31–40 of 104 posts
1. study extensive background/prior art
2. have major epiphany to solve problem
3. try to get around inevitable roadblocks and complications during the process of solving it
Earlier quoted context omitted.
I read it as a kid and it was transformative. This is one of the rare "meta" books which really help when you are not exposed to meta concepts that much yet.
Can you perhaps think of any other meta books in other (or same) domain?
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…
Some more complicated examples would probably help me understand.
Having read hundreds of books and papers over the years, no problem seems new to them. They can rapidly find a solution, especially compared to someone trying to derive a answer from first principles like Polya suggests.
What is meant by “the condition”? I am imagining that in x + 3 = 7 that x is the unknown and 3 and 7 are the data? Is the condition equality and, if so, how do you use that information? Some more complicated examples would probably help me understand.
It's more relevant in a word problem, where you need to extract the condition from text and translate it into syntactical math notation so you can compute.
"John wants to have 7 pizzas. He has already made 3 pizzas. How many more pizzas does he need to make?"
Data: 7 pizzas needed. 3 pizzas made.
Unknown: X pizzas more to make
Condition: X+3=7
Or for geometry diagram problems (diagram geometry is word problems where the words are pictures), where you have to extract the relationships from the diagram.
The book has more examples.
The best people I work with don't use this stuff. They solve problems based on pattern matching. Having read hundreds of books and papers over the years, no problem seems new to them. They can rapidly find a solution, especially compared to someone trying to derive a answer from first principles like Polya suggests.
Novel problems requires a lot more maturing and thinking, which is when slower, longer term thinking like Polya suggests goes a long way.
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 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.…
The best people I work with don't use this stuff. They solve problems based on pattern matching. Having read hundreds of books and papers over the years, no problem seems new to them. They can rapidly find a solution, especially compared to someone trying to derive a answer from first principles like Polya suggests.
Polya's book is distilling hard fought PhD wisdom into a book children can understand.
It's for solving novel hard problems, not trivial ones.