Deductive mathematical proof
Demostración matemática deductiva
- Date
- c. 580 BCE · confidence low
- Place
- Miletus, Turkey
- Credited to
- Thales of Miletus; Pythagoras and his school
- People
- 👤 Tales de Mileto650 BCE–548 BCE
- Field
- Knowledge & symbols
⚠️ Disputed: the sources disagree.
What it is
A method of establishing geometric truths from premises through chained logical reasoning, rather than empirical recipes. It is the invention of mathematics as a demonstrative science.
The attribution to Thales is a late tradition (Proclus); Babylonian mathematics already contained general reasoning but not explicit proofs.
What it led to
- Euclidean axiomatics and all subsequent rigorous mathematics
- Rationalist philosophy and Aristotelian formal logic
- The discovery of irrationals and the crisis of the Pythagorean foundations
- The theoretical scientific method: a model of certain knowledge for astronomy and physics
Built on
- Greek alphabet with vowelsc. 800 BCE
- Egyptian practical geometry
- Babylonian mathematics
Made possible
- Aristotelian syllogistic logicc. 350 BCE
- Euclidean axiomatic geometryc. 300 BCE
- Khayyam's quadrilateral and the parallel postulate1077
- Euclidean geometry
- Method of exhaustion
- Aristotelian logic