a new secular basis. Therefore the mathematical method explicitly subscribed to by Grotius meant something different from axiomatic deductive reasoning. 5. Examination of his forensic method of argument in persuasion and his historical theory of the relations of moral phenomena with phases of socioeconomic development. 6. The Grotian regime of the present and the role of military in it.

Since the pioneering work by L.F. Richardson on modelling the arms race between the World Wars, it was hoped that mathematics can contribute to conflict resolution. In this talk I shall discuss whether and how mathematical modelling might be used to analyse and resolve conflicts as well as to understand the evolution of cooperation and the formation of coalitions in social systems. It is a key question to what extent mathematics can identify conditions for the instability of social interaction, potentially leading to an escalation towards violent conflict, arms race and war. Examples will be given where mathematics was able to provide a mechanism to stabilize interactions via communication and negotiation, disarmament and verification, confidence-building and common security concepts. Another question is to what extent "dynamic games" are appropriate or inappropriate to study the relationship between conflict and cooperation in international security policy (e.g. missile defense and nuclear disarmament) as well as conflicts between environmental and economic systems (energy and climate change, fishery conflicts, sustainable resource economics).