Summary: I talk about why I decided to read this book, what I learned from it, and why I recommend reading it. In short, I learned that when we are solving problems, we can use different approaches to get different perspectives and clues to get to the solution.
Why did Manuel read this book?
I decided to read this book because it was recommended in a podcast. Also, problem solving is one of the abilities that is always mentioned as one of the core abilities of a Software Engineer.
What did Manuel learn from this book?
The author provides information about the parts of a problem, types of problems and different approaches to learn how to problem-solve.
Types of problems
The author talks about “problems to prove” and “problems to find”. It also talks about Mathematical and Practical problems.
The book provides information about these kinds of problems. But it shows more information about “problems to find” and “Mathematical problems”. So, I will talk mostly about the “problems to find”.
Also, before I continue writing about this type of problem, I want to provide some details about “Problems to prove” and “Practical problems”.
Problems to prove have these parts “hypothesis” and “conclusion”. What I understand by this is that these kinds of problems happen when you are given a statement and you want to confirm if that statement is true or not.
Moreover, “Practical Problems” are these daily problems. Problems that surround us and challenge us every day. Additionally, these problems either provide lots of data or barely provide data. And these problems are filled with more emotions and have more people involved making them more complex.
So, when dealing with these kinds of problems, it is important to learn how to use our emotions and try to understand the problem. Notably, we can aim to get better at knowing what amount of data is necessary and enough. As well as, listing the conditions (constraints) that we are going to use to solve a problem.
Parts of a “problem to find”
Mr. Pólya described these parts of a problem to find:
- The unknown (what is required?)
- The data (what is given?)
- The conditions (also known as constraints)
Approaches to solve problems
The author discusses different approaches about solving problems. These different approaches allow the reader to create a mental model about how to tackle different problems and find ways to a solution.
Generalization, specialization, analogy, decomposing and recombining, etc., are some of the options. These options allow us to view the problem from a different angle and get closer to a solution.
Also, it mentions that when you are not able to solve a problem, you can find another similar (related) problem that you cannot solve, and that it is easier. This helps us to find more data or ways to solve the original problem based on the solution for this easier problem.
Moreover, it recommends ways to tweak the problem such as adding or removing elements of the problem. Similarly, ignoring part of the conditions and trying to solve the problem can provide clues. These clues help us understand how to proceed and solve the original problem with all the conditions.
I find it interesting that the author mentioned that solving problems is not just an intellectual matter. He explains that emotions play a big role in solving problems. Showing determination, curiosity and desire to solve a particular problem is a factor in the solving problem process. And I realize from this that when I get stuck on not having a great plan to solve a problem, my effort and my attitude will be a great start.
On the other hand, if we are not focused, have low interest in the problem or finding the solution, this will impact our ability to solve the problem. This is similar to lack of understanding of the problem which leads to poor problem-solving.
We can view most of these recommendations as tools to advance while stuck on a problem. Or we can view them as ways to look at the problem in different angles to get different perspectives, and clues about solving the problem at hand.
Does Manuel recommend reading this book?
Yes, I do. I would like to note that it can be hard to read at times depending on your mathematical skills. This is because mathematical problems are the main focus of the book. Also, most of the examples are math exercises. So, depending on your math skills, you must hang in there and do some research about some math concepts.
To me, this book requires more than one reading to fully comprehend everything it has to offer. And as mentioned by the author “solving problems” is a skill, so it is helpful to apply its ideas in practice as we read.
To sum this up, ask yourself endless questions while solving problems and while reading this book if you do so.