Independent mathematical traditions flourished in fifth-century Athens through figures like Hippocrates of Chios, providing non-Pythagorean sources for Plato's mathematical interests.

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Hippocrates of Chios(as a historical figure mentioned in the statement): An ancient Greek mathematician from the 5th century BCE who made important discoveries about geometry and circles, and was not part of the Pythagorean school.
Mathematical tradition(describing the independent development of mathematics in Athens): A particular school or line of thinking about mathematics that develops over time within a culture, passed down and built upon by different scholars.
Plato(the person whose decision to write is being analyzed in this example): An ancient Greek philosopher (around 428-348 BCE) who wrote famous dialogues exploring big questions about knowledge, justice, and reality.
Pythagorean(Used to assess whether Alcmaeon's philosophical affiliation aligns with the Pythagorean tradition): A philosopher belonging to or directly associated with the Pythagorean school, characterized by doctrines including the opposition between limit and unlimited as foundational principles

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