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komponisto comments on What mathematics to learn - Less Wrong Discussion
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Comments (30)
The answer is highly dependent on one's goals, interests, and personality. Hence there is unlikely to be any particular document which successfully explains the answer in a way that applies to everyone.
What would be better would be for people interested in learning mathematics to post comments explaining the nature of their own particular interest, and to receive individually-tailored replies. If general patterns emerge from those replies, these general patterns can then be extracted and abstracted afterward, preferably with appropriate cautions and disclaimers.
Alternatively or in addition, those who already use some field of mathematics in their daily work might post examples of what they need to know. For example, in physics research I use (off the top of my head) a bit of calculus, considerable statistics, occasional trig, and large amounts of plain symbol-manipulating algebra. The most relevant math skill, perhaps, is that difficult-to-teach intuition, the fingertip-feel of how to manipulate an equation so you get it in a form you can use.
Agreed. Advice is trivial to give, especially in the abstract, and therefore likely to have a low signal-to-noise ratio. Extrapolating patterns after dealing with specific instances will probably increase the SNR substantially.