Hippasus of Metapontum is a figure of considerable importance in the panorama of philosophy and mathematics of antiquity. However, his life is shrouded in mystery, as information about his origin and activities remains rather scarce and uncertain. This thinker is recognized as one of the most significant members of the Pythagorean school, immediately after the founder Pythagoras himself. Among his most important discoveries are irrational numbers and the concept of incommensurability, which have had a profound and lasting impact on both the discipline of mathematics and philosophical thought.
His investigation of irrational numbers represented a true revolution in the way of conceiving proportions and relationships between quantities. In fact, Hippasus is known for having explored the idea that there are quantities that cannot be expressed as a ratio of whole numbers, a concept that opened the way to new frontiers in the field of mathematics.
In addition, his contribution to music theory is particularly important, as he suggested that musical chords are based on simple numerical ratios. This insight had a strong impact not only on mathematics, but also on music and aesthetics, and fits perfectly into the Pythagorean legacy, which always tried to find a link between numbers and harmony.
Furthermore, his association with Heraclitus and the doctrine that privileges fire as the fundamental principle of reality suggest a complex and nuanced interaction between different schools of thought of the time. Some authors even attribute to Hippasus the role of Heraclitus’ teacher, a connection that highlights the importance of Hippasus’ thought in the philosophical context of his time.
Finally, his death, which occurred in dramatic circumstances due to the disclosure of confidential knowledge, highlights the conflict between the search for truth and the rigid traditions of his school. Hippasus of Metapontum committed the gravest sin, contradicting the precepts by demonstrating that the root of 2 was not a rational number. In fact, the Pythagoreans did not have the same concept of numbers that we have; for them, numbers were only natural numbers (0, 1, 2, 3, 4, ...) or those that could be expressed with a quotient of natural numbers (3/4 or 5/8), the so-called fractions. Numbers were only these. But the root of 2 could not be expressed in any of these forms (like pi and all the other irrational or infinite numbers.
Tradition has it that he died for this reason, drowned for having revealed to the world the existence of a number (with the relative proof) that the Pythagoreans could not accept existed.
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