Recent content by nightdove

I think it is true in the case of doing well in exams. I don't know if it is the case in research. I would say that for exams, the majority of the marks (some 50% ?) you get from practising past year papers well enough, and only 25% comes from the lecture notes and textbook examples. Of...

It wasn't MY hypothesis, but rather an intriguing hypothesis worth testing, given the amount of anecdotal evidence, sometimes personally offered by scientists and mathematicians, in it's favour. I would in fact prefer if the hypothesis weren't true. After all, the psychologists who support it...

Perhaps. I have already mentioned that I tend to be rather parsimonious with abstraction, too much conceals more than it reveals. So it isn't abstraction for its own sake, but abstraction for the sake of yielding an "einsicht", which you could describe as subjective (what is insight to one may...

The question is, do people really have set preferences for different levels of abstraction? You are as abstract as you need to be to solve a given interesting problem or to understand an insight with aesthetic features. I find it impossible to force myself to do ugly proofs (is there...

Some mathematicians note that their intellectual powers (at least where mathematics is concerned) seem to diminish with age, for instance Hardy. Was this griping a mere excuse for their lack of talent to begin with? Other prodigies appeared to have retained their mathematical fecundity into...

That linear algebra proof was a rather simple one. Proofs in linear algebra are almost always very intuitive to me. But yes, no matter how easy I found them when I first studied them, I can safely say I have forgotten nearly all of them, now that I'm in the commercial world. For example...

The former definition already describes infinite-dimensional case sufficiently. You have no right to change my statement about "unnecessary abstraction" - it stands. There is no need to bring chimpanzees into the picture either. That would be an unneessary point of reference unless you...

It's easy enough to understand a non-trivial proof from an undergraduate textbook and memorize the intuitions and general ideas behind them (15 minutes tops?!). That gives you about 4 undergraduate theorems per hour. Of course, it's difficult to go beyond 4 new theorems a day, since your mind...

Oh well. Tough luck. Excessive knowledge hinders intuition and blunts your problem-solving skills. In this respect, some degree of 'forgetting' could be good, since it gives you a chance to rearrange your thinking. I think 10,000 hours is a good benchmark for time required to become a...

Welcome to the human race. As far as I know, not one Professor I had in university was able to reproduce high school trig identities... some were positively worse than I was in elementary computations... most made stupid mistakes on the board from time to time. One or two even made logically...

What's the point of such obvious redundancy? Unnecessary abstraction is a waste of time. Most of the pleasure comes in converting the abstract into concrete terms in my case, ie. terms I can visualise at least partially, by applying the obverse of induction.

I received a First in Math at a fairly renown UK university. Suffice to say, I can remember bollocks from the courses... though I was hell of an interested in them while I was there. It seems that level of interest doesn't really carry things into your long term permastore if the material is...

Psychologists estimate 10,000 hrs before you can match the "masters" in a field and begin producing novel work. I think university math needs to be distinguished from pre-university math as the two are entirely different animals. How many hrs did we spend in university studying Math...

Maybe you need to cut down study hours, take 2-3 day breaks to see if the eye-strain goes away, or better, yet, record on tape the material you need to read. I also used to go down into my family's wine cellar where it's dark and sit there for half an hour or so. Napping could help to...

It depends on what you're studying I guess and how long you've been doing it for. 1 day of 10 hrs is not likely to make your eyes strained. Try reading a mathematical textbook and solving problems on it for 8 weeks, 8-9 hrs a day, and you'll probably have an issue there with your eyes...