71–80 of 104 posts
I find it interesting how the link at the bottom of the page is a clearly hacked link.
Here's the original, which does indeed have a translation as one would expect: https://web.archive.org/web/20111005170154/http://webhosting...
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…
This summary really undersells the book IMO. It's one of the more interesting books I've read in that it is not structured linearly. He introduces a few ideas which have very particular language he defines in the remainder of the book which is essentially a dictionary. If you don't come from a math-y background and you are trying to get into serious mathematics, this definitely helps to 'lift the veil' on how you mig…
If you don't come from a math-y background and are trying to "get into serious mathematics", the only way to do this is to get a PhD. I realize this might come across as gatekeeping, but the reality is that each subfield of math (or any scientific discipline) has its own set of tactics for approaching problems, which have been developed over the years by the people actually in the trenches. These problem solving stra…
> I realize this might come across as gatekeeping, but the reality is that each subfield of math (or any scientific discipline) has its own set of tactics for approaching problems, which have been developed over the years by the people actually in the trenches.
There are degrees of seriousness. Sure, even a very good foundation is not enough to do novel work in say, algebraic geometry (but then again, sometimes it is enough to make progress in combinatorics) - but the strongest undergrads are still much closer to freshly minted PhDs than they are to laymen.
Mathematical maturity is the first and hardest step; after that, people will know where to go for the folklore if they want it.
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Definitely. 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.
Richard hamming lectures? I'd google, but I wouldn't know if I'd found the ones you meant.
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Of course if you solve the same problem with trivial variations, they become trivial exercises. Try harder problems.
> Try harder problems. What part of "apostol's calculus" and "hard DP" did you not understand? I love when people are so confident in their reflexive dismissal that they're literally blinded by it. So confident that they don't even stop to consider whether their dogma might be wrong.
is hard for a calculus book, i.e. is an introductory real analysis book. If you can master analysis at the level of baby Rudin without doing hundreds of problems, you're very talented. If you still don't need to do hundreds of problems by the time you finish papa Rudin, you're a mathematical genius.
This summary really undersells the book IMO. It's one of the more interesting books I've read in that it is not structured linearly. He introduces a few ideas which have very particular language he defines in the remainder of the book which is essentially a dictionary. If you don't come from a math-y background and you are trying to get into serious mathematics, this definitely helps to 'lift the veil' on how you mig…
"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…
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.
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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 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 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…
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beyond 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
Surely 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.
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…
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Any recommendations of similar books?
How to Prove it is pretty nice
How to prove it just made proofs click, and I wish I understood the material earlier, by high school the latest.
I am convinced that all the half intuitive half ("kind of like") mechanical ("just remember this") explanations we get in school and undergrad years are a huge waste of everyone's time.