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It's not a lie that, in most sciences, some of their advancement comes from war. A couple examples would be the Haber process in chemistry and none other than the Manhattan Project in both physics and chemistry, both coming from the infamous World War 2.

My question is: has there ever been advancement in mathematics due to war?

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There are stories about theorems being proved in war prison camps. –  Asaf Karagila Aug 16 at 22:51
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You're using "extrapolate" wrong. :-) –  Asaf Karagila Aug 16 at 22:52
    
Yes I am, sorry. Would you kindly extend your answer? –  Miguelgondu Aug 16 at 22:52
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@AsafKaragila You are thinking of Jean Leray. –  Zhen Lin Aug 16 at 23:02
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@AsafKaragila: I believe you mean Paul Turán. –  Dejan Govc Aug 17 at 15:15

5 Answers 5

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Operations research was explored during WW2. See, e.g., http://en.wikipedia.org/wiki/Operations_research#Second_World_War

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There is a very entertaining book by T.W. Korner called The Pleasures of Counting in which he discusses among other things how the Allies nearly lost WW2. It's been a while since I read the book but the naval effort was rescued by mathematicians in an ingenious and essentially simple way.

Cryptography is another field in which WWII may have spurred advancement but I can't say for sure whether it involved novel math or just increased attention and ingenuity.

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"Decision mathematics" was spurred by the first war regarding resource allocation, linear programming for example. My A-level teacher introduced us with this topic.

Cryptography also progressed in leaps and bounds as well as computing because of the need for cryptography.

The Curta mechanical calculator was invented by a Jew (Curta) in a concentration camp.

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Game theory's development accelerated at a record pace during World War II/Cold War. If one nation changed the balance of power (by building a missile-defense shield, for instance), would it lead to a strategic blunder that resulted in nuclear war? Governments consulted game theorists to prevent such imbalances.

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Do you mean the Cold War? –  Zhen Lin Aug 16 at 23:20

Asaf was referring to André Weil, see here: http://en.wikipedia.org/wiki/Andr%C3%A9_Weil

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No, I wasn't referring to Weil. I was talking about Jean Leray. –  Asaf Karagila Aug 16 at 23:09
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@AsafKaragila: My apologies. But Weil also belongs to the math-in-prison category. –  Frunobulax Aug 16 at 23:18

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