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"How To Solve It" does not account for actual ability. It was recommended in high school to those of us interested in math contests. My big lesson was that if
by OldGuyInTheClub 3y ago
"How To Solve It" does not account for actual ability. It was recommended in high school to those of us interested in math contests. My big lesson was that if you need this book, you're going to be roadkill in math contests. If you have the chops to be a successful mathlete, you don't need this book. And so it came to pass.
There are some people who have the ability to see a problem well enough to analyze it and make progress. Some people can do this in math, some in other technical disciplines, others in the arts, and so forth. Umpteen years later, I have not seen anyone including Polya successfully /teach/ this ability. If you want to be good at math, piano, chess, sculpture, or whatever you need the talent and then it can be nurtured.
In college I took organic chemistry[0]. The exam problems would often have redundant and/or contradictory information. The student had to figure out what to NOT believe to get anywhere.
As others have mentioned, none of Polya matters for selecting and attacking research problems.
[0] It was taught well and none of the cliches of "It's all memorization" applied. I struggled but look back fondly on it because I had to think along many axes at the same time.
- agencies 3y agoYou say that if someone has the chops to be a real mathlete they won't need Polya's _How To Solve It_ I'll say I went to college 25 years ago with people who had competed internationally in high school and who placed competitively on the Putnam, and they LOVED Polya's book. I think whether you enjoy seeing strategies laid out well--—whether or not you've been able to figure some of it out yourself---depsnds more on your personality than on how good you are at solving creative math problems.
- paulpauper 3y agobeyond the book, what contributions did he make? it would seem like the techniques should have helped him solve problems but Wikipedia does not show anything else
- bollu 3y agoSurely you’re joking. Polya pioneered so much combinatorics I don’t even know where to begin. Heck, a lot of counting problems reduces to polya’s enumeration theorem. The page of “references” to stuff named after him should be a clue to you.
- OldGuyInTheClub 3y agoDefinitely. Whatever one may think of "How to Solve It," Polya was a renowned mathematician. The book is like the Richard Hamming lectures that often come up on HN: Great thoughts from a great mind but not easily applied by the average or even above average Joe.
- boppo1 3y agoRichard hamming lectures? I'd google, but I wouldn't know if I'd found the ones you meant.
- OldGuyInTheClub 3y agoTry https://news.ycombinator.com/item?id=35776480 https://news.ycombinator.com/item?id=35776480
- lporto 3y agohttps://youtube.com/playlist?list=PL2FF649D0C4407B30 https://youtube.com/playlist?list=PL2FF649D0C4407B30
- freilanzer 3y agoBut besides combinatorics, what has he done for us lately? ;)
- fuzztester 3y ago>lately Luckily for the world, he dodged the 'startup craze' bullet ;) - by living before it started up :)
- mathisfun123 3y agoEvery so often there's a comment on here that's simultaneously so ignorant and so arrogant that it crosses from offensive to hilarious. Congrats, this one is up there with the likes of "it could just be rsync".
- jodrellblank 3y ago[flagged]
- mathisfun123 3y agothe guy clearly says >but Wikipedia does not show anything else go look at the wikipedia page for george polya and tell me what state of mind you need to be in to conclude that he didn't accomplish anything outside of publishing that book. also btw >born in 1887 he lived very long and had a very long career so you're still not close >Died September 7, 1985 (aged 97)
- jodrellblank 3y agoThe guy misread a Wikipedia page and you're "beyond offended" and call that "arrogant"? > "so you're still not close" I'm "still" not close? Still not close ... to what?
- mathisfun123 3y ago> "beyond offended" Who exactly are you quoting here? My comment doesn't contain that phrase. > The guy misread a Wikipedia page I don't know how it's possible to "misread" a wiki that's all of 500 words and has things like this: > He made fundamental contributions to combinatorics, number theory, numerical analysis and probability theory. > There are three prizes named after Pólya, > Stanford University has a Polya Hall named in his honor. Except in so far as he was temporarily blinded by arrogance. > I'm "still" not close? Still not close ... to what? Still not close to any semblance of a convincing rebuke.
- ants_everywhere 3y ago> 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. [0] https://terrytao.wordpress.com/career-advice/solving-mathematical-problems/ https://terrytao.wordpress.com/career-advice/solving-mathema...
- OldGuyInTheClub 3y ago> Conway and Tao are widely considered outside the "roadkill" category of mathematicians. Ah, but they didn't really /need/ Polya's book.
- travisjungroth 3y agoThis “need” standard doesn’t seem useful. You could say they don’t need anything besides air, water, food and shelter.
- kgwgk 3y agoCome on, you don't really /need/ shelter.
- scns 3y ago"Genius is 1 percent inspiration and 99 percent perspiration." https://quoteinvestigator.com/2012/12/14/genius-ratio/ https://quoteinvestigator.com/2012/12/14/genius-ratio/
- bigbluesax 3y ago>If you want to be good at math, piano, chess, sculpture, or whatever you need the talent and then it can be nurtured. No offense, but you sound like you don't really know anything about these disciplines, or about the science of learning (Peak is a good book to read). Getting a good piano teacher will absolutely accelerate your progress and being talented at piano as a kid is a pretty bad predictor of how good you'll be as an adult. Every outstanding Piano "talent" you see on stage today has been nurtured and nurtured themselves through practice, to hell and back.
- OldGuyInTheClub 3y agoNone taken but you don't know about my (adult) piano adventure with good teachers over 15+ years, either. I didn't say practice was not important. You can't squeeze blood from a stone.
- mejutoco 3y ago> As others have mentioned, none of Polya matters for selecting and attacking research problems. While I am not familiar with research problems, and do not pretend to be, some of the strategies to tackle problems in this book are universal. Like finding a similar problem, or a simplified case, or divide and conquer, etc. etc.
- JHonaker 3y agoYea, these are 100% exactly how you should approach a research problem, in mathematics or otherwise. Literally the first part of almost every research paper is outlining how this thing you're about to talk about is similar and dissimilar to other things. That's often followed by a simplified description of the idea. Then that's usually followed by the thing in full generality.