The ancient Greek philosopher Heraclitus once said, “I would rather count the stars in the sky than be a king.”
The words “philosophy” and “mathematics” were coined by Pythagoras himself.
- “Philosophy” means “love of wisdom,” while “mathematics” means “knowledge that can be learned.” Nobel laureate and American physicist Leon Lederman described Pythagoras as the “first cosmic thinker.” It was Pythagoras who introduced the term Kosmos to represent everything in the universe—from humanity to Earth, to the stars spinning above us. The word Kosmos embodies order and harmony, symbolizing an integrated, structured whole. In a sense, each of us is a Kosmos of our own.
Since the quantum revolution, our understanding of space and time has fundamentally changed.
- We once assumed that space could be infinitely divided, but quantum effects have shattered this notion. The continuity of space and time is an illusion—Zeno’s paradox, which assumes an infinitely divisible continuum, is no longer valid. Quantum mechanics tells us that the concept of “infinite division” is purely mathematical and does not reflect reality. Nothing is truly continuous—everything exists in discrete, quantized units.
The discovery of new numbers challenged ancient mathematical dogma.
- Previously, only “rational numbers”—ratios of two integers—were considered legitimate. However, the discovery of irrational numbers, which cannot be expressed as a simple fraction, shook the very foundation of Pythagorean mathematics. This seemingly simple mathematical fact triggered an intellectual crisis, as it contradicted the Greek belief that “all quantities can be expressed as rational numbers.” This realization sparked one of the greatest upheavals in the history of Western mathematics.
