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army1987 comments on Assessing oneself - Less Wrong Discussion

13 Post author: polymer 26 September 2014 06:03PM

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Comment author: gjm 26 September 2014 10:06:50PM 19 points [-]

A few disorganized remarks that may or may not be any help:

  • Different people are good at different things. In particular, the algebra/analysis dichotomy is a pretty standard one and if you're good at analysis and not so good at algebra, it probably matters how good you are at what you're best at.
  • It seems like simply not being fast enough could be largely irrelevant (if it's really just a matter of speed; the limiting factor in doing mathematical research is unlikely to be how fast you can do practice-test-level questions) or quite important (if what it really means is that you didn't understand the material well and therefore had to flounder about when someone with a better grasp would have headed straight for the solution). You may or may not be able to judge which.
  • Motivation is really really important, perhaps more important than talent once the talent is above a certain level. One piece of advice I've seen (specifically in the context of academic pure mathematics) is that you shouldn't become a mathematician unless you couldn't bear not to. Because mathematics research is really hard, and it will kick your ass, and how successful you are will have a lot to do with how you cope when it does.

(My own background: got the PhD, did a couple of years of postdoc, was quite staggeringly unproductive, got out of academia and into industry, have been reasonably happy there. Probably happier than I'd have been as a struggling academic. Most academics are struggling academics, especially for, say, the first 5-10 years after getting their PhDs.)

Some questions you might want to answer for yourself:

  • If you go to grad school, get your PhD, and then don't go into academia, is that a good outcome or a bad one?
  • If you don't take the academic path, what will you do instead?
  • Whichever way you go, regrettably there's a very good chance that you won't end up revolutionizing the world. If you compare possible academic futures with possible non-academic futures, and make the assumption that you do just OK -- which feels like the better outcome?
Comment author: [deleted] 03 October 2014 07:35:04PM 1 point [-]

Different people are good at different things. In particular, the algebra/analysis dichotomy is a pretty standard one and if you're good at analysis and not so good at algebra, it probably matters how good you are at what you're best at.

(I've heard people talk of branches of maths the way gender essentialists such as EY or Ozy Frantz would talk of gender identity.)

Comment author: Lumifer 03 October 2014 07:59:40PM 1 point [-]

One of my pet theories is that math and (applied) statistics require very different brains. People whose brains are wired for math make poor (applied) statisticians and people who are really good at stats tend to be poor at math.

This is partly an empirical observation and partly, I think, is a consequence of the fact that math deals with "hard" objects (e.g. numbers) that might not be known at the time, but they are not going to mutate and change on you, while statistics deals with uncertainty and "soft"/fuzzy/nebulous objects (e.g. estimates). Moreover, for applied statistics the underlying processes are rarely stable and do mutate...

Comment author: gjm 03 October 2014 08:04:06PM -1 points [-]

Possibly relevant: the relationship between algebra/analysis and how one eats corn on the cob.

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