Powerful ideas from top nonfiction
Try Blinkist to get the key ideas from 7,500+ bestselling nonfiction titles and podcasts. Listen or read in just 15 minutes.
Get started
Blink 3 of 8 - The 5 AM Club
by Robin Sharma
Listen to the Intro
How to Solve It summary
George Pólya
A New Aspect of Mathematical Method
16 mins
Brief summary
How to Solve It presents a creative approach to problem-solving, emphasizing heuristic techniques. George Pólya's timeless strategies guide us through understanding problems, devising plans, carrying them out, and reflecting on solutions.
Table of Contents
How to Solve It
Summary of 5 key ideas
Audio & text in the Blinkist app
Key idea 1 of 5
Understanding before action
A key trick in solving problems – whether you’re working with numbers or real-life situations – is one that many people skip right past. Before you do anything else, stop and look carefully at what’s in front of you.
Think about a student looking at a geometry problem about finding the length of a rectangular room’s floor. Sure, they could grab their calculator right away. But people who are good at solving problems will pause and ask three basic questions: What are they trying to find? What facts do they already know? How do these pieces fit together? Just by asking these questions, what seemed hard becomes much clearer.
Looking closely at a problem works like putting together a jigsaw puzzle. You wouldn’t just grab random pieces and try to force them together. You’d look at the picture first, find the edges, and sort out pieces with similar colors. This same idea works for any problem you’re trying to solve. Look at where you want to end up, see what you’re starting with, and figure out what rules you need to follow.
When people are teaching this to students, many want to jump in and give answers right away when someone’s stuck. But asking good questions often works better: “Can you tell me what the problem's asking for?” “What do you notice about these numbers?” “Does this remind you of anything you’ve solved before?” These aren’t just good teaching questions – they’re exactly what you should ask yourself when solving problems.
Here’s a simple example that shows why this works so well. Say you need to draw a square inside a triangle. The bottom corners of the square have to touch the bottom of the triangle, and the top corners need to touch the triangle’s sides. Instead of drawing lines randomly, someone who’s good at solving problems will first picture how it should look. They’ll think about what makes a square special (sides that are the same length, corners that are perfect right angles), and how this fits with the triangle’s shape. Once you understand these pieces, finding the answer becomes much simpler.
Taking time to understand requires stopping yourself from jumping in too fast. Yes, you might want to start working right away – but that's like starting a trip without checking where you're going. When you spend time understanding first, solving the rest of the problem becomes much easier.
Make it a habit to stop, ask questions, and really look at what you’re dealing with before trying to solve anything. This turns problem-solving from guesswork into a clear path forward.
Want to see all full key ideas from How to Solve It?
Key ideas in How to Solve It
More knowledge in less time
Read or listen
Get the key ideas from nonfiction bestsellers in minutes, not hours.
Find your next read
Get book lists curated by experts and personalized recommendations.
Shortcasts New
We’ve teamed up with podcast creators to bring you key insights from podcasts.
What is How to Solve It about?
How to Solve It (1945) revolutionized mathematical thinking by breaking down complex problem-solving into clear, manageable steps. You'll learn systematic methods for approaching any challenge, from identifying exactly what you're trying to solve to planning your steps and checking your work. These timeless strategies work just as well today for everything from daily decisions to mathematical proofs, making this enduring classic as relevant now as when it was first published.
Who should read How to Solve It?
- Students seeking to improve problem-solving skills
- Professionals wanting to enhance critical thinking
- Mathematicians exploring cognitive approaches to problem-solving
Categories with How to Solve It
Book summaries like How to Solve It
People ❤️ Blinkist
Sven O.
It's highly addictive to get core insights on personally relevant topics without repetition or triviality. Added to that the apps ability to suggest kindred interests opens up a foundation of knowledge.
Thi Viet Quynh N.
Great app. Good selection of book summaries you can read or listen to while commuting. Instead of scrolling through your social media news feed, this is a much better way to spend your spare time in my opinion.
Jonathan A.
Life changing. The concept of being able to grasp a book's main point in such a short time truly opens multiple opportunities to grow every area of your life at a faster rate.
Renee D.
Great app. Addicting. Perfect for wait times, morning coffee, evening before bed. Extremely well written, thorough, easy to use.
People also liked these summaries
4.7 Stars
Average ratings on iOS and Google Play
37 Million
Downloads on all platforms
10+ years
Experience igniting personal growth