Since then, the US military has been very keen on funding mathematical research and mathematicians, and even they are willing to invest in projects with uncertain application prospects. The United States believes that getting a first-class mathematician is much more valuable than capturing the Germans with the 10 division.
Why does America have such an idea? It turned out that they got this impression from some examples that happened during World War II.
Before 1943, the British and American fleets escorting the transport fleet in the Atlantic Ocean were often attacked by German submarines, and a large number of military materials, including tanks, artillery, gasoline, guns and ammunition, sank to the bottom of the sea before being delivered to the frontline soldiers. At that time, Britain and the United States could not send a large number of escort ships. What should we do?
The US Navy general consulted several mathematicians, and mathematicians found that the fleet and enemy submarines may or may not meet. This is a random event with certain rules. The smaller the fleet size of a certain number of ships (such as 100 ships), the larger the order quantity (such as 20 ships at a time, there must be 5 orders); The more teams there are, the greater the probability of meeting the enemy. For example, when five students come home from school, the teacher can find 1 student and go to any one. But if these five students are all in one of them, the teacher has to find a few to find them, and the possibility of finding them at one time is only 20%.
The US Navy accepted the mathematician's advice and ordered the fleet to collectively pass through the dangerous sea area after the designated sea area, and then separately sail to the scheduled port. In this way, the sinking probability is reduced from 25% to 1%, which greatly reduces the loss and ensures the timely supply of materials.
Some people think that the immigration of first-class mathematicians to the United States is one of the greatest victories of the United States in the Second World War.
In fact, during World War II, the war brought many new topics to mathematicians, such as cryptography, operational research, probability statistics and so on. Many mathematicians participated in this research, which also promoted the development of applied mathematics. Since then, the US military has been one of the biggest customers of mathematics, and a large amount of money has been invested in mathematics research every year.
1944, when Weaver attacked a large Japanese warship, he received a request to determine the type of mine array. The US Navy knows nothing about the speed and steering ability of Japanese large ships. Fortunately, the naval authorities have many photos of these warships. When the question was referred to the Weaver Applied Mathematics Group of new york State University, someone immediately provided a data: 1887. Mathematician Kelvin once studied that when the ship goes straight at a constant speed, the water waves aroused form a fan along the direction of the ship's progress, and the half angle of the ship's corner is 19 degrees 28 minutes, and its speed can be calculated by the interval between the two waves at the bow. According to this formula, the speed and turning ability of Japanese ships are calculated.
At the beginning of the war, Hitler's air superiority posed a great threat to the Allies. In the face of German air strikes, Britain asked the United States to help increase ground air defense forces. The Soviet Union lost at the beginning of the war and asked mathematicians to help the army defend Moscow, especially the German air strikes. At this time, Wiener of Britain and Colmo Golov of the Soviet Union began to study filtering theory and automatic control of artillery almost at the same time. Wiener provided an accurate mathematical model for the military to command artillery, which greatly improved the hit rate of artillery. This mathematical theory forms the basis of stochastic process and cybernetics.
In the battle between the two armies, many problems need quick estimation and approximate methods. Von Neumann, who specializes in pure mathematics, immediately focused on numerical analysis. Engaged in the movement and filtration of compressible gas, and carried out the research on shock wave collision and shock wave emission. At the end of 1943, at the invitation of Oppenheimer, he visited Los Alamos Laboratory as a consultant and participated in the project of making atomic bombs, which made great contributions to the theory of inward explosion and the calculation of nuclear explosion characteristics.
The consumption of arms in World War II is staggering, so it is urgent to study how to save money on arms quality control and sampling inspection. Walter, head of the Statistical Research Group of Columbia University, which belongs to the Applied Mathematics Group, developed a new statistical sampling scheme, which is now called "sequential analysis method". This plan has saved a lot of arms and materials for the US military, and this alone far exceeds all the funds of AMP.