# The Controversial Discovery of Irrational Numbers

TLDR The discovery of irrational numbers, such as the square root of 2, challenged the Pythagorean belief in a rational universe and led to conflict and expulsion. However, these numbers were more readily accepted in India and the Middle East, and their acceptance in Europe was solidified with the adoption of the Hindu-Arabic number system.

### Timestamped Summary

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Irrational numbers are real numbers that cannot be expressed as the ratio of two integers and their discovery caused controversy in the past.

02:08
Irrational numbers are real numbers that cannot be expressed as the ratio of two integers and their discovery caused controversy in the past.

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Irrational numbers are numbers that cannot be expressed as the solution to any algebraic equation and their discovery caused controversy in ancient Greece.

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The discovery of irrational numbers, specifically the square root of 2, challenged the Pythagorean belief in a completely ordered and rational universe, leading to conflict and the expulsion of a Pythagorean named Hepassus.

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Irrational numbers, including the square root of 2, were accepted more readily in India and the Middle East due to their use in trigonometry and solving equations, and their acceptance in Europe was solidified with the adoption of the Hindu-Arabic number system and the invention of mathematical notation for roots.

09:24
The square root of 2, pi, phi (the golden ratio), and Euler's number are all examples of irrational numbers with unique properties and applications in mathematics, art, and nature.

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E, the number that sits behind exponential growth and radioactive decay, has a special place in calculus as it is the only function whose derivative is itself and is essential for basic mathematics.