Born: c. 570 BC · Samos

Died: c. 495 BC (aged around 75) · either Croton or Metapontum

Era: Pre-Socratic philosophy

Region; Western Philosophy

School; Pythagoreanism

Main interests: Ethics · Mathematics · Metaphysics · Music theory · Mysticism · Politics · Religion

Notable ideas: Communalism · Metempsychosis · Musica universalis

Attributed ideas: Five climatic zones · Five regular solids · Proportions · Pythagorean theorem · Pythagorean tuning · Sphericity of the Earth · Vegetarianism

Major contributions of Pythagoras include:

• Formulating the Pythagorean Theorem.

• Discovering irrational numbers.

• Developing mathematical proofs.

• Exploring the golden ratio and geometric proportions.

• Studying mathematical relationships in music.

Problem/events that influence Pythagoras' mathematical ideas:

Pythagoras’ mathematical ideas were shaped by his curiosity about the world and the cultural influences he encountered during his travels. His exposure to Egyptian and Babylonian mathematics, particularly their use of geometry in construction and land measurement, inspired him to explore the theoretical principles behind these practices, leading to his work on the Pythagorean Theorem. He was also deeply influenced by his observations of natural harmony, such as the relationship between musical intervals and numerical ratios, which connected mathematics to the physical world. His philosophical belief that numbers govern the universe fueled his quest to find patterns and order in everything. Additionally, the discovery of irrational numbers during his study of right triangles challenged the idea that all quantities could be expressed as whole-number ratios, pushing him toward more abstract mathematical thought. Pythagoras’ travels to Egypt, Babylon, and possibly India exposed him to diverse mathematical traditions, further broadening his understanding and shaping his revolutionary contributions to mathematics. 

His Impact on the modern mathematics: 

Pythagoras’ contributions to mathematics have profoundly shaped modern life, particularly through the Pythagorean Theorem, which is fundamental in fields like architecture, engineering, navigation, and computer graphics. His emphasis on rigorous proofs laid the foundation for the logical structure of mathematics, ensuring that mathematical principles are universally applicable and reliable. By exploring the relationships between numbers, he inspired advancements in number theory, a cornerstone of modern cryptography and digital technology. Pythagoras also bridged mathematics and natural phenomena by linking numerical ratios to musical harmony, influencing the study of acoustics and showing how math explains the world around us. His belief that "everything is number" continues to inspire abstract mathematical concepts, driving innovation in science, technology, and beyond.