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> Despite this, math professors kept presenting us with patterns to match, but no exhaustive algorithms. This is basically what math is all about. If a problem
by xyzzyz 11y ago
> Despite this, math professors kept presenting us with patterns to match, but no exhaustive algorithms.
This is basically what math is all about. If a problem can be effectively and easily solved algorithmically, it is considered trivial, and little attention is given to it. The focus is on actually difficult problems, ones that need clever tricks to get a handle of.
- eli_gottlieb 11y agoTo be frank: bull. A problem that can always be solved algorithmically is "trivial", in the mathematical sense, but since the mind is algorithmic, you can't just say, "Well, clever tricks, not algorithms." A mathematician's mind works somehow.
- JadeNB 11y ago> the mind is algorithmic Huh? If you mean this: > A mathematician's mind works somehow. then it seems like you may be using 'algorithmic' to mean something like "unfolding according to (possibly unknown, possibly probabilistic) laws", in which case it seems so broad a term as to be almost useless.
- eli_gottlieb 11y ago>then it seems like you may be using 'algorithmic' to mean something like "unfolding according to (possibly unknown, possibly probabilistic) laws" They're certainly currently unknown, and we have good reason to believe they're probabilistic. Even such vague, loose descriptions are better than invoking "mathematical intuition" or "it just comes to me" or other explanations for how one does math.