Yes, the solution seems to work, it appears to be correct; but how is it possible to invent such a solution? Yes, this experiment seems to work, this appears to be a fact; but how can people discover such facts? And how could I invent or discover such things by myself?

What Does It Take to Be Original?

Over the last few years, I've noticed that I don't actually deeply understand many things. This makes it hard for me to solve tough problems or create something original. Here are some examples of what I mean:

• Math: If I want to calculate the probability of event A given data B, I know that I can use Bayes' theorem: P(A|B) = P(A)*P(B|A)/P(B) to compute it. But why does that formula give the conditional probability? Why does it work? How did someone figure this out?
• Cooking: The recipe tells me to add salt and sugar to a dish, but why are salt AND sugar together necessary for this dish? How does it lead to the dish tasting better?
• Engineering: Someone at work suggested using a state machine to model and track an operations workflow. I thought that made total sense. A state machine is perfect for modeling this! But how can I myself sooner figure out how to map real-life problems to computer science problems and therefore, come up with an automated and efficient solution (like a state machine)?

I can learn formulas pretty well, but I don't often deeply and intuitively understand why the formula works from first principles.

On a larger scale, I read all the time about how people make startling discoveries in the realm of science, business, and even cooking:

• Richard Feynman derived new groundbreaking ideas in quantum electrodynamics from simply trying to understand the wobble rate of a plate.
• Bob Noyce revolutionized tech economics by selling integrated circuits for less than a dollar because he realized that software has zero material costs, making the best route to profitability through volume.
• Nancy Silverton had grown interested in how to make great bread. She obsessed over and ultimately created and perfected her own unique recipe for great bread.

I've realized that I'm unable to make these kinds of leaps in thinking in order to come up with out-of-the-box and creative solutions that no one else can. When I'm faced with unknown or seemingly insurmountable problems, I take a defeatist approach: I give up, thinking it's impossible to solve or that I'll never get the solution. Then I just either lean on someone else's expertise or look up the solution, understand it, and memorize it for next time.

The only way to expand one's abilities in creativity and problem-solving is to learn how to discover and build solutions yourself rather than simply understand existing ones. After all, there are so many unsolved problems in the world. A lot of them are pretty different from already solved problems.

However, contrary to many people's thoughts, solving them or building something unique doesn't often require a super arcane or technical skill. You just have to learn how to understand those problems inside and out, deeply understand the fundamentals and building blocks, and construct solutions yourself. That is the difference between simply evaluating someone else's creative design versus proposing and devising your own design, or following a recipe versus creating your own unique and tasty dish. Plus, discovering the solutions to interesting problems yourself also creates a sense of pure joy and triumph that simply reading and understanding someone else's solution could never.

The Key to Discovery: Heuristics

Again, solving tough problems or coming up with creative solutions doesn't usually require extremely complex or technical skills. Instead, difficult problems are solved in a multitude of other heuristics:

• Problem Identification: mapping another similar problem or subproblem to the current problem and adapting the solution accordingly
• Inductive Reasoning: breaking up the problem into multiple subproblems and constructing the final solution via solutions to these subproblems
• Building Connections: forming interesting connections between multiple fundamental ideas
  • The building blocks are simple, but the connections you make between these blocks to incrementally build a solution are extremely important.

Given this, I believe there are a few ways to become an extremely adept and creative problem solver:

• Practice looking at completely unknown problems and identify what class or type of problems they are and what techniques or algorithms could solve them.
• Learn the building blocks and fundamentals extremely well. Build an intuitive understanding on why it works. It should also be second-nature to understand, explain, and implement them.
  • An example of understanding something intuitively in math is understanding how it solves a problem and why it works. That means you can recognize when to use it and how to adapt or modify the formula to solve a different but related problem.
  • Spaced repetition helps a lot with retaining these concepts.
• Have a willingness to explore different solutions. Don't be afraid to try out different approaches, even if most of them lead to nothing. Understand why multiple solutions can work, don't work, and how they would break or change depending on different constraints.
• Learn how to apply inductive reasoning to simplify and incrementally build solutions to more complex problems.
• Practice unknown problems constantly and really struggle with them (a couple hours/problem) before looking up or understanding the solution.
  • This persistence is really important since the brain won't build these connections without some stress and struggle.
  • Problem-solving is not a spectator sport. The only way to get better at solving problems is to actually solve problems!
• Be able to articulate the solutions to these problems very clearly and concisely out loud. After listening to your explanation, a person outside your field should be able to understand how the solution works (this is inspired by the Feynman technique).

A More Interesting Approach to Life

Over the course of high school, college, and the first couple years of work, I discarded the value of thinking deeply and discovering solutions to problems.

I thought it was far more efficient to simply learn what I needed to know, apply it to what I do, and achieve the objective or get the best grade I can. After all, someone else already solved it! Trying to discover the solution myself is just a waste of time. Right?

However, I now realize the most efficient approach is not always the best approach. The time-consuming and sometimes painful process of learning how to discover and build solutions on my own is incredibly valuable, even if the problem has already previously been solved by millions of other people. Because it gives you the skill to effectively solve other problems in the world with original and unique solutions that few others can.

Everything in my life was all about the external objective (better grades, a good job, etc.) and moving as quickly as possible to the next thing. Somewhere along the way, I forgot about the joy of curiosity, figuring out something for yourself, and toying around or experimenting with a challenging task. There's no better feeling than when you can deconstruct a complex concept, learn why it works from first principles, and apply that skill to solve tough problems and create something unique.

Discovery is far more rewarding and powerful compared to simply recalling a previous solution or reading an existing one. I want to rediscover that joy.