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gjm 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: roystgnr 27 September 2014 01:48:43PM 5 points [-]

if you're good at analysis and not so good at algebra

Then he might also want to consider applied mathematics programs, especially if he also excels at programming and engineering but feels they're too easy.

Comment author: IlyaShpitser 27 September 2014 03:53:22AM *  4 points [-]

Endorsing this post. I am an academic that mostly proves theorems for a living.

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.

Comment author: polymer 30 September 2014 01:23:20AM 1 point [-]

So, my point regarding the speed.

In the middle of working out a problem, I had to find the limit of

S = 1/e + 2/e^2 + ... + n/e^n + ...

I had never seen this sum before, so now cleverness is required. If I assumed guess C was true, that would imply

e/(e - 1) = (e - 1)S

This claim is much easier to check,

(e - 1)S = 1 + 1/e + 1/e^2 + ... = 1/(1 - 1/e) = e/(e - 1)

We know what S is, and the solution to the problem follows. In retrospect, I understand one method for how I could find the answer. But during the test, I can't see through the noise fast enough (although I can smell the clue). I could go through each guess one by one, but I'm just too slow. Maybe there's something else I'm missing that would've made the guess simpler, but that's what I'm basing the slow opinion off of.

I don't know if being slow at inference in this sense is a barrier, or indicative, of deeper creativity issues (or if I'm just suffering from the availability heuristic.)

Anyways your questions all very good, I don't care for academia perse, I care about the questions. If I don't keep doing academic stuff, I would hope I would've formed enough connections to find some route towards practical problems that still require some creativity.

Your last question is very interesting. I'm not sure how to answer it. My unhealthy worry, I think, is I really don't like wasting peoples time. I suppose I don't care about either being "just OK", if "just OK" isn't wasting peoples time, but I still get to be creative.

I guess I don't want to be a pundit? I mean I'll teach, but I'd be much happier if I was doing something theoretically. If this is impossible for me, I'd like to know the reasons why, and fail out as soon as possible.

Your questions are very interesting though, I still need to think about them more. Thank you for your thoughts, they give very good context to think about this, and its clear you've worried about analogous issues.

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