I study liberal arts, but I know Archimedes once defeated the Roman army by mathematical methods.
Here are some answers from others.
When it comes to mathematics and military affairs, people may think that mathematics can be used to help design new weapons. For example, Archimedes' hearsay story: Archimedes' Syracuse kingdom was attacked by the Romans, and King Heron asked his friend Archimedes to help him design various crossbows and military equipment, use parabolic mirrors to gather sunlight and burn enemy ships. Of course, such military applications do not use more advanced mathematics. In fact, ancient mathematics was only used to this extent in the military. The calculation of soldiers and Cao Cao in Wu Cao Shu Jing is limited to multiplication and division; Further, it is just measuring and sailing. It was not until the 20th century that scientific development promoted the progress of weapons, and mathematics could really be closely related to war. For example, the study of mathematics may involve aerodynamics, fluid dynamics, ballistics, radar and sonar, atomic bombs, codes and intelligence, aviation maps, meteorology, calculators, etc., which directly or indirectly affect weapons or tactics.
Example: An anti-fascist team with high IQ forced the American government to combine mathematics with science, technology and military goals in an unprecedented way, which opened up a new era for the development of American mathematics. 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 U.S. Scientific Research and Development Agency (OSRD) established the National Defense Science Committee (NDRC) in 1940 to provide scientific services for the military. 1942, NDRC established the applied mathematics group (AMP), whose task is to help solve the increasing number of mathematical problems in the war. AMP signed contracts with famous universities in the United States 1 1, and the most talented mathematicians in the United States devoted themselves to the sacred work of containing fascist forces. AMP's extensive research involves "improving design to improve theoretical accuracy of equipment" and "making full use of existing equipment", especially its achievements 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. For the problems of shock wave and sonic boom caused by supersonic aircraft, the hyperbolic partial differential equation solutions of these problems are obtained by using Courant-Friedrich-Levy finite difference method. 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. G boekhoff of Harvard University studies underwater ballistics for the navy. Columbia University focuses on air-to-air shooting. For example, the ballistics of air-launched shells; Deflection theory; Tracing curve theory; Observation and characterization of its own speed in the tracking process; Basic theory of central fire protection system; Analysis of radar test program for air launch equipment.
Princeton University and the University of New Mexico have determined "the best tactics for applying B-29 aircraft" for the Air Force. Von Neumann and Ulan study atomic bombs and computers. Wiener and Colmo Golov studied the automatic gun sight. Logistics scientists led by Dan Zexi invented the simplex algorithm to understand linear programming, which directly benefited the US military in strategic deployment.
Example 2 Scalpel for Deciphering Codes-Mathematics The British mathematician Turing was born in a wealthy family./Kloc-0 went to Princeton, USA in 1935 after receiving his doctorate from Cambridge University. He provided a theoretical basis for designing an ideal general-purpose computer. Turing returned to England on 1939, and was immediately hired by the Communication Department of the Ministry of Foreign Affairs. At that time, the telegraph used by German fascists for top secret communication was called Enigma. Turing regarded the process of telegraph transmission as a perforation in a piece of paper. Using Turing's computability theory, Britain designed a "super" (transcendence) machine to deal with Enigma, and deciphered a large number of German codes.
194 1 May 2, 20081day, British intelligence agencies finally intercepted and deciphered a secret telegram from Hitler to General Lei Deer. As a result, Hitler's Bismarck, known as the most powerful giant battleship in the world at that time, was buried in the belly of a fish on its maiden voyage.
1In April, 943, the top secret radio waves sent by the Supreme Command of the Japanese Navy crossed the Pacific Ocean and reached the Japanese fleet stationed in the South Pacific and the Japanese-occupied China seaport. Commanders of various fleets have been ordered that General Isoroku Yamamoto, Commander-in-Chief of the Japanese Joint Fleet, will fly to Kathiri Bay at 9: 45 a.m. on April 9 18, protected by six Zero Fighters, accompanied by all the subordinates of Isoroku Yamamoto.
This telegram was immediately deciphered by an expert deciphering team composed of mathematicians in the US Navy, and was immediately sent to President Roosevelt's desk through Secretary of the Navy Frank Knox. As a result, the American lightning fighter group intercepted Yamamoto's plane over Kathiri Bay, and the plane exploded among the thorns just a few miles away from Yamamoto's destination, Kathiri.
The Midway naval battle was also caused by the United States deciphering Japanese codes, which led to the sinking of four Japanese aircraft carriers and cruisers, and the shooting down of 330 planes. Hundreds of experienced pilots and crew members were killed. The United States only lost 1 aircraft carrier, 1 destroyer and 147 aircraft.
Since then, Japan has lost its air superiority and sea superiority in the Pacific battlefield.
Case 3 Barton's warships and Bogo are an important branch of military intelligence. It is based on probability theory, statistics and simulation experiments. By testing and calculating natural conditions such as topography, climate, waves, hydrology, and the weapons of both sides in the battle, it is found that in the sinister environment that most people think cannot be overcome, it is even easy to be at a disadvantage. In fact, the highest or lowest limits of basic tactical parameters of various natural conditions can be used through calculation and operation, such as by calculating the slope of mountains.
1In June, 942, General Barton led more than 40,000 American troops and arrived in Morocco, which is 4,000 kilometers away from the United States, by 100 warship. It is planned to land in the early morning of 165438+ 10. 165438+1October 4th, northwest wind suddenly blew at sea, and the stormy waves made the ship tilt 42. The weather didn't improve until165438+1October 6th. Worried that the fleet would be destroyed by strong winds, Washington headquarters ordered Barton's fleet to land at any other port along the Mediterranean coast. Barton called back: No matter what the weather is like, I will stick to the plan.
165438+1At midnight on October 7, the sea suddenly became calm, and Barton's army landed successfully as planned. Afterwards, people said it was a lucky victory, and "Red General" gambled on the lives of his soldiers.