A Problem-Solving Lab
A complete framework to understand any problem, find solutions, and build real things — using the foundations of mathematics and computer science.
The Complete Framework
Phase 1
Six lenses to see any problem clearly
"You can't solve what you don't understand. Most people skip this — and fail."
What do I know? What's missing?
Every problem starts with understanding what information exists and what you need to find.
What's the shape of this?
Finding the right structure turns chaos into something workable. Is it a tree? A graph? A sequence?
What connects to what?
Dependencies, cause and effect, inputs and outputs — meaning lives in connections.
What transforms over time?
Problems involve state, transitions, and dynamics. What was? What is? What will be?
What's impossible?
Constraints aren't obstacles — they're the rules that shape good solutions. Time, memory, physics, logic.
Have I seen this before?
The same structures appear across math, systems, nature, and everyday life. Recognition is power.
Phase 2
Eight strategies to find solutions
"Understanding without action is philosophy. Action without understanding is chaos. You need both."
Break big into small. Solve pieces, combine results.
Map to a problem already solved. "This is like..."
Solve an easier version first. Remove constraints temporarily.
Start from the goal. What's the last step? Work back.
Get any solution first. Make it work, then make it good.
Find the right level. Ignore irrelevant details.
Try things. See what fails. Learn from errors.
First draft → feedback → improve. Cycles beat perfection.
Phase 3
Make it real
"Ideas are cheap. Execution is everything. The only way to know if it works is to build it."
Build the smallest version that tests your idea. Quick and dirty.
Does it actually work? Where does it break? Find the edges.
Make it better. Faster, cleaner, more robust. Polish.
Capture the learning. What worked? What didn't? Why?
Who This Is For
Learn to think, not just memorize
Build deeper foundations
Frame problems in new ways
Understand systems and constraints
Break down complex challenges
Anyone who likes figuring things out
You don't need a math degree. You don't need to code. You just need the willingness to think carefully.
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