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How to Solve It (1945)

math.utah.edu

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Re: How to Solve It (1945)

#91

Post by mathisfun123 »

jodrellblank wrote: post #86
mathisfun123 wrote: post #59

Earlier quoted context omitted.

the 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)

The 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?

> "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.

Re: How to Solve It (1945)

#92

Post by OldGuyInTheClub »

bigbluesax wrote: post #69
OldGuyInTheClub wrote: post #28

Earlier quoted context omitted.

"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…

>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'l…

None 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.

Re: How to Solve It (1945)

#93

Post by jodrellblank »

mathisfun123 wrote: post #91
jodrellblank wrote: post #86

Earlier quoted context omitted.

The 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?

> "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…

I am not exactly quoting anyone. So now that's settled, you can't use that as a dodge to get out of responding to the point.

> "I don't know how it's possible to "misread" a wiki"

Great, thanks for your informative contributions. Don't forget to be offended and accuse someone of ignorance and arrogance just because you don't understand. That's useful.

> "Still not close to any semblance of a convincing rebuke"

His death was still so long ago that more than half the population of Earth wasn't even born at the time.

Re: How to Solve It (1945)

#94

Post by mathisfun123 »

jodrellblank wrote: post #93
mathisfun123 wrote: post #91

Earlier quoted context omitted.

> "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…

I am not exactly quoting anyone. So now that's settled, you can't use that as a dodge to get out of responding to the point. > " I don't know how it's possible to "misread" a wiki " Great, thanks for your informative contributions. Don't forget to be offended and accuse someone of ignorance and arrogance just because you don't understand. That's useful. > " Still not close to any semblance of a convincing rebuke " Hi…

> I am not exactly quoting anyone.

conventionally (but you're free to diverge of course) double quotes, like in

> "beyond offended"

are for quoting someone/something.

Re: How to Solve It (1945)

#95

Post by R41 »

Loved the way polia's explained the basics of solving challenges by asking questions - - Can you find a problem analogous to your problem and solve that? - Can you add some new element to your problem to get closer to a solution? etc we always asks new onboard people to read this .It's like a bible for problem solving .

Re: How to Solve It (1945)

#96

Post by JHonaker »

mejutoco wrote: post #76
OldGuyInTheClub wrote: post #28

Earlier quoted context omitted.

"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…

> 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.

Yea, 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.

Re: How to Solve It (1945)

#98

Post by ergocoder »

mathisfun123 wrote: post #20
ergocoder wrote: post #8

I read it and it doesn't help much. What helps with solving problems like math and algorithmic problems is to go through a lot of problems to see different patterns and strategies of solving problems. I'm talking about going through thousands of problems. That is very effective.

> I'm talking about going through thousands of problems. you don't need thousands of problems. you don't even need hundreds, unless, no offense, your medium-term memory is very poor. personal anecdote 1: in between undergrad and grad school i decided i was gonna try this "solve all of the problems" approach, as opposed to my usual "sit there and ponder approach", in order to prepare for eventual quals in grad school.…

Yes you'd need to go through a lot of problems because every problem is slightly different

Realistically, it is rare that you would encounter hundreds of identical problems.

Take realistic examples: topcoder.com, Facebook's Hacker cup, and Google codejam. Or any university exam. Or SAT. Or Olympiam math. Their problems are unique because they can't just create the same problems over and over again.

There are also other aspects like solving the problems faster and being able to write up a solution correctly. Coding it correctly at the first try is really a magical moment.

Re: How to Solve It (1945)

#99

Post by lcuff »

apocadam wrote: post #85
lcuff wrote: post #45

On a totally orthogonal axis: My biggest problem with tackling math problems early in life was psychological. My inner critic would say nasty things to me when I didn't get the answer right away, making it impossible to stick with exploring the problem. Once I overcame that, I got lots better at math. And working on yet another axis, the most useful tip I've gotten on how to think about problems is to "think in extre…

If you don't mind, could you share how you overcame that? I think for me at least a lot of it is/was not being able to be comfortable struggling with a hard problem for an extended amount of time, probably due to being used to only solving fairly trivial exercises and thus feeling dumb/the problem feeling impossible if it wasn't clearly solvable under a short timeframe.

Mostly, talk therapy. As you say, struggling with a hard problem for an extended period of time and feeling dumb is part of the process. For me, the shame was excruciating, so I'd turn my attention to anything else to stop feeling shame. The shame was intense enough that the underlying "felt sense/thought" was "I don't deserve to be on this planet". With the help of a therapist, I managed to start looking at myself and _managing_ the shame, so I could then examine my behavior and experience: Oh, I said that mean thing to somebody - I (deservedly) feel bad and want to change how I treat people. Oh, I couldn't get a math problem right away: I don't need to feel negatively about myself because of that. Frustrated, sure, but NOT "I don't deserve to be on the planet". Shame that intense tends to be (and was for me) rooted in childhood: Weak/bad parenting. It's a project to overcome it.

Re: How to Solve It (1945)

#100

Post by jodrellblank »

mathisfun123 wrote: post #94
jodrellblank wrote: post #93

Earlier quoted context omitted.

I am not exactly quoting anyone. So now that's settled, you can't use that as a dodge to get out of responding to the point. > " I don't know how it's possible to "misread" a wiki " Great, thanks for your informative contributions. Don't forget to be offended and accuse someone of ignorance and arrogance just because you don't understand. That's useful. > " Still not close to any semblance of a convincing rebuke " Hi…

> I am not exactly quoting anyone. conventionally (but you're free to diverge of course) double quotes, like in > "beyond offended" are for quoting someone/something.

I'm being unconventional. So now that's settled, you can't use that as a dodge to get out of responding to the point.
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