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For instance, when asked to prove that sqrt(2) is irrational, most people wouldwe go straight for the proof by contradiction where we assume it’s equal to a/b in lowest terms and end up with a and b not being in lowest terms. On the other hand, the proof of some other theorem might always be done directly, or happen to be feasible using multiple proof types. If it hasn't already been done, could studying which proof types are feasible for which theorems in mathematics ever have any practical use, or would this just not be useful information to look into?

For instance, when asked to prove that sqrt(2) is irrational, most people would go straight for the proof by contradiction where we assume it’s equal to a/b in lowest terms and end up with a and b not being in lowest terms. On the other hand, the proof of some other theorem might always be done directly, or happen to be feasible using multiple proof types. If it hasn't already been done, could studying which proof types are feasible for which theorems in mathematics ever have any practical use, or would this just not be useful information to look into?

For instance, when asked to prove that sqrt(2) is irrational, we go straight for the proof by contradiction where we assume it’s equal to a/b in lowest terms and end up with a and b not being in lowest terms. On the other hand, the proof of some other theorem might always be done directly, or happen to be feasible using multiple proof types. If it hasn't already been done, could studying which proof types are feasible for which theorems in mathematics ever have any practical use, or would this just not be useful information to look into?

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asdf555
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Has anyone ever studied which proof types are feasible for which theorems in mathematics? If not, why not?

For instance, when asked to prove that sqrt(2) is irrational, most people would go straight for the proof by contradiction where we assume it’s equal to a/b in lowest terms and end up with a and b not being in lowest terms. On the other hand, the proof of some other theorem might always be done directly, or happen to be feasible using multiple proof types. If it hasn't already been done, could studying which proof types are feasible for which theorems in mathematics ever have any practical use, or would this just not be useful information to look into?