Pythagoras Biography: Philosopher, Mystic, and Father of Numerology

Key Facts in Brief

Pythagoras of Samos (circa 570 - circa 490/495 BCE) — ancient Greek philosopher, mathematician, and religious reformer, founder of the Pythagorean League in the city of Croton (Southern Italy). His name is associated with the theorem (known, however, before him), the thesis "all is number," the teaching of the transmigration of souls (metempsychosis), and the idea of the musical-numerical harmony of the cosmos.

In the history of numerology, he occupies the place of the founder — with the caveat: both "numerology" itself and the "Pythagorean square" with the letter table 1-9 are phenomena of the twentieth century and have only an indirect connection with the ancient philosopher.

Introduction

Pythagoras of Samos — ancient Greek philosopher, founder of the Pythagorean League; his name stands at the beginning of the history of numerology. Little is reliably known about his life: he left no writings of his own, and all biographies were written several centuries after his death and are full of legends. He is called the "father of numerology" in the modern tradition — this is a popular designation, not an ancient formulation.

Origin and Early Years

Pythagoras was born on the island of Samos in Ionia. His father was named Mnesarchus: according to Herodotus and Isocrates, he was the son of Mnesarchus; according to Porphyry, Mnesarchus was a stonecutter or a wealthy merchant — the versions differ. His mother — Pythais; according to tradition (Apollonius of Tyana), she descended from the mythical founder of Samos, Ancaeus. Some ancient authors named other birthplaces — Lemnos, Phlius, and others — but these are marginal versions.

The date of birth "circa 570 BCE" is a reconstruction, not a documented fact: it is calculated from the testimony of Aristoxenus (fourth century BCE), transmitted by Porphyry in Life of Pythagoras (section 9) — Pythagoras left Samos under the tyrant Polycrates at the age of 40. Polycrates seized power in 538 BCE — hence the approximate date of birth.

Samos was then a prosperous cultural center (under Polycrates, the Eupalinian tunnel was being built, among other things). According to the biographical tradition, in his youth Pythagoras listened to Anaximander in Miletus; the tradition also insists on his closeness to Pherecydes of Syros, to whom later authors attributed the teaching of the transmigration of souls. All this is the information of tradition, not verified facts.

Legendary Travels

Almost the most legendary part of Pythagoras's biography is his travels. According to tradition, he spent many years in the East: in Egypt and Babylon.

Egypt

Isocrates (fourth century BCE) already writes about Pythagoras's visit to Egypt as a well-known fact. According to the legend set out by Antiphon of Athens, Pythagoras had a letter of recommendation from Polycrates to Pharaoh Amasis II and studied under the priests of Thebes — medicine, mathematics, and the mysteries; according to Iamblichus, it was Thales who sent him to Egypt. The legends name impressive terms: 22 years in Egypt, then another 12 years in Babylon.

Babylon

The Persian king Cambyses II conquered Egypt in 525 BCE. The legend says he took Pythagoras to Babylon, where he spent 12 years studying under the magi. Other versions add study under Persian magi and even Zoroaster; according to Philostratus, Pythagoras reached India; Iamblichus adds the Celts and Iberians. There is also a tradition of a descent into a cave on Crete (Mount Ida, with Epimenides). In the later tradition, the travels are "distributed" among subjects: the Phoenicians supposedly taught him arithmetic, the Chaldeans astronomy.

What Modern Science Says

The culture of archaic Greece was indeed influenced by the Levant and Mesopotamia — in this sense, the Egyptian-Babylonian "backdrop" of the biography is not fantastical. But later authors explained Pythagoras's unusual views by his travels retroactively: neither 22 years in Egypt nor 12 years with Babylonian magi are confirmed by independent sources. Therefore, the travels in this article are presented "according to tradition."

Pythagoras's School: The Pythagorean League in Croton

Around 532-530 BCE (BRE and Britannica say circa 532, English Wikipedia circa 530; Aristoxenus says "at age 40") Pythagoras moved to Croton, a Greek colony in Southern Italy. The reason, as Britannica puts it, was "apparently, a desire to avoid the tyranny of Samos." Here he founded the Pythagorean League — an organization that the BRE characterizes as a combination of a philosophical school, a religious community, and a political party.

The Structure of the School

Within the League, there was a division into two groups:

• acousmatics ("listeners") — keepers of the religious-ritual side of the teaching, the tradition of oral prescriptions-acousmata;
• mathematici ("learners") — who studied the four "mathemata": arithmetic, geometry, harmonics, and astronomy.

By tradition, the acousmatics did not consider the mathematici "true Pythagoreans" and traced them to Hippasus — who revealed the secrets of the teaching and began teaching for payment.

The community lived by strict rules: communal property ("all things in common among friends"), joint meals "in the Spartan manner," novices — five years of silence, an oath to keep the teaching secret, secret signs for recognizing fellow believers; for disclosure, one was exiled, with tombstones "as for the dead" placed for the remaining members. Women participated in the life of the school: Iamblichus provides a list of 235 Pythagoreans, among whom 17 were women.

The Political History of the Pythagoreans and the Destruction of the League

The Pythagorean League was not only a philosophical circle but also a political force. Around 510 BCE, Croton defeated Sybaris (the army was commanded by the Pythagorean Milo); after the victory, the Pythagoreans' influence became excessive, they came into conflict with the democrats, and Cylon (along with Ninon), who had been rejected for admission to the League, led a conspiracy. According to tradition, the Pythagorean meeting was attacked, the house was set on fire, and some members perished.

The circumstances of Pythagoras's own death are known in several versions, none of which is confirmed. According to Dicaearchus, he fled and died of hunger after forty days in the shrine of the Muses at Metapontum; according to Diogenes Laertius and Iamblichus, he perished after refusing to cross a bean field (the story goes back to Neanthes, who told it about later Pythagoreans); Porphyry gives a version of escape over the bodies of students and suicide; there is also a tradition that Pythagoras was on Delos. Cicero, who visited the place of Pythagoras's death about 450 years after the events, mentions this tradition.

After the founder's death, the League was finally destroyed in the mid-fifth century BCE: in Croton, the Pythagoreans were killed and burned in the meeting house, and in 454 BCE an uprising followed in Metapontum. Survivors fled, spreading the teaching to other cities. By the end of the fifth century, influence was revived — most vividly in the person of Archytas of Tarentum, who was elected strategos seven times and was friends with Plato — but in the fourth century BCE, Pythagoreanism was absorbed by Platonism.

The Teaching

Metempsychosis

The teaching most reliably attributed to Pythagoras is metempsychosis — the transmigration of the soul into a new human or animal body. It is attested already by contemporaries: Xenophanes (a satirical verse about recognizing a friend's soul in a dog's body), Ion of Chios, Herodotus. According to Heraclides Ponticus (via Diogenes Laertius), Pythagoras "remembered" four former incarnations — Ephalidus, Euphorbus, Hermotimus, and Pyrrhus; this motif is considered the seed of the Platonic teaching of anamnesis.

"All Is Number"

The central thesis of Pythagoreanism — "all is number" — is attributed to the school as a whole on the testimony of Aristotle (Met. I, 5): the Pythagoreans "recognized that the elements of number are the elements of all things and that the whole heavens are harmony and number." This is an attribution to the school, not a direct Pythagorean quotation: according to a number of researchers, specific Pythagoreans may not have had such a teaching. The very formula "all is number" is a later paraphrase (in the Russian translation of Aristotle the wording is different). According to Walter Burkert's interpretation (1972), the "philosophy of numbers" is in general an innovation of Philolaus, not of Pythagoras himself (more in the section on the "Pythagorean question").

The Tetractys and the Harmony of the Spheres

The sacred symbol of the school — the tetractys: numbers from 1 to 4 laid out as dots in the form of an equilateral triangle. Their sum 1+2+3+4 = 10 — "perfection and fullness of being"; the BRE defines the tetractys as the "musical-numerical structure of the cosmos." The Pythagoreans swore by it: Iamblichus gives the oath "I swear by him who transmitted the tetractys."

Connected with the tetractys is the idea of the "harmony of the spheres" (musica universalis): planets and stars move according to mathematical ratios corresponding to musical notes and produce an inaudible music; according to Porphyry, the seven Muses are the seven planets, singing together.

Musical Intervals

Pythagoras is credited with the discovery that musical consonances are determined by the simplest numerical ratios: the octave — 2:1 (half the string), the fifth — 3:2 (two thirds), the fourth — 4:3 (three quarters); "the most perfect harmony" — the tetrad 6, 8, 9, 12. Sextus Empiricus provides testimony about these proportions (Against the Logicians, I, 94-97). Isopsephy and onomatomancy — Greek letter-number practices, predecessors of gematria — the ancient tradition also associated with the Pythagoreans (according to Aristotle); more in the article on the Pythagorean system.

Pythagoras and Numerology: What Is Historical and What Is Not

This section is key for readers who came for "Pythagorean numerology." It is important to distinguish two layers here.

Historical (ancient tradition). The Pythagoreans did think of numbers as real entities of the world (according to Aristotle), revered the tetractys, and developed the teaching of musical proportions and the harmony of the spheres. Isopsephy and onomatomancy — divinatory-religious practices with numbers — are attested, but this is not "numerology" in the modern sense. Russian Wikipedia, citing the BRE, notes: the numerological component of Pythagoreanism was probably attributed to Pythagoras retroactively, and its creators may have been Philolaus, Hippasus, and others.

Not historical (twentieth-century reconstructions). Modern "Pythagorean numerology" — a Latin alphabet letter table 1-9 with reduction — is a simplified version of the ancient pythmenes technique ("roots"); English Wikipedia directly warns not to confuse it with ancient Pythagoreanism. The very term "numerology" is recorded only from approximately 1907; master numbers 11 and 22 are not attested among the ancient Pythagoreans. The "Pythagorean square" (also "psychomatrix") is a modern Russian-language method by A. F. Alexandrov (books of the 1990s), absent from open encyclopedias; no direct continuity with ancient Pythagoreanism has been attested. Details in the articles on the Pythagorean system, Pythagorean square, and history of numerology.

Historical Authenticity: The "Pythagorean Question"

No authentic writings of Pythagoras have survived; in the time of Plato and Aristotle they no longer existed. Everything we know comes from later biographies: Diogenes Laertius (Lives and Opinions of the Eminent Philosophers, Book VIII, third century CE), Porphyry (Life of Pythagoras, third century), Iamblichus (On the Pythagorean Life, third-fourth centuries), and the anonymous Life of Pythagoras, epitomized by Photius. These biographies are full of legends and become more fantastic the further they are from Pythagoras's time. They partially go back to "primary" literature of the fourth century BCE: Aristoxenus, Dicaearchus, Heraclides Ponticus, Timaeus, and the lost work of Aristotle on the Pythagoreans. The earliest testimonies are the most reliable — Xenophanes, Heraclitus, Empedocles, Ion of Chios, Herodotus, Isocrates, Plato (collected in the Fragments of the Pre-Socratics by Diels-Kranz). L. Ya. Zhmud counts only about 15 mentions of Pythagoras and the Pythagoreans by authors of the sixth-fifth centuries BCE; the earliest is Xenophanes's satire on the teaching of the transmigration of souls.

Philolaus — the first writer to give a written account of the Pythagorean doctrine; before him the teaching was not recorded in writing, and all the school's achievements tradition attributed to the founder (the principle of autos epha — "he himself said").

Burkert's position. In the book Lore and Science in Ancient Pythagoreanism (1972), Walter Burkert proposed a radical reconstruction: Pythagoras was a charismatic political and religious teacher, the "philosophy of numbers" was an innovation of Philolaus, and Pythagoras himself "never worked with numbers" and made no contribution to mathematics. This is one of the influential interpretations, not the only one: the BRE warns that the conservative continuity of the "school doctrine" from Pythagoras to the Neopythagoreans should not be underestimated, and the reconstruction of the original teaching is one of the most difficult problems in the history of ancient philosophy.

Myths and Their Debunking

• "Pythagoras discovered the theorem." The relationship of the sides of a right triangle was known to the Babylonians and Indians centuries before Pythagoras; a proof in general form is attributed to him, but this is not attested. Burkert altogether denies Pythagoras's connection with the theorem ("in antiquity Pythagoras was not attributed the proof of any theorem"); Proclus reports that the original proof was more difficult than Euclid's. The legend of the hecatomb — a hundred oxen on the day of discovery — is given by Diogenes Laertius citing Apollodorus; Cicero rejected it (Pythagoras supposedly forbade bloody sacrifices), and Porphyry explained that the "ox" was made of dough.
• The prohibition of beans. This is attested fairly reliably (according to Zhmud), but both the prohibition and its absence have ancient confirmations. Explanations: ritual purity/metempsychosis or favism — a form of Mediterranean anemia (hypothesis).
• Vegetarianism. According to Eudoxus of Cnidus, Pythagoras was a strict vegetarian; according to Aristoxenus, he permitted meat except beef and mutton; according to Heraclides Ponticus, he ate sacrificial meat. The contradiction of sources is documented, not smoothed over.
• Pythagoras the miracle-worker. Legends arose already during his lifetime: the golden thigh (shown at the Olympic Games), son of Apollo, bilocation (seen simultaneously at Metapontum and Croton), a river greeting him by name, tamed animals (an ox refusing to eat beans, a bear swearing not to harm). G. Ridweg admits that Pythagoras himself may have supported these legends — but without direct evidence. Aristotle called him a "miracle-worker"; the BRE compares the legend of his katabasis with the Gospel typologically — this is a mythologization of the image.
• Criticism by contemporaries. Heraclitus mocked: "Pythagoras, son of Mnesarchus, investigated more than all men and, choosing these writings, composed his wisdom — much learning, artistry" (paraphrase). Lucian in The Dream (or The Rooster) ridiculed the prohibition of beans and the five years of silence.
• "The first philosopher." By tradition, it was Pythagoras who first called himself a "philosopher" — a "lover of wisdom" (Cicero, Tusculan Disputations 5.3.8-9, citing Heraclides Ponticus; Diogenes Laertius I.12, VIII.8; Iamblichus, section 58).

Influence and "After Pythagoras"

The Pythagorean tradition outlived the school. Plato — according to C. Kahn, Meno, Phaedo, and Republic have a strong "Pythagorean tint," and Philebus and Timaeus are Pythagorean in essence; according to Copleston, Plato's tripartite theory of the soul may have been borrowed from the Pythagoreans. Aristotle himself wrote that Plato's philosophy was heavily dependent on the Pythagoreans; Cicero — that "they say Plato learned everything Pythagorean."

In the first century BCE – first century CE, Neopythagoreanism flourished: Eudorus, Philo of Alexandria, Apollonius of Tyana (who declared himself a reincarnation of Pythagoras), Moderatus, Numenius, and Nicomachus, who developed numerology and music theory. In the Middle Ages, Pythagoras was revered as the founder of mathematics and music — two of the seven liberal arts (his images are in Chartres Cathedral); the Timaeus was the only Platonic dialogue in Latin translation, and through it Platonism was read as Pythagorean. Copernicus, Kepler, and Newton drew upon the Pythagorean tradition; Whitehead and Einstein — the "Pythagorean tradition" in science.

In the Renaissance, Heinrich Cornelius Agrippa in Occult Philosophy (1531-1533) called Pythagoras a "religious magician" and believed that his numerology operated at an extraplanetary level (see the article on Kabbalah and gematria). In the twentieth century, Cheiro (William John Warner, 1866-1936) in Cheiro's Book of Numbers formed two schools — "Pythagorean" and "Chaldean"; this is a modern tradition, not an ancient practice (see the Chaldean system). Freemasons built their societies on the model of the "school of Pythagoras," Rosicrucians used Pythagorean symbolism.

Criticism and Scholarly Status

From a scientific standpoint, numerology is pseudoscience: the Skeptic's Dictionary calls it superstition, using numbers "for the appearance of scientific gloss." Direct tests — in Great Britain (1993) and in Israel (2012; professional numerologist and 200 participants, experiment repeated twice) — yielded negative results. Important: this criticism concerns modern numerology as a practice, not the historical biography of Pythagoras — his life and teaching are described here as a subject of history, "according to tradition," not as established facts (see disclaimer).

Controversial and Gaps

• Life dates vary: circa 570 - circa 495 BCE (en-wiki), circa 570 - circa 490 (BRE), circa 570 - circa 500-490 (Britannica). The article uses "circa 570 - circa 490/495 BCE."
• Date of move to Croton: circa 532 (BRE, Britannica) vs. circa 530 (en-wiki) vs. "at age 40" (Aristoxenus).
• Circumstances of death: four or more versions (Dicaearchus; Diogenes/Iamblichus — but Neanthes's story about later Pythagoreans; Porphyry; Delos). None confirmed — presented "according to tradition."
• Travels: Isocrates considered the trip to Egypt a fact, but all details (22 years, priests, Babylon) are later legends.
• "All is number" — attribution to the school by Aristotle; according to Burkert, an innovation of Philolaus.
• The theorem — the relationship was known before him; the proof is not attested.
• The prohibition of beans and vegetarianism — sources contradict each other; favism is a hypothesis.
• Numerology vs Pythagoreanism — modern methods ("Pythagorean numerology," "Pythagorean square"/psychomatrix) are twentieth-century reconstructions; the term is from ~1907.
• Gap (for fact-checker): a stable URL for the full text of Porphyry's Life of Pythagoras in public domain is not confirmed (facts taken via en-wiki and BRE); quotations from Iamblichus (tetractys oath, list of Pythagoreans) and Diogenes (hecatomb, four incarnations, death) are verified against Gutenberg #63300 and #57342; the "circa 15 mentions" from Zhmud are taken from ru-wiki and not verified against the primary source.
• Discrepancy in the list of Pythagoreans: en-wiki (citing Iamblichus) names 235, of whom 17 women; in Taylor's translation (Gutenberg #63300) the list ends with "In all, two hundred and eighteen" — an editorial discrepancy; the article uses the figure from en-wiki.

See Also

• Pythagorean System — calculation method, letter table, and Pythagorean square
• History of Numerology — from the school of Pythagoras to modern schools
• Pythagorean Square — calculation by date of birth and interpretation
• What Is Numerology — introductory article of the section
• Kabbalah and Gematria — the letter-number tradition of Judaism
• Chaldean System — the "Chaldean" table of Cheiro
• Number 7 — the "right moment" (kairos) and the number of virginity among the Pythagoreans