Who were the mathematikoi

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The Mathematikoi were a group of followers or students associated with the ancient Greek philosopher and mathematician Pythagoras. They formed a distinct philosophical and religious community, often referred to in connection with the Pythagorean school. The term "Mathematikoi" roughly translates to “those who are dedicated to learning” or “the mathematicians,” although their studies went far beyond just mathematics. Here's a breakdown of who they were and what they were known for:

1. Philosophical and Religious Community

• The Pythagoreans were both a philosophical and religious group. Pythagoras himself was a mathematician, but he was also deeply interested in the spiritual and ethical aspects of life. His teachings combined mathematics, music, astronomy, ethics, and mysticism, all seen as interconnected aspects of the cosmos.
• The Mathematikoi were the more intellectually oriented members of the Pythagorean community. They were scholars who studied Pythagoras’s teachings in a rigorous, intellectual manner. In contrast, there were also the Akousmatikoi, who were more focused on the mystical and religious aspects of Pythagorean doctrine. The Akousmatikoi were typically less engaged with abstract reasoning and more focused on the rituals and oral teachings.

2. Mathematics, Music, and Philosophy

• The Mathematikoi were heavily involved in the study of mathematics and its relationship to the natural world. They believed that numbers and mathematical ratios were at the heart of all existence, and they sought to understand the underlying harmony of the universe through mathematics. For them, mathematics was not just a tool for solving practical problems but a way to understand the divine order of the cosmos.
• The Pythagoreans are famously associated with the discovery that mathematics could explain musical harmony. They noticed that vibrating strings produce harmonious sounds when the lengths of the strings are in simple numerical ratios (e.g., 2:1, 3:2), leading to the development of the concept of musical intervals.
• In addition to mathematics and music, the Mathematikoi also delved into astronomy and geometry, considering the universe to be governed by numerical relationships and geometric shapes. For example, the idea that the Earth and other planets move in perfect, harmonious orbits was an idea that later influenced the development of Western cosmology.

3. Lifestyle and Beliefs

• Pythagoras and his followers believed in the immortality of the soul and the idea of reincarnation. They practiced strict asceticism, including dietary restrictions, such as a vegetarian diet, and other rules of conduct meant to purify the body and soul. Some of their rules and rituals were secretive, and they followed a way of life that aimed to align them with the harmony of the cosmos.
• They also believed in the importance of numbers in understanding the nature of reality. For example, the number one symbolized unity and the beginning of all things, while the number ten (or the decade) was considered a symbol of completeness and harmony.

4. Mathematical Contributions

• The Pythagoreans made significant contributions to mathematics, some of which were attributed to them through the figure of Pythagoras, although much of what we know about his actual work is shrouded in mystery. However, the Pythagorean theorem, which relates the sides of a right triangle (a² + b² = c²), is often credited to them.
• They were among the first to explore number theory in depth, recognizing properties of numbers such as prime numbers, even and odd numbers, and perfect numbers (numbers equal to the sum of their divisors, such as 6 = 1 + 2 + 3).
• They also studied the concept of irrational numbers. The discovery that the square root of 2 cannot be expressed as a ratio of two integers (i.e., it is irrational) is attributed to the Pythagoreans, and it is said to have caused a crisis in their community, as it challenged their belief in the perfection of numbers.

5. Influence and Legacy

• The teachings of the Mathematikoi had a profound influence on later Western philosophy and mathematics. Their blending of philosophy, religion, and mathematics laid the groundwork for the development of Platonic philosophy and the later tradition of Neoplatonism.
• In terms of their mathematical influence, the Pythagorean school contributed to the development of geometry, number theory, and the idea that mathematical laws govern the structure of the natural world.
• Though much of the original Pythagorean writings have been lost, later philosophers like Plato were heavily influenced by Pythagorean thought, particularly in their belief that the universe could be understood through mathematical principles.

6. Secrecy and Structure

• The Pythagorean community, including the Mathematikoi, had a strong element of secrecy. They believed that the highest forms of knowledge should be kept within the community, and initiates were often required to undergo a period of silence and study before they were fully admitted into the inner circle.
• The Pythagoreans were organized in a hierarchical manner, with Pythagoras himself often seen as a divine leader. The teachings were passed down through oral tradition, and much of what we know about them comes from later sources, such as Philolaus, Plato, and Aristotle.

Conclusion

The Mathematikoi were the intellectual core of the Pythagorean community, focused on the study of mathematics, philosophy, and the natural world through a lens of spiritual and ethical purity. Their work contributed to the foundations of both mathematics and Western philosophy, influencing figures like Plato and later developments in number theory, geometry, and the philosophy of science. While they are perhaps best known for their work with numbers and geometry, their broader philosophical and mystical teachings helped shape the intellectual landscape of ancient Greece.