Ronna Pennington, a college instructor, has a Master of Liberal Arts degree with emphasis in history.
Bust of Pythagoras
Pythagoras is More than a "Math Dude"
In the study of truth, order, and beauty, Pythagoras and his followers deserve credit for examining order and creating a numerical system that attempted to explain many aspects of the universe. Pythagoras and his followers used number theories to examine various universal properties, including the idea of planes, cubes, squares, and the triangle-based theorem that bears his name: a2+b2=c2.1 His greatest accomplishment, however, was the introduction of a monadic deity principle based on his study of the number one. Pythagoras claimed that the number one really was not a number at all. Since there are no other whole numbers that can be added together to equal the number one, he viewed it as the precursor to all other numbers. As such, one is the beginning of all numbers, the source from which they all emanate. Since he and his followers believed all things were associated with numbers, they believed all things originated from the number one. Number one existed before anything else, anyone else, and any other number. Pythagoras, born in about 560 BC, developed this theory about numbers and delved into the mystical qualities of number one long before Christ walked the earth. He introduced the idea of a single god to fellow Greeks who worshiped a bevy of them. It was this philosophy and personal charisma --not his mathematic aptitude -- that drew followers to him.2
To call Pythagoras an important ancient mathematician requires proof that the man indeed made significant mathematical advancements. Such a claim is difficult to make because Pythagoras recorded none of his number theories in writing.3 It is reasonable to believe that if mathematics had been Pythagoras’ primary concern, he would have diligently tracked his methodology and results. Most accounts of Pythagoras did not even arise until hundreds of years after his death. The accounts today’s culture has of Pythagoras actually come from his followers – students who studied directly from him and those who picked up the Pythagorean lifestyle long after his death. By today’s standards, Pythagoras was more cult leader than mathematician.
The proof that Pythagoras was more interested in pursuit of mysticism over math lies in the foundation of the school he started in Croton, a Greek colony in southern Italy. It was not a school based on math curriculum. Instead, it was a school of philosophy that adhered to many strict principles in a communal setting. He and his Pythagoreans considered the mystical aspect of numbers while living a vegan lifestyle that was accompanied by a five-year vow of silence upon joining the group.4 The fact that Pythagoras had followers and influenced thinking even after his death is further testament to his role as a cult leader. The term “cult leader” has an offensive meaning in today’s society that it did not carry with it in Pythagoras’ day. From all accounts, he was a virtuous man who promoted ethics and contemplation. In no way should Pythagoras be confused cult leaders making modern-day American news. Contemporary cult organizers like Tony Alamo or Warren Jeffs face criminal charges for sex crimes in coordination with their organizations.5 Despite having a wife and daughter, Pythagoras viewed sex as evil because it distracted humans from contemplation. He said intercourse should be reserved for the summer months, likely because stormy weather in spring and fall or cooler temperatures in winter might create health issues.6
Like many modern cult leaders who seem bigger than life, Pythagoras’ notions for a philosophical lifestyle gave way to many legends and folklore. Some said he made his own odyssey into the Underworld to talk with the dead for insight into the soul, or as he naturally called it, the One. The truth is that he hid in a cave for weeks and relied on notes from his mother to inform him about the community’s events. When he emerged from the cave with knowledge of what happened while he was gone, he pretended to have gained the knowledge supernaturally.7
Word traveled regarding Pythagorus’ "supernatural” powers. He supposedly tamed a wild bear just by whispering to it, domesticated an eagle, and correctly predicted the number of dead returning on a cargo boat. One tale even claimed he had a gold hip, a trait that would have earned him the status of at least a demi-god. Claims that he recalled previous incarnations fueled such folk lore for Pythagoras. 8
One might think that such folk lore and mystical tales would subtract credibility from the study of numbers on which Pythagoras and his followers focused. Nothing could be farther from the truth. Since the number theories themselves were mystical in nature, the lore and philosophy actually correlated nicely. To better understand the impact of Pythagoras on the Middle Ages and beyond, one must first have a basic knowledge of his number theories.
Pythagoras developed his mathematical theories based on ancient numbering principals. Most Greek math was reserved for the marketplace, and therefore concentrated on the money system. Despite suggestions that he might have picked up mystical mathematic information during his rumored travels to Egypt or Babylon, those cultures also used math predominantly for financial purposes. Besides, number mysticism has not been uncovered in any other ancient civilization before Pythagoras’ time. Pythagoras withdrew from the concept of money regarding math and began to study what he determined to be mystical characteristics of numbers.9
The first important development Pythagoras made was the idea of the monad. Number one, he said, is not a number at all. Because it cannot be divided equally to get a product other than itself and because it cannot be divided unequally with a remainder, Pythagoreans concluded that one was not a number at all. Instead, it is a producer of numbers.10
Viewing number one as a producer, a number from which all others emanate, Pythagoras and his followers took their theory a step further by sexualizing the numbers. One, since it is neither odd nor even by Pythagorean standards, was assigned both female and male attributes. Odd numbers were deemed male; evens, female. One, however is both, because when used to reproduce (add), it creates the opposite of that to which it was added. For instance one added to an odd number equals a female number, and vice versa.11
Seeing number one as a producer, a number that existed before all other numbers, Pythagoreans respected it as divine. When multiplied by any other number, one only creates the beginning number again. To Pythagoras and his followers, this lack of multiplicity proved that one was a divine number symbolizing a spirit that had nothing to do with material things. In other words, number one is supernatural.12
Pythagoras’ supernatural one became a symbol of universe, nature, and eventually, God. It is important to understand this divine nature of one when considering the evil nature of two, or the dyad. From the most basic math skills we know that 1+1=2. By that standard, two should be doubly good rather than evil. But Pythagoras saw two as evil because something divine, in this case the number one, could never duplicate itself. To do so would be blasphemy because he viewed duplicating divinity as a perversion of perfection, making the product of one plus one an evil number.13Two is also the first female number, a division away from the divine number One.14
Three, which Christians today recognize as an important symbol of the Holy Trinity, was deemed by Pythagoras to be the first-born number, reproduced by the monad and dyad, and the first true male number. Because of the unity associated with one reproducing with the division associated with two, three results in harmony. Pythagoras also discovered that Three is the only number with a sum that also equals its product: 1+2=3; and 1+2+3=1x2x3.15
Triangles, a geometrical shape with which Pythagoras is still today associated, have three sides and angles. To him, they represented balance and it is no wonder he devoted much time to their study. Students still learn the Pythagorean theorem that states both sides of a right triangle squared and added together will equal the length of the hypotenuse squared. The theorem is more recognizable in its mathematical form: a2+b2=c2.16
Four presented an unusual contradiction for the Pythagoreans. Despite being an evil, even number, Pythagoreans related it closely to ten, the number of perfection. Because 1+2+3+4=10, Pythagoras and his followers embraced four as a good, solid, square number reflective of justice.17
Aside from viewing it as the number of marriage, Pythagoreans largely overlooked the number five. They link it to marriage because the sum of two, the first female number, and three, the first male number, equals five.18 Pythagoreans omitted it from the music scales they identified by experimenting with ratios. Centuries later in his book Against the Heresies, Iraneus accuses the Gnostics, also interested in number mysticism, of intentionally skipping the number. Since the Gnostics based their number theory on those by Pythagoreans, Iraneus' accusation challenges Pythagoras' credibility. By then, the number had strong Christian affiliations with it, such as the five wounds of the crucified Christ and the five loaves of bread he miraculously used to feed the masses.19
Pythagoreans saw six as a perfect number. Remember, one is divine and therefore not a number. Six is the sum and the product of the same numbers: 1+2+3=6 and 1x2x3=6. For Pythagoras and his followers, this novelty outweighed the fact that six was an even, evil number. Other than this brief discussion of six, Pythagoreans do not dwell on the number.20
Pythagoras called seven a universal number because it represented the seven planets and seven spheres. The number also had ties with ancient Greek culture in folklore regarding Apollo and Athena. According to Greek legend, swans circled the island of Delos seven times before Apollo was born on the seventh day of the week.21 Philoalaus, a Pythagorean student in the fifth century BC, claimed that the number seven was like Athena – an eternal deity, steady, and unique. Another follower, Nicomachus, noted the importance of the number because of the seven tones in an octave and the seven Greek vowels.22
Even in antiquity, different cultures assigned the number eight to represent Heaven or a paradise of some sort. If the world was made up of seven spheres, the eighth would have been a realm beyond, tying it directly with the mystical notion of life after death or the place where gods lived. For Pythagoras, however, eight was interesting for other reasons. When an odd number, (not counting the divine number one) is squared, the result is a multiple of eight plus one. For instance, 32=9=8+1 and 72=49=8x6+1. Despite the interesting number game with eight, Pythagoreans did not delve into it as they did some of the lower numbers.23 The Pythagoreans also skipped over the number nine, even though – or perhaps because – it is the square of three, thus connecting it with the lower number's symbolism.
The Critics of Pythagoras
Pythagoras, as Aristotle points out in his book Metaphysics, is known to simply skip over numbers that do not work in his theories. He also accuses Pythagoras and his followers of creating “knowledge” in order to make their principles work.24 Number ten presents an example of this. For the Pythagoreans, ten was the perfect number. The first four natural numbers (including one here instead of omitting it because of its divinity) added together equal ten: 1+2+3+4=10. By adding the two digits of the number ten together, the one and the zero, the answer is one, the divine, primordial number. Ten items can also be displayed as an equilateral triangle, representing the geometric balance that was so important to Pythagoras and his followers.25
Pythagoras wanted to keep the nature of ten sacred, so he constructed a “harmony of the spheres.” Earth and each of the seven plants were placed into a concentric circle. The sun, or “globe of divine fire” was the center. With only nine circles filled, Pythagoras simply invented something to put in the tenth. He called it Antichthon, a wandering planet that was never seen.26
With this haphazard methodology, Pythagoras and his followers naturally fell prey to criticism and ridicule by other philosophers. As previously noted, Iraneus criticized them for greatly overlooking the importance of five, and Aristotle complained that they created "evidence" to complete the "harmony of the spheres" theory. Between the fifth and sixth centuries B.C., Xenophanes poked fun at Pythagoras' idea of reincarnation. He said he witnessed Pythagoras interrupt the beating of a puppy, telling the tormentor that the puppy spoke with the soul of one of his old friends.27
While Xenophane's anecdote paints the picture of simply an eccentric man, criticism by Timos of Phlius looks at Pythagoras from a different angle -- a charismatic swindler.28 A comedic poet of the fourth century BC, Cratinus the younger, joked about the Pythagoreans using rhetoric to confuse people interested in their doctrine. Around the same time, Heraclitus accused Pythagoras of practicing created wisdom and "artful knavery" proving that many of his contemporaries saw him as cult leader instead of a serious mathematician.29
Decline and Reemergence of Pythagoreanism
The study of mystical numbers decreased in the fourth century BC due to ongoing progress in Greek civilization. During this time frame, the Parthenon was built, Aristotle developed physics, and Hippocrates made medical discoveries. Mystical numbers were associated with the ancient civilization, not progress. When construction and advancement began to slow in the second century B.C., interest in mysticism revived, introducing Neopythagoreanism into the culture. The number symbolism developed by Pythagoras and his early followers introduced Greek mythology to both Jewish and Christian traditions as they evolved.30 The study of numbers also introduced gematria, the ancient practice of assigning number values to each letter in the alphabet, into the Jewish religion.31 The goal of gematria was to develop a numeric value for words to unlock their mystical meaning.32
Pythagoras himself was influenced by Thales, a Greek philosopher who lived near the beginning of the sixth century BC. Thales believed that the soul was like a magnet, drawing itself back to a larger, universal soul.33 This view of the soul fit Pythagoras' theory of the divine number one perfectly.
Plato's thoughts on the soul reached much farther than did those of Pythagoras, probably because Plato was a prolific writer. Even in his era, 429–347 B.C., he wrote volumes of persuasive material. Readers familiar with Pythagoras' views on the soul, however, quickly relate them to Plato's works. He, too, taught that the soul was not corporeal. Plato also contributed to the philosophical world with the methodology he developed. Given the critiques on Pythagoras' methodology, it is reasonable to say that Plato's logical and documented approaches to philosophy were great accomplishments in and of themselves.34
Plotinus, from the third century A.D., revived Plato's ideas in the Neoplatonist movement, also teaching the oneness of the universal soul. By this time, however, the idea of a universal soul had less connection with the number one and more religious connection with the God of Christianity.35 Plato and Plotinus shared and expanded upon Pythagoras' theory of reincarnation. They believed that the universal soul distributed itself among other living creatures, then gravitated back to the All-Soul upon the body's death.36
In the third and fourth centuries, people continued to search for spiritual knowledge. Christians who became known as the Gnostics, a Greek term meaning knowledge, subscribed to philosophies regarding triads and tetrads, making them seem in alignment with the Pythagorean philosophies. The Gnostics, however, used their geometrical shapes in ritualistic ways that defied the principles taught by both Pythagoras and Plotinus. The Gnostics perverted the knowledge derived from numbers, teetering beyond the line of mystic religion into magic idolatry.37
Magic was just one of the crucial elements to Gnosticism. They were affiliated with mystical numbers through astrology, too. To the Gnostics, seven was a perfect number that represented Mercury, Venus, Mars, the sun and moon, Jupiter, and Saturn. Their reference to numbers hints to Pythagoreanism or Neopythagoreanism. The difference between the groups lay in their theories of the soul, Holy Trinity, and role of Jesus Christ. According to the Gnostics, Jesus was not the savior, nor did he suffer during His time on earth. Instead, they saw Him as a teacher who simply set many good examples for humanity.38
Gnosticism was deemed heretical at the First Council of Nicea in 325 A.D. after coming into question by the Church for its views on the Holy Trinity. Despite the heresy stamp, the study of numbers never completely died. The heresy was in the fact that they worshipped the numbers, Besides, by then, biblical number symbolism had already been established and was difficult to deny.39
By the fifth century A.D., interest in numbers grew yet again with a resurgence of Neopythagoreanism brought about by Boethius. He never claimed to be a Neopythagorean, but his interest in the science of mathematics and music theory inadvertently connected the two. Boethius struggled to explain the idea of universal oneness with Aristotelian and Stoic logic. He concluded that "oneness" that is simultaneously common to many cannot possibly be one in reality. They can, however, be one in thought. In his Christian terminology, he reasoned that God exists simple because one questioned whether or not He does.40
Despite the Neopythagorean emphasis on numbers to gain knowledge, the Catholic Church does not deny the movement's influence on development of the Church. The communal living and vow of silence actually paralleled the monastic life of early Catholicism. Additionally, they believed that the Pythagoreans lived a humble life, just like the lifestyle Jesus portrayed during his time on Earth.41 Perhaps their acceptance of Pythagoras had input on the continued symbolization of numbers.
Expansiveness of Number Symbolism
Consider Pythagoras' initial determinations regarding numbers. According to his philosophy, the number one was recognized as the universal soul. The Bible correlates this theory. Like Pythagoras' one, the spirit of God is omnipresent and in existence before anyone or anything else.42 He was the producer, just like One was the producer in Pythagoras' theory. Beyond biblical and philosophical references, cultures adopted the symbolism Pythagoreans associated with the number one. Today, a number one ranking means a person is at the top, the best of the best.
The number two has symbolic representation in the Bible as well. Recall that the number two was deemed an evil, female number by Pythagoras. Biblically, it is the second man -- actually woman -- who disobeys God and eats the fruit of the Tree of Knowledge of Good and Evil. She is sentenced to beget two sons, and one of them will commit the first violent murder of mankind.43 In Chinese culture, the Yin and Yang represents the duality of male and female.44 Based on these brief examples, it seems as though Pythagoras' theories are right on the mark. In today's culture, terms such as "two-faced" or "double-edged sword" reflect the continued negative connotation of the number two. The number has come to represent polarity and diversity, based on the mystical symbolism assigned to it by Pythagoras thousands of years ago.
The number three, a symbol of universal balance to Pythagoreans, enjoys pleasant symbolism in the Bible with the Holy Trinity. Dante used the symbolism of three in structuring his Divine Comedy. By dividing it into the categories -- Inferno, Purgatorio, and Paradiso -- he reflected the beliefs of his Catholic faith in eternal life after death.45
Plato also utilizes the symbolism of the number three to express his notion of human ideals: truth, order, and beauty. Augustine's human ideals are best described as being, recognizing, and willing. In other words, humans could simply exist; they could locate or recognize a problem or deficiency; and they could be willing to find ways to combat whatever problem they uncover. By the standards set forth by Plato and Augustine, three is a very virtuous number.46 Because modern students still study the works of Plato, Augustine, Plotinus, and the Bible, symbolism for three continues today.
Some fairy tales are based on a character's receipt of three wishes. Always, the first two are thoughtlessly wished, but the third and final wish balances the story back to a happy ending.47 Even baby Jesus received three symbolic gifts -- gold, frankincense, and myrrh.48 Three gifts were a fitting choice for a member of the Holy Trinity. Because of these three gifts, the shepherds who gave them are often referred to as the "Three Wise Men." Even though no exact number of shepherds who made the pilgrimage was biblically expressed., three is affiliated with the Christmas story.49
Symbolism of the number four is also embedded in today's society. There are four primary directions: north, south, east, and west. Calendars reflect the four phases of the moon. Organizers design cities on systems of blocks, often around a courthouse square, symbolic of good city design, infrastructure and justice -- the same qualities assigned to the number by the Pythagoreans.50
Pythagoreans saw the number five as a representative of marriage. Pop culture adapted the same. The best example of this is the song, "The Twelve Days of Christmas." The line "Five golden rings" is a clear representation of marriage. Symbolism associated with five made its way into literature as well. In Sir Gawain and the Green Knight, Gawain's special shield featured a pentagram, an infinite star shape that is also known as a lover's knot.51 Like Gawain's shield, the people of ancient India found protection in the number five. The spot where five points of the cross met was considered to be a protection from evil. They likewise elected five elders to lead their village.52 Chinese adopted the symbolism of the number five into their culture as well. They recognized five types of relationships: prince/subject, father/son, man/woman, elder brother/younger brother, and friend/enemy.53
In terms of modern culture, the phrase, "Give me five" in which a person extends his or her and for another person to slap has become a standard greeting for some. In referring to the hand's five fingers, this popular greeting initiates contact with another and creates a moment of union when the skin of two different people touches. It is not exactly marriage like the Pythagoreans' association, but the contact of skin does denote an intimate union of sorts.
As previously explained, the novelty of number six was enough to satisfy the Pythagoreans and to encourage them to have favorable symbolism of the number. The number is represented biblically in the creation story. God created the world in six days, then rested on the seventh.54 Until the twentieth century, many American communities observed this principle with blue laws to prohibit shopping on Sundays which were widely regarded as the Sabbath day.55 Symbolism of six in Christianity does not stop there. Jesus was crucified on the sixth day of the week in the sixth hour.56 While this could be seen with negativity, the Book of Matthew looks at it in a different light: a life of good works produced by practicing the six virtues of Christ.57 Symbolism of six extends beyond Christianity. In Zoroastrianism, six periods of creation relate to six supreme angelic creatures.58 The "Star of David," a six-pointed star, is a symbol commonly associated with Judaism since the seventeenth century.59
The Pythagoreans respected seven as a universal number, but over time it has developed an affiliation with luck, goodness, and wonder. God's rest on the seventh day symbolized to Christians that it is appropriate, or good, to take a day off for relaxation.60 An Arabic proverb lists seven good things of which a person never gets too much: bread offered in kindness, lamb meat, cool water, soft clothing, beautiful fragrances, comfortable place to sleep, and a view of beautiful things.61 Islam depicts the number seven as good because it teaches there are seven levels to Earth and seven levels in Heaven.62 Jewish wedding traditions likewise recognize the seven by reciting seven blessings during the ceremony and celebrating the new wedded union for a period of seven days.63
The luck aspect associated with seven is likely rooted in magic. For example, a concoction to cure tertain fever required several items to be collected, all in groups of sevens. Some of these included seven prickles from seven palm trees, seven chips from seven beams, seven handfuls of cumin, and seven hairs from an old dog's face.64
The number eight was interesting to Pythagoras, but the octagon had wider influence than the philosopher's fixation on his theory of the multiples of the number. The octagon served as a transition from square architecture to circular, paving the way for domes to enter into building design concepts.65 In Christianity, Jesus discusses the eight beatitudes.66 Buddha likewise teaches followers about an eightfold path that leads to cosmic balance.67 Islam gives its rules to aspiring Sufi in eight sentences in the "Path of Junayd." 68 The Christian, Buddhist, and Islamic principles are still studied by followers today, keeping symbolism for the number eight alive in modern times.
Nine was largely overlooked by Pythagoras because it held no special properties. Despite that, symbolism of the number developed throughout the ages, especially in Celtic and Germanic culture. Both societies used the number as a tool of measurement, counting distance in nine steps rather than feet.69
The number also made its way into folklore. King Arthur possessed the ninth part of his father's strength. A Germanic hero could hold his breath under water and stay awake for nine days and nights.70 Nine was a number commonly used in medieval healing. In Scotland and Germany, the prescription for a person with a sprained foot or hand was a ribbon tied in nine knots. Additionally, healers repeated some rituals nine times.71
Nine holds important symbolism artistically as well. Nine muses inspired many writers, including Herodotus who divided his work in nine parts in honor of them.72 Even Plotinus expanded his Neoplatonic ideas in nine books of the Enneads.73 Dante likewise reflected the symbolism of the number nine in his order of angels in his Divine Comedy.74
Today, one might hear a common phrase like "Cloud Nine" to express that someone is happy. While modern society knows the old saying that a cat has nine lives is not true, it is still a popular element of fiction and selected folk lore.
Ten, for Pythagoras, stood for complete perfection. That symbolism remains today. In pop culture, Melissa Rycroft won television's "Dancing with the Stars" all-star competition, earning several perfect scores of ten.75Romanian gymnast Nadia Comaneci scored the first perfect ten in the 1976 Olympics.76Bo Derek became the archetype for female perfection thanks to the 1979 movie, "10."77
In terms of religion, Judaism recognizes the symbolism of ten in several ways. As with Christianity, it acknowledges the Ten Commandments God gave to Moses. There are likewise ten generations between Adam and Noah.78Ten is symbolic in Islamic tradition, too. Mohammed speaks of the ten people who were promised paradise.79
The Number Values of Letters
Number symbolism certainly does not stop with ten, but to Pythagoras anything above and beyond ten was repetitious. This is best seen in the charts of gematria used to convert words into number values. A revival of gematria coincides with the introduction of a Roman alphabet in 1583. The chart used single digits to represent the first nine letters, tens to represent the next nine, then hundreds to complete the alphabet. Since zeros have no value, even the letter "Z," listed with a value of five hundred would have only been counted as a five. A 1683 chart was similar, but counted the last six letters by tens rather than hundred. The diagrams in Figure 1 easily show the difference between the two conversion charts.81
Today it is clear to see why gematria does not work. The method of conversion is based on the alphabet of the interpreter. With one hundred year's difference, the two charts above prove that alphabets do change. Those studying the words may assign different number values to the letters at will. Gematria, therefore, is just as fickle as the alphabets and the people reading them are.
Perhaps Pythagoras was onto something when he began studying the mystical nature of numbers. As many have proven by continuing his studies even into modern times, any mystical nature of numbers will remain just that -- mystical. While his fascination of numbers led him to make strides in geometry and mathematics, Pythagoras' largest contribution was to that of philosophy. After his death, the studies of Pythagoras and his followers inspired many philosophers -- Plato and Plotinus among them. During his own time, however, Pythagoras's contemporaries were very critical of him. They called Pythagoras a quack while folk lore circulated about him performing miracles or having a golden hip. The opinions and lore recorded by his contemporaries prove that Pythagoras was more cult leader than mathematician.
The fact that number symbolism is still very much alive in the twenty-first century in no way dilutes the fact that Pythagoras was really a cult leader. Pop culture's recognition of this age-old symbolism does not justify or sanctify Pythagoras as a revered mathematician. Rather, the number symbolism that enthralled Pythagoras remains current simply because it was never banned by the Catholic Church. Even when the Council of Nicea convened in 325 to thwart the Arian Gnostics, their practice of numerology was not addressed. They were guilty of the ritual worship of geometric shapes and teaching an incorrect view of the Holy Trinity. So, Pythagoras was a charismatic cult leader more so than a brilliant mathematician. From this angle, he clearly had greater impact on truth, order, and beauty.
Notes and Sources
1. Annemarie Schimmel. The Mystery of Numbers (New York: Oxford, 1993), 11.
2. Colin Wilson. The Occult (New York: Random House, 1971), 196.
3. "Pythagoras and Pythagoreanism." New Advent.org. http://www.newadvent.org/cathen/12587b.htm (accessed November 2, 2012).
4. Christopher Riedweg. Pythagoras: His Life, Teaching, and Influence (New York: Cornell, 2005), 101.
5. Guy Lancaster. "Tony Alamo." Encyclopedia of Arkansas History and Culture.net. http://www.encyclopediaofarkansas.net/encyclopedia/entry-detail.aspx?entryID=4224 (accessed November 23, 2012); Weber, Paul J. "Warren Jeffs' Polygamist Ranch Could Be Seized By Texas." Huffington Post.com. http://www.huffingtonpost.com/2012/11/29/warren-jeffs-polygamist-ranch-seized_n_2210642.html (accessed November 29, 2012).
6. Wilson, The Occult, 196.
9. Underwood, Dudley. Numerology or, What Pythagoras Wrought (Washington: Mathematical Association of America, 1997), 17.
10. Schimmel, The Mystery of Numbers, 41.
12. Schimmel, The Mystery of Numbers, 43.
13/ Schimmel, The Mystery of Numbers, 44.
14. Nazih Malak. "Pythagoras." Mission College.org. http://www.missioncollege.org/depts/math/malak/malak.htm (accessed November 18, 2012).
16. Schimmel, The Mystery of Numbers, 60.
17. Malak, http://www.missioncollege.org/depts/math/malak/malak.htm (accessed November 18, 2012).
19. Schimmel, The Mystery of Numbers, 118.
20. Schimmel, The Mystery of Numbers, 121.
21. Schimmel, The Mystery of Numbers, 137.
22. Schimmel, The Mystery of Numbers, 138.
23. Schimmel, The Mystery of Numbers, 56.
24. Schimmel, The Mystery of Numbers, 15.
25. Schimmel, The Mystery of Numbers, 180.
26. "Pythagoras." Fun Trivia.com. http://www.funtrivia.com/en/People/Pythagoras-20164.html (accessed December 1, 2012).
27. Riedweg, Pythagoras: His Life, Teaching, and Influence, 49.
29. Riedweg, Pythagoras: His Life, Teaching, and Influence, 50.
30. Underwood, Numerology or, Wh
at Pythagoras Wrought, 18.
31. Underwood, Numerology or, What Pythagoras Wrought, 20.
32. Underwood, Numerology or, What Pythagoras Wrought, 35.
33. "Plato." Stanford Encyclopedia of Philosophy.org. http://plato.stanford.edu/entries/presocratics/ (accessed December 2, 2012).
36. Ibid.; Plotinus. The Six Enneads. MacKenna, S., Page, B. S., trans. http://www.ccel.org/ccel/plotinus/enneads.pdf (accessed October 31, 2012)
37. "Gnosticism." New Advent.org. http://www.newadvent.org/cathen/06592a.htm (accessed November 16, 2012).
39. "First Council at Nicea." New Advent.org. http://www.newadvent.org/cathen/11044a.htm (accessed November 11, 2012).
40. "Boethius." Stanford Encyclopedia of Philosophy.org. http://plato.stanford.edu/entries/boethius/ (accessed November 30. 2012).
41. "Pythagoras and Pythagoreanism." New Advent.org. http://www.newadvent.org/cathen/12587b.htm (accessed November 2, 2012).
42. "Genesis 1:1-28." Bible Gateway.com. http://www.biblegateway.com/passage/?search=Genesis+1&version=NIV (accessed November 13, 2012).
43. "Genesis 4: 1-25." Bible Gateway.com. http://www.biblegateway.com/passage/?search=Genesis%204%20&version=NIV (accessed November 13, 2012).
44. Schimmel, The Mystery of Numbers, 50.
45. Schimmel, The Mystery of Numbers, 63.
46. Schimmel, The Mystery of Numbers, 65.
47. Schimmel, The Mystery of Numbers, 82.
48. "Matthew 2:11." Bible Gateway.com. http://www.biblegateway.com/passage/?search=Matthew+2:11&version=NIV (accessed November 13, 2012).
50. Schimmel, The Mystery of Numbers, 108.
51. Schimmel, The Mystery of Numbers, 109.
52. Schimmel, The Mystery of Numbers, 114.
54. "Blue Laws." The Free Dictionary.com. http://legal-dictionary.thefreedictionary.com/Blue+Laws (accessed December 1, 2012).
55. Schimmel, The Mystery of Numbers,124.
59. Schimmel, The Mystery of Numbers, 126.
60. Schimmel, The Mystery of Numbers, 153.
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RonnaPennington (author) from Arkansas on June 15, 2016:
Raxin on June 14, 2016:
Typo: "Six is the sum and the product of the same numbers: 1+2+3=6 and 1x2x6=6."
Suggested correction: "Six is the sum and the product of the same numbers: 1+2+3=6 and 1x2x3=6."
RonnaPennington (author) from Arkansas on June 28, 2013:
Thanks, Jennifer! This was class project I completed for a medieval history/literature class :) I put it here in its entirety to help other students who might be looking for similar info. It was tough to find info on Pythagoras...but the fun is always in the research. Thanks for reading and commenting!
jennifer west on June 27, 2013:
Wow! Overwhelming amount of information! I so appreciate the research into your article! I am hoping you will edit it and break it down a little, as I get a little lost at times. It is amazing the understanding of ancient scholars!! Extremely full of info!! Thank you!
Amanda Littlejohn on March 12, 2013:
What an exhaustive and fascinating essay about one of the greatest thinkers of ancient times and the founder of modern mathematics.
It is extraordinary how, back then, the business of science, myth, art and religion was all rolled into one, isn't it?
That was a very well researched piece, jam packed full of detailed information.
Bless you :)