I think the last section is a great set of questions to ask after coming to any decision and is certainly not isolated to mathematics! It, combined with the rest, seems like a nice recipe for both internalizing one’s methods and data as well as trying to avoid duplicating efforts on related/similar issues. Thanks for sharing.
Very cool. Some of those questions seem a little redundant, such as:
Have you seen it in another form? An analogous problem?
These aren’t redundant in the context that Polya is talking about. In math, these are different. The first means the same problem but with different notation or some equivalent problem. The second means a problem that is similar in some way (say for example something over a finite field having an analog over the real numbers or rationals.)
I appreciate the explanation, especially when considering a math context (which is the intended context anyway, but I was thinking generally with my comment).
Very cool. Some of those questions seem a little redundant, such as:
Perhaps not the same, but reading the list made me wonder if it could be “simmered” a bit to distill the key points. In particular, I really liked the Looking Back section. Absolutely wonderful. It reminds me of my own post as well as many other LW posts: not attacking the strong points of a theory, but the weakest, being careful to avoid leaky generalizations, really knowing the purpose of your actions, internalizing vs. parroting, and not being so quick to assume you’ve thought of all the options.
I think the last section is a great set of questions to ask after coming to any decision and is certainly not isolated to mathematics! It, combined with the rest, seems like a nice recipe for both internalizing one’s methods and data as well as trying to avoid duplicating efforts on related/similar issues. Thanks for sharing.
These aren’t redundant in the context that Polya is talking about. In math, these are different. The first means the same problem but with different notation or some equivalent problem. The second means a problem that is similar in some way (say for example something over a finite field having an analog over the real numbers or rationals.)
I appreciate the explanation, especially when considering a math context (which is the intended context anyway, but I was thinking generally with my comment).