Another shortpost since I haven't digested it, but tonight I watched a video [UPDATE 6/7 now private] on the memory/time tradeoff in computation. One important summary, which she linked, is Lance Fortnow's last February. There's also this last year on tree evaluation.
Overall if you can take up space to save time, you should. Space is fungible. Time, once used, is lost.
This affects those of us who were attempting to solve equations by means of power-series where the coëfficient of said series needed to be easily-accessible from some database. This could include RAM but, as noted, for quintics this nearly fried the computer I'd used.
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