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Key points
- People can apply math mindsets to improve their approach to everyday problem-solving.
- Solving a smaller or bigger problem can provide some much-needed perspective.
- Changing one's mindset and paying attention to intuition can boost problem-solving abilities.
Mathematicians excel at handling complexity and uncertainty.
Mathematical reasoning strategies aren't just useful for dilemmas involving numbers.
We can apply math mindsets to improve our approach to any kind of problem-solving, including the typical challenges of everyday adult life.
To make your everyday problem-solving less stressful and build your expertise in self-management, try these five mathematical mindsets.
1. Solve a Smaller Problem
Imagine you're given a math puzzle that asks you how many ways you can rearrange the letters in the word quicksand. That's 10 letters.
To recognize the pattern and develop an intuitive sense of it, begin with a simpler version. How many ways are there to rearrange the letters in "to" (to, ot) or "cat" (cat, cta, act, atc, tca, tac)?
Humans find it difficult to visualize large numbers. We're better able to visualize solutions when we dramatically shrink a problem to make it easier to visually and mentally manipulate it.
Application to everyday problems: This approach can help with decluttering, fitness goals, habit formation, packing for vacation, parenting, or relationships.
- If you're overwhelmed by packing for a two-week vacation, how would you pack if you were going for two hours or two days?
- When shrinking a problem, remember that your ultimate goal is to identify the key patterns and develop your intuitive sense of how to solve it.
2. Reverse Engineer From a Correct Solution
This is an enjoyable video of a mathematician teaching himself to fold a fitted sheet. In it, he reverse-engineers from the desired outcome, using a neatly folded sheet he takes fresh out of the package. As he talks through his process, he gives us a tour of several aspects of mathematical reasoning that aren't always recognized as such.
He first identifies the "u-shape" formed by the elastic corners as a key pattern to aim for during the folding process. When he gets stuck, he uses a "just following my nose" approach to attempt to follow the part of the pattern he's stuck on.
Application to everyday problems: When you encounter a solution that works really well, reverse-engineer it. For example, if you usually hate running on the "dreadmill," but one day you quite enjoy it, think about what was different. Or if your child is usually impatient in a particular scenario but isn't on one occasion, what was different?
3. Solve a Bigger Problem
It’s obvious how imagining a smaller problem can help us reason more easily. Although less obvious, imagining how you'd solve a bigger problem can have a similar effect.
It helps develop your intuitive sense of the core issue and reveals patterns. It can spark different solutions, prompting you to consider new angles and approaches and gain a clearer understanding of the challenge.
Application to everyday problems: If you're making dinner for 15 people, it might be more helpful to think of how you'd make dinner for 200 people than for three people.
- Sometimes small numbers feel troublesome because they're small—for example, 0.03 is mentally harder to work with than 3.
4. Intuition
I’ve mentioned problem-solving intuition numerous times because of how important it is. People often forget that in a hard science like math, developing intuition is a core, explicit part of the learning strategy. In self-improvement and self-management, people tend to devalue this or don’t even consider it.
Intuitive reasoning involves, for example, seeing the deeper, rather than superficial, aspects of patterns, understanding how problems relate to ones you've already solved, and initially articulating brute-force (highly inefficient) strategies to understand a problem deeply before refining your solutions to be more optimal and efficient.
Application to everyday problems:
- Learn to pay attention to the small pieces of intuition you have. Consider how a problem you're facing now might be similar to one you’ve seen solved before, whether in your own life or through observing others. For example, when facing mid-career challenges, you might think back to strategies you used to survive college because, intuitively, something about the challenges feels similar.
- Use your observations to guide your decisions, even when they conflict with traditional advice, such as when you've observed that a degree of task-switching improves your work quality rather than interferes with it.
5. Change Your Expectations of How Quickly You'll Solve a Problem
Mathematicians often work on a single problem for years or even decades. They don’t abandon the problem but keep revisiting it, allowing new insights and deeper understanding to develop over time. Along the way, solutions to other problems, new analogies, and even mistakes in their problem-solving attempts can all contribute to eventually solving the problem that has vexed and eluded them.
When it comes to improving our lives—through better self-management, learning how to learn, and making better decisions—we often assume that if something takes a long time to figure out, we’re doing something wrong.
Try shifting your assumption about how long it’s reasonable to work on a problem that continues to vex you.
Application to everyday problems:
- The frustrations you experience with self-management, navigating the world, or understanding yourself are often long-term challenges rather than quick fixes.
- Rather than seeing a years-long problem-solving process as a sign that something is wrong with you, consider that it may simply mean that you haven’t yet encountered the mental models or technologies needed to resolve it.
Key Takeaway
Solving everyday problems becomes easier when we borrow strategies from mathematicians. By shifting how we approach challenges, we can reduce frustration and build long-term expertise in self-management.
If you'd like a visual reminder of some of the mathematical strategies covered here and some others, this excellent, simple handout from Stanford Professor Jo Boaler is suitable for adults or kids.
If you find you have challenges with overthinking, mathematical reasoning can help with that too.
