Pythagoras of Samos (c. 570–495 BC) was one of the most defining figures in the history of human thought. Although mysterious, surrounded by legends, the essence of his teaching does not belong to the realm of miracles but to the understanding of nature through numbers. Pythagoras founded a new worldview, where the universe is order, harmony, reason, and its laws are expressed in mathematical relationships. From this starting point begins the long path that leads to modern science.
Nature as Order, Beauty and Harmony
For the Ionian natural philosophers, nature was the all, the self-generating principle of all things. Pythagoras went one step further: he sought not only matter, but also form, the structure that organizes the universe. “Things are numbers,” his students said, meaning that the essence of reality is manifested through numerical relationships and geometric proportions. The world is not random, but rhythmic; every phenomenon obeys rules of symmetry and reason.
The mathematical principles of Pythagoras are presented by the so-called Pseudoplutarch: "Starting again from another beginning, Pythagoras, son of Mnisarchus of Samos, the first to call this thing 'philosophy', considered as principles the numbers and the symmetries that exist within them — which he also calls harmonies — and from both together the composite elements, which are called geometric." "Again from another beginning Pythagoras of Mnisarchus of Samos, the first to introduce this philosophy into the language, began by numbers and the symmetries in them, which he also calls harmony, the four from both composite elements, which are called geometric,"
Music was the first major field of experimental confirmation of this thought. Pythagoras, studying the monochord, discovered that pleasant intervals correspond to simple numerical ratios — 2:1, 3:2, 4:3. From this empirical observation was born the idea that all of nature "sings" in the same way. Thus was formed the famous term harmony of the spheres, according to which the heavenly bodies, moving in proportion, produce a silent but perfect music of the world.
This concept was not a poetic metaphor; it was a mathematical conception. For the first time, man conceived of nature as a mathematically expressible structure.
The Pythagorean Metaphysics of Nature
Pythagoras believed that behind the changing natural world lies an unchanging pattern—a world of numerical principles. Numbers for him were not simply a quantitative measure, but an ontological principle: One, Two, Three, Four, forming the tetraktys, a symbol of the harmony of all.
Nature, then, is not chaos but calculus· that is why its study is possible only through mathematics. Pythagoras connected ethics with physics; just as the world obeys rules of rhythm and measure, so too man must live "according to reason." Purity of body and soul, dietary rules, discipline in speech and work, were not just rituals, but a biology of harmony.
The Rules of Life and Nature
The Pythagoreans believed that the laws that govern the body are the same that govern the stars. The balance of the elements, heat, cold, moisture and dryness, are expressions of the same mathematical measure that defines nature.
This view led to an ecological and ascetic ethos. Pythagoras forbade violence against animals and blood sacrifice, considering all living beings as relatives. His diet was strictly plant-based, and he taught that fire, earth, air, and water are sacred elements, which we must use with respect.
These rules survived for centuries in popular tradition, especially in the Peloponnese and Evia, where until the mid-20th century prohibitions such as not throwing garbage into the fire, not eating broad beans, or not speaking loudly near a burning fireplace survived. Ordinary people were unaware that they were observing ancient Pythagorean commandments.
The ban on broad beans, which was so much discussed in antiquity, now seems to have a medical basis. Some Greeks suffer from a deficiency of the enzyme G6PD, which causes poisoning after consuming broad beans. A "mystery" of Pythagorean wisdom thus proves to be preventive knowledge of physiology.
The Pythagorean Geometry of Matter
The Pythagoreans did not limit themselves to numbers but proceeded to geometric interpretation of natureEarth, water, air and fire were considered connected to the normal solids:
- the tetrahedron with fire,
- the octahedron with air,
- the icosahedron with water,
- the cube with the earth,
- and the dodecahedron with the universe in its entirety or the ether, the quintessence.
At Timaeus Plato will analyze this teaching in amazing detail, noting that all solids consist of two types of triangles: the isosceles rectangle and the rectangle with angles of 30°–60°–90°. Thus, physical bodies are reduced to simpler mathematical units — to triangles, that is, to primary “elements” of form.
This thought connects form with physical substance, as Democritus would later do with atoms. Matter is harmony, not disorder; and the transmutations of the elements (e.g. fire into air) are changes in their geometric structures.
Pythagoras and the Science of Nature
Pythagoras' contribution to science lies not in individual experiments but in the shift of the mental paradigm. He introduced the idea that the laws of nature are immutable and mathematical. Physics, as we know it today, was founded on this principle: that behind the complexity of phenomena lies the simplicity of numbers.
From Pythagoras to Galileo, Kepler and Newton, the same Pythagorean conviction is maintained: that “the book of nature is written in the language of mathematics”. Kepler, studying the movements of the planets, recognized in their ellipses and harmonic proportions the same musical structure that Pythagoras had seen in the strings of the lyre. Newton, combining mathematical relations with natural forces, realized the fullest justification of the Pythagorean vision.
From Myth to Logic
The miraculous stories surrounding Pythagoras—that he remembered his past lives, that he spoke with animals, that his soul wandered—should not be taken literally. In Pythagorean thought, “transmigration” denotes the change of forms within the unified life of nature. No being is lost, but is transformed.
The deepest meaning of these beliefs is the unity of the world: all beings participate in the same rhythmic breathing. The study of nature is therefore not simple observation; it is participation in the cosmic measure. Pythagoras teaches that whoever knows nature also knows himself, because the soul is a microcosm of the world.
The Pythagorean Principles in Modern Technology
Today, the Pythagorean principles permeate every technological application. The laws of physics are expressed in mathematical models, based on symmetries, simplicity, and generalizations — precisely what Pythagoras considered the essence of nature. Wave theory, sound vibrations, electromagnetic frequencies, and even computer algorithms presuppose the harmonious relationship between number and reality. From quantum physics to machine learning, the Pythagorean dogma “that which is is number” remains the cornerstone of all modern science.
Epilogue
Pythagoras was not only a mathematician or philosopher; he was a hierophant of nature. He highlighted the mathematical dimension of the world, but also its ethical dimension: the knowledge of nature is at the same time an exercise of the self. From the strings of the lyre to the equations of physics, the Pythagorean tradition teaches that nature is not chaos but measure, reason and music.
In summary, the entire philosophy of science: nature is revealed only through its laws expressed mathematically.
photo by Matthias_Groeneveld, https://pixabay.com
