Assertion Quote by Ronald Graham
“Incidentally, when we're faced with a "prove or disprove," we're usually better off trying first to disprove with a counterexample, for two reasons: A disproof is potentially easier (we need just one counterexample); and nitpicking arouses our creative juices. Even if the given assertion is true, our search for a counterexample often leads to a proof, as soon as we see why a counterexample is impossible. Besides, it's healthy to be skeptical.”
About This Quote
Source Lecture: Discrete Mathematics, Ronald Graham, 1990s
Using counterexamples first can simplify proof attempts and spark creative thinking, even leading to proofs when none exist.
In simple terms: Start with a counterexample to test claims.
Key Takeaway
Try disproving before proving.
Themes
logic
problem solving
creativity
Mood
analytical
curious
Type
educational
motivational
When to use this quote
- math class
- research
- software debugging
- legal analysis
Key Concepts
counterexample
proof strategy
skepticism
Questions to Reflect On
- When does a counterexample become a proof?
- How can skepticism improve problem solving?
A Different Perspective
Counterexamples may not exist for true statements, leading to dead ends.
