Problem Solving#
Problem solving is an important skill that is hard to teach and takes practice. It takes a mindset, a passion, knowledge, and a skill set, all of which can be learned and improved over time. But like sports, knowing (in your brain) what needs to be done and having the skills to actually get it done is different: it takes practice!
Good problem solvers have four pillars:
Mindset: the habits of thought that keep you engaged, especially perseverance and comfort with uncertainty.
Passion: the curiosity or satisfaction that keeps you coming back, even when it’s hard. It is an interest that is deep enough to tolerate frustration. Passion is one of the two foundations of Grit, the other being perseverance.
Knowledge: the concepts and facts you build over time, giving you material to reason with.
Skills: the techniques for applying knowledge: analyzing, strategizing, trying examples, testing ideas, and refining solutions.
None of these are fixed traits, and they can all be developed with practice.
Mindset & Passion#
I read the book Grit by Angela Duckworth, and it presents a case for why Grit is the key to success in students. It talks about how to “teach” grit. It is NOT a book about how to become a better problem solver. I did enjoy it because it helped me embrace a mindset and to appreciate how & why some people are successful—it isn’t that they are born with the ability, it is that they are blessed with the mindset of grit.
Here is another book that sounds good. But to be honest, I haven’t read it. The Art of Learning by Josh Waitzkin. It is a reflective exploration of how people develop mastery, based on Waitzkin’s experiences as both a chess prodigy and a world‑class martial artist. Through stories from his training journeys, he illustrates how deep focus, resilience, and an embrace of incremental progress form the foundation of high-level learning. The book emphasizes turning setbacks into fuel for growth, breaking skills into their component parts, training under increasing levels of stress, and cultivating a mindset that values quality of attention over quantity of effort. Rather than offering rigid instructions, Waitzkin shares principles and processes that can be adapted to any discipline, making the book a guide to cultivating long-term excellence rather than achieving short-term wins.
To build your own mindset and to fuel your own passion, it is good to be inspired by other stories. When you see the success of others who experienced setback after setback, it can be inspiring. I read a book called Eat and Run by Scott Jurek which was inspirational to me. This guy experienced an intense amount of pain on his journey to becoming one of the best ultra marathon runners ever.
Knowledge and Skills#
You are attending school to get the knowledge. Some classes teach a few skills. Most classes, on the other hand, don’t teach skills but instead give you opportunities to discover & develop skills. I find that I happen-chance to discover my skills and techniques over time. While there are books (such as The Art and Craft of Problem Solving by Paul Zeitz, who centers his problems around math), I believe mentorship is a better approach. We can all benefit from a coach.
Here are some techniques I’ve used:
Q&A
Writing down your questions forces you to break the problem into smaller, concrete parts instead of wrestling with a vague cloud of confusion. Writing down the answers creates a visible chain of reasoning, helping you track what you know and what you still need to figure out.
Stream of consciousness
Putting your thoughts on paper externalizes them, revealing that your mental fog is actually a small, manageable set of ideas. This also gives you a private “thinking partner” that echoes your reasoning back to you, helping you notice gaps or connections you would’ve missed.
Challenge assumptions
Many obstacles are self‑created because we unconsciously restrict the solution space based on assumptions we never questioned. By identifying and testing these assumptions, you often remove the very barrier that was making the problem feel impossible.
Simplify the problem
Solving a dramatically easier version of the problem gives you insight into its structure and reduces cognitive load. Once you understand the simple version, you can gradually add complexity back in, often revealing patterns or strategies that apply to the full problem.
Validate against simple examples
Simple examples act as a quick sanity check that prevents you from spending hours pursuing an incorrect idea. They expose hidden assumptions or errors early, saving time and keeping you grounded in concrete reality.
What‑if questions
“What if…?” opens the mental door to possibilities that your default thinking never considers. It allows you to explore alternative perspectives, edge cases, and surprising consequences that can lead to breakthroughs.
Assume we can do X, how then can we do Y?
Temporarily assuming that a key result is true lets you explore the downstream implications and structure of a possible solution. This often reveals which intermediate steps matter, or shows that even with X solved, the direction is unproductive, both of which are extremely valuable.
Go for a walk
Stepping away resets your mind, allowing subconscious processing to continue without the pressure of staring at the problem. Physical movement and a change of environment often produce clarity, new ideas, and a more flexible perspective when you return.