Proofs
Ὅσα τὰ αὐτὰ τῷ αὐτῷ ἴσα, καὶ ἀλλήλοις ἐστὶν ἴσα.
“Things equal to the same thing are equal to one another.”
Let 𝑀 be the set of mathematical ideas (proofs, lemmas, theorems).
∀t ≥ 0: I(t) ∈ Learners ∧ Love(ℳath) = ⊤ ∧ Ambition(I) ≠ “claim-to-mastery”.
Purpose: maximize Growth(I,t) subject to Ethics ∧ Clarity ∧ Rigor.
Method: Write(I, proofs) ⇒ (Practice ↑) ∧ (Insight ↑) ∧ (Error → Lesson).
Therefore: lim t→∞ Skill(I,t) ↑, while Humility(I,t) ≥ constant ＞ 0.
Irrationality of √2
Four distinct proofs
Proof of Cauchy–Schwarz Inequality
A classical algebraic argument