Arithmancy at Hogwarts
Exploring Hermione's Favorite Subject
By Witherwings

"Arithmancy looks terrible' said Harry, picking up a very complicated-looking number chart.

"Oh no, it's wonderful!" said Hermione earnestly. "It's my favorite subject!" 1

Hermione Granger is the personification of logic in the Harry Potter books. Her skepticism of "woolly" 2 fortune-telling is so open and so extreme it leads her to storm out of Divination class in a rage, leaving her classmates astounded by her uncharacteristically rebellious behavior. Her very sense of logical thought seems to be affronted by Professor Trelawney and her dramatic-sounding yet completely unsubstantiated "Inner Eye." 3 The realm of soothsaying is not backed up by any concrete proof, so apparently it fails to earn rational Hermione's respect. She openly scoffs at her teacher's claim to be able to see into the future, laughs out loud at her predictions (although they often appear to come true), and finally drops the class altogether, never to return.

However, at the same time in Hermione's life she discovers a class at Hogwarts that quickly becomes her favorite: Arithmancy. Derived from the Greek words arithmos, meaning number, and mantei, meaning divination, arithmancy is the study of divination through numbers. A precursor to today's numerology, arithmancy focused more on predicting future events and rooting out hidden, mystical correlations than finding lucky lottery numbers and compatible mates.

Even so, one wonders what is so wonderful about number divination that has Hermione hooked. If she dismisses Professor Trelawney's foggy crystal balls and soggy tea leaves as "absolute rubbish' 4 how can Hermione have faith in a system of number omens simply because it is mathematical in nature instead of folkloric? Furthermore, why is this fictional subject taught at Hogwarts shrouded in almost as much mystery as its real-life hermetic history? The reader is never made aware of any other students besides Hermione taking Arithmancy, nor do we meet the Arithmancy professor or learn anything about the subject. All we are told is that Hermione loves it. Like every other class taught at Hogwarts School of Witchcraft and Wizardry, it must have its roots in ancient magical tradition.

Magic Studies, Pre-Hogwarts

Modern numerology, often called "Pythagorean' is a very streamlined version of the teachings of Pythagoras, who learned the power of numbers while studying mathematics and mysticism with the people of ancient Chaldea. Though the practice of number divination has been recorded in various early civilizations from China to Egypt, the Chaldeans were particularly renowned for their knowledge of the subject. In fact, their culture was so steeped in the occult that term "Chaldean" was frequently used by the Romans as a synonym for "astrologer" or "magician." 5 Pythagoras later established his own secret school at Crotona in 529 B.C.E., shortly after Chaldea fell to the Persian dynasty and existed no more. Like Hogwarts, this institute was a private, hidden sanctuary for select students of magic. Unlike Hogwarts, it unfortunately had no spells protecting it from the prying eyes of non-believers who eventually killed Pythagoras, destroying his school and all of its records as well. A loyal follower was able to reconstruct some of the sacred teachings, and these scraps serve as the basis for all later numerological studies.

Since Pythagoras left behind few documents, we can only form speculations about the Pythagorean school's lesson plan and what was really studied there. It is known that Pythagoras believed:

Number rules the universe.

Number is the within of all things.

Number is the ruler of forms and ideas,

and the cause of gods and demons.6

Regarded by mathematicians today as the father of numbers, Pythagoras' interest in numbers far surpassed the pragmatic way they are viewed by modern society. In his world, there was no chasm between arithmetic and arithmancy. Numbers were not seen merely as passive digits representing amounts in formulas and equations, they were alive with profound spiritual significance; humming with the music of the universe. Each and every number had its own unique personality and contained a vast well of secrets, a shrouded storehouse of connections to man, nature, the gods, and even other planets. The numeral shapes formed on paper were "but veils concealing from the vulgar gaze divine things." 7 According to this belief, then, knowledge of numbers was not only the key to unlock all the mysteries of our earth, but could be used to unveil the future and better understand one's self. Combine their esoteric properties with their ability to bring order to chaos and construct reason in the midst of ignorance, and those little symbols take on an incredible power. It certainly sounds more interesting than tea leaves, doesn't it?

At some point after the demise of Pythagoras, the history of numbers shifted and split into two distinct directions. In a chasm that could be compared to the division of the once-united Muggle and wizard communities, math took one path while numerology took another. The empirical use of numbers for purposes like architecture soon overshadowed the abstract use of numbers to enrich the human soul; the wisdom and beauty of numbers as esoteric symbols was left behind in a cloud of suspicion and ridicule. Any information we now possess about number mysticism has either been handed down within families or secret societies through the generations (like the gypsies), or has survived but been significantly adapted to apply to our modern lifestyle.

Inside Numerology and Grammatica

So many different branches of number divination have evolved in various cultures over the years that much of the original art of numerology as Pythagoras taught has been lost or rearranged beyond recognition. However, the basis of most numerological systems has been boiled down to the belief that every letter of the alphabet is linked to a corresponding number, and when all the numbers in a word or name are added together and reduced to a single digit, the result is a number that can give clues to the hidden nature of the word or name. This simplified form has its roots in gematria, the Hebrew discipline concerned with finding hidden meanings and correlations in words by establishing their numerical values. In the Hebrew alphabet, each letter symbol also stands for a number; tabulating number values in words grew naturally from this kind of alphabet. Often used for religious purposes, gematria is less a fortune-telling device than a study of arcane relationships. For example, the Hebrew words Yayin (wine) and Sod (secret) both have a numeric value of 70. This fact is believed to be evidence that the two words share a connection, as in the expression "when wine goes in, secrets go out." 8

The famous magician Heinrich Cornelius Agrippa first applied this concept to our current Latin alphabet in the sixteenth century and it's been widely used by mystics ever since. Though often referred to as "Pythagorean' there is little to connect it with the Greek alphabet-based system Pythagoras actually used so long ago. These days, symbolism is usually only applied to the numbers 1 though 9; all larger numbers are simply compound forms of the first 9 pure digits. Usually a person's full name is subjected to analysis, but it is believed that light may be shed on any word's true nature or meaning using this method. Many of us are familiar with the numerology conversion table created by Agrippa, and may even have played around a little with our own names.

Agrippa's System
1 2 3 4 5 6 7 8 9

Table 1: Agrippa's system, called "Pythagorean."

Given the fact that Hermione's first Arithmancy textbook is titled Numerology and Grammatica, 9 we can make an educated guess that applying number symbolism to words and names is a primary focus of the class. But how do we know that wizards and witches use Agrippa's Muggle-familiar method? After all, students at Hogwarts aren't likely to be taught anything they could learn from pulling up a website or grabbing a book in a Muggle library. A lesser known but possibly more authentic numerological conversion system is the Chaldean method, which more closely recreates the original Chaldean science of number divination based on the sound vibrations of the letters, not necessarily the order in which they fall in our modern alphabet. I find it more likely that wizards would discover meaning in this forgotten system than the one commonly ’ often trivially ’ used by non-magic folk, although it could be that both systems are studied. The most significant difference in the two methods is that the Chaldeans did not use 9 in their calculations. The form we all recognize as nine, a high complete circle with either a straight or an under-curled tail, represents "a sphere in heaven [that] connects to Earth through a downward-focused flow" 10 and has been long revered by mystics as the most sacred numeral because within it are contained all other numbers. The early mathematicians shared this reverence because they discovered that when added to another number, 9 always disappears into that number; in a sense it is like an invisible force absorbed by other numbers, so it was seen as magical.

The “Chaldean” System
1 2 3 4 5 6 7 8
I C* G M H V Z P

Figure 2: The "Chaldean" system. *Indicates a soft "c" as in the word "once."

Finding numeric values of words is easy. Using the Chaldean system and Hermione's name as an example, we simply add together the corresponding numbers of all the letters in her name, HERMIONE JANE GRANGER, which gives us 67. Then we reduce this number by adding together 6 + 7, which gives us 13. The final reduction to a single digit occurs by adding 1 + 3, and the result is a 4. In the Pythagorean system, HERMIONE JANE GRANGER adds up to 106, which becomes a 7 when reduced. Numerologists generally associate seven with studiousness, introspection and intelligence, while four is thought to represent practicality, logic and order.11 Either one would be a loose fit for Hermione, but the number derived from the total value of a person's name, called the destiny number, in fact tells us very little of importance on its own.

In addition to the destiny number, numerologists would also consider the soul essence or heart's desire number, derived from the vowels in the name, the social or life path number, derived from the consonants in the name, and also study the relationship between these numbers; how they interact with each other. This still only glosses the surface of a true numerology reading. Numerologists often calculate around thirty different numbers for any given personality, not including transit and cycle numbers used in casting a person's fate. Fate is determined in many ways, most commonly by comparing an individual's personal numbers with the numbers of a future date and contemplating what events are likely to occur from the interaction.

One of the most essential numbers to a numerology reading, however, is the birth or character number, which comes not from the name but from the date of birth. Names can change and often do, but the moment we are born remains connected with us our whole lives and even after we die. It marks our entrance into the world and it never varies. Hermione was born on September 19, 1979,12 or 9/19/1979. Look at the numbers themselves ’ most of them are nines! Indeed, when we add them all up and reduce them, the final value is 9. Therefore nine, the most sacred of all the numbers to the ancients, number of the humanitarian archetype, the helper, healer and enlightener,13 is a very important number to Hermione. Her primary role in the series is clearly that of a helper to Harry and others, often enlightening them whether they ask for her help or not. It is not the objective of this essay to provide a complete numerological analysis for Hermione or to explain the significance of each and every number, but to explore a few possibilities beyond those which can be found in oversimplified sources such as The Sorcerer's Companion Arithmancy Calculator and others which only offer a surface view of the full discipline of arithmancy.

Arithmancy's Appeal

Whether the students at Hogwarts study Chaldean or Pythagorean numerology, or both, the question still remains: why is Hermione so fond of this course? It is obviously a form of divination, in many ways similar to astrology and other "imprecise" 14 branches of magic touted by Trelawney. According to J.K. Rowling, a good part of Arithmancy class at Hogwarts also concerns "predicting the future using numbers' 15 or forecasting, which is synonymous with Sibyll's stock-in-trade, divining. It turns out that Hermione's favorite class is closely related to her least favorite! This becomes less surprising when we examine the different styles of divination and how they apply to the two subjects.

Professor Trelawney's Divination class relies chiefly on interpretive divination, a type which demands a leap of faith on the part of the student, whereas Arithmancy represents a type of inductive divination. Interpretive forms of divination include crystal-gazing and tea leaf-reading; any method which "requires the combination of correct procedure with the special gift of cunning sight that sets a diviner apart from his fellows." 16 According to Trelawney, anyone can look into a crystal ball and attempt to see visions or omens, but only those with a special talent for Seeing will be able to discern and decipher symbols with any relevance to future events. Upon entering her class, her pupils are expected to abandon all reason and accept that some have been anointed with a special ability to see into the future and some haven't ’ Trelawney of course being one of the anointed. This idea is difficult for anyone to swallow, but for a character as dependent on logic as Hermione it is impossible to accept. In fact, one might almost suggest that the whole concept of being born with a "Gift" 17 for the "Sight" 18 strikes Hermione as just as unfair as the suggestion that pure-blood witches are in any way superior to Muggle-borns. Inductive divination, which "assumes a deterministic procedure, free from mundane control, yielding non-ambiguous decisions or predictions' ,small>19 is more likely to appeal to her. Although a certain amount of interpretation and insight is required for any branch of the divinatory arts, anyone willing to learn and work would be able to calculate and form sound conclusions about number omens.

We can only speculate about the practical benefits of teaching young wizards arithmancy, but the rewards of number knowledge would appear to outweigh the fear and confusion the students gain from Divination class. For example, if we take a cue from gematria and apply the Pythagorean numerology system to solving the mystery of the enigmatic Prince, we see an obvious correlation that would have been beneficial for Hermione to happen upon:


Eleven is a special number, a master number signifying intuition and the duality of positive and negative forces, among other qualities.20 This duality certainly fits the character of the secretive double-agent Snape! Unlike other numbers, 11, 22 and sometimes 33 are not reduced to a single digit but remain as they are. These double numbers are believed to possess extraordinary spiritual power, so their energy would be compromised if they were reduced.

The depth of spiritual symbolism within the number symbols could take years to fully comprehend, but the numbers themselves and their mathematical functions are certainly more empirical and concrete than Trelawney's misty forms of divination. Arithmancy has the solid predictability of math working in its favor: 7 is always 7, 7 minus 3 is always 4, and 4 is always an even number. Numbers are a rare form of universal symbolism with which practically everyone in the world is familiar from a very young age, though we might not be aware of their metaphysical properties. There is no indication that Hermione is opposed the concept of the spiritual realm, only that she has no faith in Trelawney's methods of communicating with and interpreting that realm. Perhaps when Hermione has the familiar structure of numbers to cling to, she is less reluctant to enter the "beyond."

It's Wonderful!

Essentially, Pythagoras taught that all reality is mathematical in nature ’ so why not apply numbers to every aspect of reality as we know it? If numbers had the power to improve the quality of life so vastly in the early days, could they not also add clarity to the invisible, frightening regions of the unknown: the mind and soul? Imagine living in the early days of civilization. Number symbols are formed, then simple arithmetic is explored, then the fascinating world of geometry is discovered. Now imagine the thrill of finding that the same correlations you have seen proven on paper also exist in nature ’ in the geometric designs of flower petals, patterns in crystals and even in elements as ethereal as music. It is no coincidence that a sound the ear interprets as exactly the same note an octave higher is produced by a string exactly half as long.21

Today most Muggles have become jaded to the power and wonder of numbers, but their magic still holds sway over us whether we admit it or not. Gamblers still hope to roll lucky sevens, and many buildings do not label their thirteenth floors with the notoriously unlucky number but skip straight from 12 to 14, as do hotel rooms and rows of airplane seats.22 These superstitions are usually brushed aside and explained away with logic, but they still affect us to some degree, even if only subconsciously. The fact is that we as humans remain mysteriously yet undeniably driven to search for supernatural significance in the numbers we experience around us every day. Given the fact that the mysticism of numbers is taught at Hogwarts, it seems the wizarding community has an advantage over Muggles in maintaining this awareness. Would it be too naïve too hope that our mathematicians someday rediscover a bit of the spiritual in numbers, without the irrationality of superstition? The two worlds used to be linked, after all, in the eyes of the Pythagorists.

Without the rationality of math behind it, modern numerology can seem somewhat illogical. Without numerology's abstract conceptualism behind the numbers, plain old math seems to be lacking something in order to be a truly fulfilling discipline to both mind and spirit. Perhaps somewhere, hidden away and waiting to be rediscovered, exists a missing link to connect the split that occurred so long ago between legitimate mathematics and what many refer to as the pseudo-science of numerology. I like to think that link might exist at Hogwarts; that the wizarding world has access to a secret wealth of number knowledge that we Muggles have abandoned centuries ago. Maybe Hermione has discovered the bridge between the two worlds in Arithmancy class! That would be wonderful, indeed.


1. Rowling, Prisoner of Azkaban, 251.

2. Ibid., 111.

3. Ibid., 103.

4. Ibid., 111.

5., "Topic: Chaldea."

6. Crystalinks, "Quotes 12."

7. Heline. The Sacred Science of Numbers, 1.

8. Fiery, Book of Divination, 68.

9. Rowling, Prisoner of Azkaban, 315.

10. Elinwood, The Everything Numerology Book, 60.

11. Astrology ’ Numerology, "Numerology Key Words."

12. The Harry Potter Lexicon, s.v. "Wizards A-Z: Granger, Hermione."

13. Acumind, s.v., "Tarot: The Hermit."

14. Rowling, Prisoner of Azkaban, 109.

15. Rowling, Interview by Stephen Fry.

16. Hedgewytchery, "On Divination."

17. Rowling, Prisoner of Azkaban, 103.

18. Ibid.

19. Hedgewytchery, "On Divination."

20. MCUniverse, "Numerology: Master Numbers."

21. Kitto, The Greeks, 192.

22. Wikipedia, s.v., "Triskaidekaphobia."


Acumind, s.v. "Tarot: The Hermit." (accessed 22 September 2006.) "Topic: Chaldea." (accessed 5 August 2006.)

Astrology ’ Numerology. "Numerology Key Words." (accessed 16 September 2006.)

Crystalinks. "Quotes 12." (accessed 31 August 2006.)

Elinwood, Ellae. The Everything Numerology Book. Avon, MA: Adams Media Corp., 2003.

Fiery, Ann. The Book of Divination. San Francisco: Chronicle Books, 1999.

The Harry Potter Lexicon, s.v. "Wizards A-Z: Granger, Hermione." Member of the Floo Network. (accessed 9 September 2006.)

Hedgewytchery. "On Divination." (accessed 5 August 2006.)

Heline, Corrine. The Sacred Science of Numbers. Los Angeles: New Age Press, 1977.

Kitto, H.D.F. The Greeks. Chicago: Aldine Publishing Co., 1964.

MCUniverse. "Numerology: Master Numbers." (accessed 22 September 2006.)

Occultopedia: The Occult and Unexplained Encyclopedia. "Arithmomancy." (accessed 22 September 2006.)

Pither, Steven Scott. The Complete Book of Numbers: The Power of Number Symbols to Shape Reality. St. Paul, MN: Llewellyn Publications, 2002.

Rowling, J.K. Harry Potter and the Prisoner of Azkaban. New York: Scholastic, Arthur A. Levine Books, 1999.

Rowling, J.K. Interview by Stephen Fry, Harry Potter and the Magic of the Internet, 26 June, 2003. Transcript, Quick Quotes Quill, (accessed 9 September 2006).

The Sorcerer's Companion. "The Sorcerer's Companion Arithmancy Calculator." (accessed 30 July 2006.)

Thompson, Leeya. Chaldean Numerology: An Ancient Map for Modern Times. Three Lakes, WI: Cole Publishing Group, 1999.

Wikipedia: The Free Encyclopedia. "Triskaidekaphobia." (accessed 16 September 2006.)

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The Leaky Cauldron is not associated with J.K. Rowling, Warner Bros., or any of the individuals or companies associated with producing and publishing Harry Potter books and films.