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  "body": "\n## Summary\n\nConstructivism is the view in the philosophy of mathematics that a mathematical object exists only when one can construct it.\nTo prove that something exists, one must give a method to find it, as in a [[constructive proof|01XM7JEKHY]].\nAs a result, constructive mathematics does not accept the [[law of excluded middle|0RYYK8PG4S]] as a general principle.\nIts main schools are Brouwer's intuitionism, Markov's recursive constructive mathematics, and Bishop's constructive analysis.\n\n## Explanations\n\n### L1 human\n\nA constructivist accepts \"there is a number with this property\" only if you can, at least in principle, produce it.\nA [[proof by contradiction|0J0XBKG64S]] that only shows \"it cannot be that no such number exists\" is not enough.\nFor example, the classical proof that there are irrational $a, b$ with $a^b$ rational does not say which pair works.\nA constructivist asks for a proof that names the pair.\nIn return, every constructive existence proof contains an algorithm.\n",
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