Pythagoras

Born: c. 570 BCE
Died: c. 495 BCE
Title: Father of Mathematics

The Mystical Leader of "All Things Are Numbers"

Pythagoras was not just a mathematician, but the leader of a religious-like "Pythagorean School." He believed that mathematics was not merely a computational tool, but the language for understanding God and the universe.

Core Contributions - Deep Analysis

Pythagorean Theorem

Although the Babylonians and Chinese mathematician Shang Gao discovered this relationship earlier, the Pythagorean School (possibly Pythagoras or his students) provided the general proof. That is, for any right triangle, $a^2 + b^2 = c^2$ always holds. This was the first moment in mathematical history when a special case was elevated to a universal truth.

Music and Proportions

He discovered that when the length ratios of strings are integer ratios (such as 2:1, 3:2), the sounds produced are most harmonious. This was the first time humans used mathematics to describe physical phenomena (acoustics).

Historical Anecdotes and the "First Mathematical Crisis"

The Discovery of √2 and Murder

The Pythagorean School firmly believed that all numbers could be written as the ratio of two integers (rational numbers). However, his student Hippasus discovered that for a square with side length 1, the length of its diagonal (√2) could not be expressed as a ratio of integers. This directly overturned the school's belief. Legend has it that to keep the secret, Hippasus was thrown into the sea and drowned. This is the famous First Mathematical Crisis—the discovery of irrational numbers.

Legacy

Pythagoras established mathematics as a discipline requiring proof. His work laid the foundation for mathematical rigor and influenced mathematical thinking for centuries. The Pythagorean theorem remains one of the most widely used mathematical principles today.