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Proofs Give Mathematical Certainty
- A mathematical proof gives absolute certainty that a statement must be true in every case.
- Mathematicians distinguish between conjectures supported by many examples and airtight proofs that hold universally.
Examples Motivate But Don't Prove
- Seeing a statement true in many examples motivates conjectures but doesn't replace proof.
- Mathematicians want arguments that show a pattern holds for all untested cases, not just observed ones.
Team Primes And Lead Changes
- Melanie uses the residue classes modulo 3 to show primes split into two 'teams' with different remainders.
- She notes tallies up to 600 billion once favored one team but the lead swaps later around ~608 billion.