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Abstract: Pythagoras can be seen as a mathematician and a mystical philosopher. His theory of numbers and his mystical philosophy of the transmigration of the soul are outstanding. There are various postulations as to the originality of Pythagoras in his philosophy. The question is how can we justify him as either a mathematician or mystic? Which of these thought mostly affect or has an influence on mankind? The essence of this paper is to make clarifications on this issue
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EUROPEAN ACADEMIC RESEARCH
Vol. IV, Issue 12/ March 2017
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Pythagoras: Mathematician or Mystic?
JOHN NWANEGBO BEN Ph.D
Directorate of General Studies
Federal University of Technology, Owerri, Nigeria
Abstract:
Pythagoras can be seen as a mathematician and a mystical
philosopher. His theory of numbers and his mystical philosophy of the
transmigration of the soul are outstanding. There are various
postulations as to the originality of Pythagoras in his philosophy. The
question is how can we justify him as either a mathematician or
mystic? Which of these thought mostly affect or has influence on
mankind? The essence of this paper is to make clarifications on this
issue.
Key words: Numbers, Transmigration, Soul, Mysticism, Theorem.
INTRODUCTION
Pythagoras is more or less a legend taking cognizance of his
philosophical leanings. He is noted as the first Greek
Philosopher who stressed on the reality of numbers and
postulated a mystical philosophy that has deep religious
overtone. There have been various interests among
philosophers and historians of philosophy as regards this
legendary figure. His philosophy is of great interest to both
mathematicians and mystics. Born a lonian in 530 BC and later
migrated to Croton in Southern Italy, a native of the Island of
Samos, he distinguished himself in the theory of numbers and
esoteric mystical philosophy. The Pythagorean theory is
John Nwanegbo Ben- Pythagoras: Mathematician or Mystic?
EUROPEAN ACADEMIC RESEARCH - Vol. IV, Issue 12 / March 2017
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attributed to him. The question we may wish to ask is, is
Pythagoras well known as a mathematician taking cognizance
of his theory or can he be ascribed as a mystic?
The Question of the Mathematical Theory of Pythagoras
Pythagoras of Samos was the founder of the central
mathematical school of the fifth and sixth centuries BC known
as the Pythagorean School. He saw the universe from a
mathematically inspired observatory. Nature or the universe is
composed of numbers in various shapes squares, cubes,
oblong, triangle etc. The individual points were boundary
stones which marked out fields” moreover, these, “triangular
numbers”, squares numbers rectangular numbers and
“spherical number” were differentiations by the Pythagoreans
as being “old” and “even” thereby given them a new way of
treating the phenomenon of conflict of opposites1. Numbers
were seen as specific kinds of entities not as abstractions. They
believe there is a numerical base for all things that has shape
and size. With this conception of the universe, they graduated
from Arithmetic to Geometry and the structure of reality.
The most popular modern image of Pythagoras is that of
a master mathematician and scientist. His well-known
geometric theory which posit “that the sum of the squares on
the legs of a right triangle is equal to the square on the
hypotenuse (the side opposite the right angle) or, in familiar
algebraic notation a2 + b2 = c2. Scholars however have argued
that though this theory has long been ascribed to Pythagoras,
but they posit that it has already been used by the Babylonians.
It has also been noted that the same theory has been recorded
in the “Budhayana sulba-sutra of India” in 800 – 400 BC 2.
Scholars and historians of philosophy have argued on
Pythagorean indebtedness to Thales of Miletus in the area of
Mathematics and his journey to Egypt where it was believed
that he spent twenty two (22) years3 and received instructions
in mathematics, physics, music, theology and philosophy in
Egyptian mystery schools.
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The overriding dictum of the Pythagorean philosophy was “
Reality is number” and they appeared to practice a kind of
numerology or number worship and considered each number to
have its own character and meaning. The number One, was the
generation of all numbers, two represented opinion, three
harmony, four justice, five marriage, six creation, seven
the seven planets, Planets or wondering stars. Odd numbers
were thought of as female and even numbers as male.4 All
things for Pythagoras consists of points and units and all
distance or lines consists of infinite number of points. To them
reality is number and number constitutes the nature of all
things.5
Generally Pythagoras is being taken as a principal
mathematician, however, the question is, is he really the
proponent of the theorem?
Some scholars posit that he was not the initiator of
Pythagoreanism in the light of the fact that the Pythagorean
standard was particularly present also in China in the tenth
century BC.
Why Pythagorean Theory and Not Another
The interest and popularity of Pythagorean theory is not
doubtful bearing the background from which we received
information about him. It may interest most of us to note that
almost all knowledge all over the world is western education.
There are several theories as to how and why the
theorem came to be named after Pythagoras. The Egyptians
belief that only the divine was capable of genuine universal
knowledge. They had the practice of not ascribing knowledge to
any mortal man. This explains why there are no extant names
as father of Ancient African Philosophy. Though the calculation
now termed Pythagorean was developed by Aahmes, an
Egyptian Priest 6 it was never attributed to him by name. But
when Pythagoras who himself, a student of the Egyptian
Mystery school returned to Greece and began to teach, this
mathematical science became a custom among the Greeks to
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regard this teaching as the Pythagoras theorem. There is
nowhere in ancient writings did Pythagoras claim that he was
the originator of this writing; rather he admitted that he
acquired his wisdom from Egypt where he stayed for twenty
two years7.
However, western scholars of pre-colonial and colonial
era had made it available to the world that nothing good or
scholarly came from Africa. While back, Homer himself a Greek
historian stated: “In Egypt the men are more skilled in
medicine than any of human kind” 8. In Plato and Aristotelian
writings there were statements that postulate that the
Pythagorean Theorem was not original to Pythagoras.9
The knowledge we have of Pythagoras is from western
account. Western education exposed us to many lost and
forgotten accounts of legends and their contributions to
mankind. However, our western orientation to knowledge did a
dis-service to western oriented scholars such that we had little
or no knowledge of advancement in relation to China and India
hundreds of centuries before the advent of the Pythagorean
theory.
Thus, our knowledge of Pythagoras as the exponent of
the theory is predicated on our orientation as western oriented
scholars.
The Pythagorean Theorem has been known as Kuo-Ku
of the theorem in China. It is said that “the Kuo-Ku of the
Chiu-Chang indicates that the Chinese had accumulated a
wealth of experience in working with the right triangle in
various mathematical situations well before the Christian era.10
Guthrie, a western Philosopher, probably unaware of the
existence of this theory in China and India before the advent of
the theory wrote “The discovering which he made were totally
and astonishingly new.”11
Evidence has been shown that he was not the first to
discover the theory, but that it has been known also by the
Babylonians and Chinese at least a thousand years before
him.12
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Pythagoras as a Mystic
The popularity of Pythagoras may have its basis on the theory
we have discussed so far, but an indebt analysis of all his
teachings appear to reflect his mystical world view.
Pythagoras teachings show that he is interested in
mathematics for religious reasons. This implies that they tried
to use mathematics to interpret religious issues. This can be
buttressed from the fact that he posits that the study of
mathematics is the best way to purify the soul. According to
Samuel Enoch Stumpf “what gave rise to the Pythagorean sect
was the yearning among men for a deeply spiritual religion that
could provide the means for purifying the soul and for
guaranteeing its immortality.” 13
The Pythagorean philosophy postulates that the human
soul is immortal and lives in a world for better than the present
one we live in. the soul of man descended into this world for
purification from sins committed from past incarnations. Its
presence here is a punishment for offence committed. The body
is the prison of the soul. At death the soul transmigrates into
another body, thus leaving one prison for another.
The soul can move from a human body to an animal
body depending on the gravity of the offence committed. It is
based on this doctrine of transmigration of souls that the
Pythagoreans forbid the killing or eating of animals. They
believe that even to maltreat an animal is wrong because one
could be maltreating a reincarnated soul of a friend or a
member of one’s own family. The process of reincarnation and
transmigration of the soul continues until the soul achieves
freedom or liberation.
The Pythagoreans believe that through philosophy and
abstinence from eating any animal flesh, the soul will be able to
achieve salvation and return to the world of the divine and
reconcile with the universal spirit or soul.
Pythagoreanism as a philosophy was clearly concerned
with the mystical problem of purification and immortality, and
it was for this reason they turned to philosophy and
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mathematics as a solution to purge the soul. The Pythagoreans
were basically a mystic sect, a religion or order, brotherhood
dedicated to orphic cult. They were seen as the orphic mystic
religion. Orphism was not just a philosophy but an oriental
mystery cult that preached the divine nature of man.
Man is seen as a dual creature, a combination of the evil
and divine. Man’s soul or mind is a fragment of Dionysus (god)
his body, a heritage from the Titans. Salvation for them is the
liberation of the divine nature in us from the bondage of the
body. To effectively execute this, they posited that man should
abstain from eating meat, beans or fish. The avoidance of beans
as was posited is that it smells like the human fetus and many
have magico-religious reason.(14) In addition, there was a belief
that beans and human beings were created from the same
material(15) thus eating it implies eating a human being which
could also imply eating a close relation or friend.
The Pythagorean Mysticism in Relation to others
The Pythagorean mystical religious philosophy is very
interesting and reflects the ideology of many ancient religions
and mysticism. H. I. Summer however argued against the
concept that Pythagoras posited in his philosophy that man
should avoid beans. He states “what Pythagoras said to his
disciples “Abstain from beans” he had no reference to them as
an article of diet, for he ate them himself. What he did mean
and what his immediate followers already understood was that
they should abstain from the intrigues of politics as being
antagonistic to a philosopher pursuit.16
Pythagoras knowledge of mysticism may not have come
from the blues or should we say that he did not probably tap his
knowledge from the world of universals but have acquired it
through studies in Egyptian mystery schools, or got a hint of it
in China or India.
The mind has been treated by the Pythagoreans as
divine. It is the one, the source of all knowledge. Our souls are
immortal but the part or portion of the One is not permanent
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within the human body. Its dissolution is the “release” in death.
The One was seen as Fire, as well as the Supreme God. The
One according to them does not grow, but is responsible for the
growth of everything.
The doctrine of the soul explains the spiritual mission of
the soul or earth. It was taught that the only way to free
ourselves from this cycle of reincarnation and transmigration of
the soul was to obtain a higher understanding of the universe
through introspective thought and philosophical study.
The influence of other cultures and religion on
Pythagoras was highlighted by Daniel Farley, he state “…he
was initiated for the first time into the “Ancient mysteries” of
the Phoenicians and studied for 3 years in the temple of Tyre,
Sidon and Byblos from there, he navigated to Egypt, the source
of “Ancient Mysteries”, on the road, he lingered for a while in
the gulf of Haifa at a temple of Mount Carmel, Israel (after the
destruction of the first Jewish temple of Jerusalem). In Egypt
he was initiated and studied for 22 years’. Farley went further
to post that the philosophy and many theories on the
Pythagorean way of life transmitted orally by Pythagoras, were
considerably influenced by the way of life of Judaism and the
Bible.17
The Egyptians are said to have taught him geometry,
the Phoenicians arithmetic, the Chaldeans astronomy, the
Magians the principles of religion and practical maxims. He
visited the Hebrews from whom he acquired the conduct of life,
expert in the interpretation of dreams, and he was the first to
use Frankincense in the worship of divinities.18
Modern science traces its mathematical origins to
Pythagoras, but in development dropped off the mystical
teaching. This idea of shelving the mystical teachings predicted
on the idea of scientism as scientific realism. This is the view
that the world as described by science is the real world as it is
independent of what we might take it to be. Scientific realism
usually holds that science makes progress. The characteristic
product of successful scientific research is knowledge of largely
John Nwanegbo Ben- Pythagoras: Mathematician or Mystic?
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10447
theory, independent phenomena and that such knowledge is
possible (indeed actual) even in those cases in which the
relevant phenomena are not observable.19
CONCLUSION
Pythagoreanism, which is a word describing the philosophy of
Pythagoras and his followers revolved around two major areas.
These areas are the Pythagorean Theorem and the
Pythagorean mysticism. Our study has showed that Pythagoras
did not just dabble into mathematics because it was his major
interest. He tried to use mathematics to interpret religious and
mystical issues. This is buttressed from the fact that he posited
that the study of mathematics is the best way to purify the soul.
Thus, what gave rise to Pythagoreanism or the sect was the
yearning among men for a deeply spiritual religion. His
doctrine of transmigration, reincarnation and immovability of
the soul affect many lives and this mystical philosophy can be
found in many religious doctrines and esoteric religious sects.
Invariably, bearing in mind these leanings, it would be
reasonably to deduce that Pythagoras was more of a mystical
philosopher, hence a mystic than of a mathematician.
REFERNCES
1. Samuel Enoch Stumpf. Philosophy, History and Problems.
New York: McGraw Hill. Inc.1989.P.11.
2. Pythagorean Theorem, Encyclopedia Britannica. retrieved
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3. Samuel Enoch Stumpf. Socrates to Sarte: A history of
philosophy. New York: McGraw-Hill. 1983.P.3.
4. The story of mathematics “Greek mathematics-Pythagoras”
www.storyofmathematics.com/greek-pythagoras.retrieved.
9/2/2017.
5. John Nwanegbo-Ben. The Mind of Philosophy Owerri: Advance
Graphics, 2012, p.25.
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6. The Aahmes Papyrus dates to about 200-1700 BC c/o Durant.The
story of civilization. Vol.1.P.180
7. Keita and Olela “African Philosophy” in African philosophy. An
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13. Samuel Enoch Stumpf. Opcit.p.9.
14. See Gabrielle Hatfield, Review of Fredrick T. Simeon’s ;
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15. Riedweg Christopher; Pythagoras: His life, teaching and
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16. H. I. Summer; The Beans of Pythagoras. www.theo-
society.org/pasidence/path. Theosophical university press. Online.
Retrieved 20/2/2017.
17. Daniel Farley; Pythagoras and Mystic science
web.mit.edu/dryfoo/masonry/essay/Pythagoras.html. Retrieved
24/2/2017.
18. Kenneth Syivan Couthrie (Trans): The life of Pythagoras.
www.tertullian.org/fathers/porphyry_life of Pythagoras -02.
Retrieved 26/2/2017.
19. John Nwanegbo-Ben. The Anatomy of History and philosophy
of science. Owerri: Advanced Graphics. 2016.p.182.
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Article
4th Ed Bibliogr. s. 911-918
The Mind of Philosophy Owerri: Advance Graphics
  • John Nwanegbo-Ben
John Nwanegbo-Ben. The Mind of Philosophy Owerri: Advance Graphics, 2012, p.25.
  • M P Motley
M. P. motley Africa Its Empires, Nations, and people, Detroit: Wayne states university press. 1969. P.66.
Was Pythagoras Chinese? University Park. Peninsula state university press
  • J Frank
  • T I Swetz
  • Kao
Frank, J. Swetz and T. I.Kao Was Pythagoras Chinese? University Park. Peninsula state university press. 1988.p.66
The Pythagoreans theorem: Princeton University press
  • Eli Maor
Eli Maor: The Pythagoreans theorem: Princeton University press.2007.p.xi.
Review of Fredrick T. Simeon's ; plants of life, plants of death University of
  • See Gabrielle Hatfield
See Gabrielle Hatfield, Review of Fredrick T. Simeon's ; plants of life, plants of death University of Wisconsin press.1999
Pythagoras: His life, teaching and influence. Ithaca; Cornel university press
  • Riedweg Christopher
Riedweg Christopher; Pythagoras: His life, teaching and influence. Ithaca; Cornel university press 2005. Pp. 39, 70