> if you need this book, you're going to be roadkill in math contests
> I have not seen anyone including Polya successfully /teach/ this ability.
This is a pretty wild take. For alternate takes, see John Horton Conway's foreword to the most recent edition of the book. There he talks about how amazing the book is for both students and teachers, including the things he learned from it as both a student and teacher. Or see Terry Tao's blog post on solving mathematical problems [0], in which he says he learned from the Polya book when preparing for Mathematics Olympiads. Conway and Tao are widely considered outside the "roadkill" category of mathematicians.
> If you want to be good at math, piano, chess, sculpture, or whatever you need the talent and then it can be nurtured.
The "either you got it or you don't" theory used to be common wisdom, but it's not supported by empirical evidence and these days it's mostly relegated to grouchy coach stock character stereotypes. You need a sustained level of interest, you need practice, and you need some amount of courage, but there's no real evidence for an innate ability that some people got and some people don't.
Thank you for taking the time to debunk such comments. I have serious imposter syndrome as a minority woman in software, literally the only one among 60 others and everyday is a battle with my inner thought process. For an onlooker, I have amazing achievements behind me and there's no reason I shouldn't be confident, but I'm not and seeing such comments as before has made it worse over time, without me questioning it.
> I have not seen anyone including Polya successfully /teach/ this ability.
This is a pretty wild take. For alternate takes, see John Horton Conway's foreword to the most recent edition of the book. There he talks about how amazing the book is for both students and teachers, including the things he learned from it as both a student and teacher. Or see Terry Tao's blog post on solving mathematical problems [0], in which he says he learned from the Polya book when preparing for Mathematics Olympiads. Conway and Tao are widely considered outside the "roadkill" category of mathematicians.
> If you want to be good at math, piano, chess, sculpture, or whatever you need the talent and then it can be nurtured.
The "either you got it or you don't" theory used to be common wisdom, but it's not supported by empirical evidence and these days it's mostly relegated to grouchy coach stock character stereotypes. You need a sustained level of interest, you need practice, and you need some amount of courage, but there's no real evidence for an innate ability that some people got and some people don't.
[0] https://terrytao.wordpress.com/career-advice/solving-mathema...