Why Mathematics Feels Certain
- Mathematics often carries a special aura in TOK discussions because it's seen as the gold standard of certainty.
- This reputation comes from its unique approach to building and verifying knowledge through axioms, theorems, and proofs.
Axiom
A basic assumption taken to be true without proof. Axioms are the foundations of a mathematical system.
Theorem
A statement that has been logically proven based on axioms and previously established theorems.
Proof
A step-by-step logical argument that demonstrates why a theorem must be true.
Axioms are self-evident truths that form the foundation of a mathematical system. Theorems are statements proven to be true based on axioms and previously established theorems. Proofs are logical arguments that demonstrate the truth of a theorem.
Why Mathematics Is Perceived as Certain
- Mathematics relies on logical deduction , where each step follows inevitably from the previous one.
- This creates a sense of certainty that is hard to find in other areas of knowledge.
Pythagorean Theorem: In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides ($a^2 + b^2 = c^2$). This theorem is proven using logical steps, making it universally true in Euclidean geometry.
