"World War II" forced the American government to combine mathematics, science and technology and military goals more closely than before, and opened a new era of American mathematics development. 194 1 year, when the United States entered the war, the federal government began to substantially increase its investment in scientific research.
Allocation of expenses. From 194 1 to 1945, the proportion of research and development funds provided by the government in the total amount of similar funds in China has suddenly increased to 86%. The Scientific Research and Development Bureau of the United States established a "state" in 1940.
The National Defense Science Committee (NDRC) provides scientific services for the military. 1942, NDRC established the applied mathematics group.
(applied mathematics group, abbreviated as AMP). Its task is to help solve the increasing mathematical problems in the war. AMP belongs to 1 1 a famous American school.
At the same time, America's most talented mathematicians also devoted themselves to this work. AMP's extensive research involves "improving design to improve the theoretical accuracy of equipment" and "making the best use of existing equipment", especially in air combat.
By the end of the war, 200 major studies had been completed.
At new york State University, the team led by Courant and Friedrich studied aerodynamics, underwater blasting and jet rocket theory. The problem of shock wave and sonic boom caused by supersonic aircraft was solved by "Courant Friedrich-Le"
The hyperbolic partial differential equations solutions of these problems are obtained by the finite difference method of dimensions. The applied mathematics group headed by praeger at Brown University focuses on classical dynamics and distorted medium mechanics to improve the service life of armaments. bend
G from the University of Florida? Boekhoff studies underwater ballistic problems for the navy. Columbia University focuses on air-to-air shooting, such as ballistics, deflection theory, tracking curve theory, and its own speed during tracking.
Observation and characterization of temperature, basic theory of central fire system, test scheme analysis of air launch equipment, stability, radar. Princeton University and the University of New Mexico determine the best application of B-29 aircraft for the Air Force.
Tactics. "Feng? Neumann and Ulan study atomic bombs and computers. Wiener and Colmo Golov studied the automatic gun sight. Turing cracked the German code. In short, the crazy expansion of fascism seriously threatens the interests of the United States.
Safe. Therefore, how to use the latest scientific and technological achievements to arm modern military weapons to contain the enemy? It was quickly put on the central agenda of American wartime science and technology strategy.
British mathematician Turing was born in a rich family. 1935 After receiving his doctorate from Cambridge University, he went to Princeton, USA. In 1937, he wrote the article "computable number and its application in judging problems", which is
Designing an ideal general-purpose computer provides a theoretical basis. He was one of the first people to discuss the concepts of intelligence and computability of digital computers. Turing returned to England on 1939, and was immediately hired by the Communication Department of the Ministry of Foreign Affairs. at that time
Teller Germany's telegram used for top secret communication is called Enigma. Turing regarded the process of telegraphy as a perforation in a piece of paper. Using Turing's computability theory, Britain designed a deciphering machine.
Beyond specifically dealt with the "Engma" machine and deciphered a large number of German codes. 1in April, 943, the extremely confidential radio waves sent by the Supreme Command of the Japanese Navy flew over the vast Pacific Ocean and arrived.
After visiting the Japanese fleets stationed in the South Pacific and the Japanese-occupied China seaport, the commanders of the fleets have received orders: Admiral Isoroku Yamamoto, commander-in-chief of the Japanese Joint Fleet, will leave at 9: 45 am on April 18.
Under the protection of six Zero fighters, he flew to Kathiri Bay by two Mitsubishi bombers, and all Yamamoto's subordinates went with him. The top secret telegram was immediately deciphered by experts from the US Naval Communications Intelligence Agency and passed by the Secretary of the Navy.
Frank. Knox's hand was immediately placed on the desk of President Roosevelt. As a result, a battle plan for a surprise attack on Admiral Yamamoto's plane by sea and air is being brewed and formulated. April 16 at 7: 35 am, USA
China's lightning fighter group took off, and finally Yamamoto's plane stopped over Kathiri Bay. Major Langfield fired two shots in hot pursuit. The right engine and left wing of Yamamoto plane exploded and caught fire, and the last two wings broke eastward.
When it crashed, the fuselage exploded among thorns just a few miles from Yamamoto's destination, Kathiri.
On May 26th, British intelligence agencies intercepted and deciphered a secret telegram from Hitler to General Lei Deer. As a result, Hitler's "Pride of the German Navy" and "Bismarck", the so-called most powerful giant battleships in the world at that time, were buried in the belly of fish.
1940, Hitler's air superiority caused great difficulties 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 failed at the beginning of the war and asked scientists to help the army defend it.
Moscow, especially to defend against 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 believes that there are two battles between submarines and bombers.
The main threat to our application of mathematics to help uniforms.
The difficulty in studying automatic tracking artillery is that the speed of aircraft is similar to that of shells. To attack enemy planes, it is necessary to predict the future position, observe the actual position data and correct the azimuth and elevation of the artillery, so that the shells can
Hit the enemy plane. Because of the observation error, the flying position of the enemy plane and the firing angle of the gun are random, so it is necessary to study the theory of stochastic process prediction. Filter out error components from observation data and use accurate figures.
According to the command of artillery, the hit rate of artillery is greatly improved. This mathematical theory forms the basis of stochastic process and cybernetics.
In modern warfare, many problems need to be quickly estimated and approximated. Feng who specializes in pure mathematics? Neumann immediately attached importance to numerical analysis, and he proposed and solved the inverse problem of higher-order matrix. He comes from
The problem of compressible gas motion and shock wave opens up the study of shock wave collision and shock wave reflection. He not only made theoretical analysis, but also gave the best calculation scheme-difference scheme and mathematics of calculation scheme.
Stable conditions. At the end of 1943, he was invited by Oppenheimer to visit Los Angeles as a consultant. Alamos laboratory, participated in the project of making atomic bomb, engaged in inward explosion theory, calculation of nuclear explosion characteristics, thermonuclear reaction zone.
All aspects have made great contributions.
The consumption of arms in World War II is staggering, so it is urgent to study how to save on arms quality control and sampling inspection. Waldorf is the head of the statistical research group of Columbia University, which belongs to the applied mathematics group.
At present, the traditional statistical sampling inspection needs many steps, and the data obtained from each step is only related to the final conclusion, but there is no relationship between each step. So Wald developed a method, and the previous step decided how to sample next.
And whether to stop the next statistical sampling scheme, which is now commonly known as "sequential analysis". The invention of this scheme has saved a lot of weapons and materials for the US military, and this alone far exceeds the entire AMP.
Expenses.
1944, weaver received a request to determine the type of mine array that attacked large Japanese warships. However, the US Navy knows nothing about the speed and steering ability of Japanese warships. Fortunately, the naval authorities have a lot of such equipment.
Photos of warships. When the question was referred to the Applied Mathematics Group of new york State University, someone immediately provided a message: 1887, the mathematician Kelvin once studied that when a ship moves in a straight line at a constant speed, it will stir up water waves along the ship.
Only the forward direction forms a fan, and the half angle from the ship's side to the corner edge is19 28', and its speed can be calculated from the interval between the two waves at the bow. According to this formula, the speed and turning ability of Japanese ships are calculated.
During World War II, nearly 200 scientists from Germany and Austria immigrated to the United States, including the best mathematicians in the world. The influx of foreign talents has saved the United States a huge intellectual investment. The United States believes
For a first-rate scientist, it is more important than capturing the Germans of the 10/0 division. More valuable. 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.