The Pythagorean Tradition in Freemasonry

by Wor.Bro. The Rev. J. R. Cleland, M.A. D.D.
Source :



Over the Gates of the ancient Temples of the Mysteries was written this injunction, "Man,

Know Thyself".  It meant that each Candidate must try to contact that Inner Self which

is the only Reality, - Paul Brunton calls it the Overself, - that Self which lies at the very

Centre of his Being, in the Silence and Darkness of the Holy Place which, to those who

have penetrated to the Sanctum Sanctorum, becomes the deafening Music of the

Spheres and the blinding Light of Truth.  As the DORMER is the window giving light to

the Sanctum Sanctorum, it is but right that here, among your members who have

chosen to work under that name, one should attempt to find some light upon the Secret

of Secrets, which each must ultimately solve for himself, which "no man knoweth" save

"he that overcometh", he that has mastered it for himself. It "passeth all understanding"

and is the mystery of his own being.


Freemasonry is closely allied to the ancient Mysteries and, if properly understood, and

in spite of repeated revision and remoulding at the hands of the ignorant and sometimes

the malicious, it contains "all that is necessary to salvation", salvation from the only "sin"

that ultimately matters, that which lies at the root of all other sin and error, the sin of

ignorance of the self and of its high calling.


The First T.B. opens with the statement that "the usages and customs among

Freemasons have ever borne a near affinity to those of the Ancient Egyptians; The

Philosophers of Egypt, unwilling to expose their mysteries to vulgar oyes, concealed

their systems of learning and polity under heiroglyphical figures, which were

communicated only to their chief priests and wise men, who were bound by solemn

oath never to reveal them. The system of Pythagoras was founded upon similar

principles and maintained under the same conditions."


We might, therefore, reasonably expect that a study of the system originated, or

adopted, by the great teacher, Pythagoras, would tend to throw some light upon this

Masonic Craft of ours. There are four questions which we might put to ourselves in this



1. Who was Pythagoras?


2. What was the basis of his philosophy?


3. What are his and its connections with Freemasonry as we know it?


4. Can we from a study of these, formulate a code, and by following it, open up a path,

whereby, if trodden by the individual student, he can, and should, reach that state,

which, for want of a better name, we may call "Realisation", - the full knowledge of that

which alone is real, - The Oneself?


I believe that all these questions can be answered and, tonight, I am going to make an

attempt to condense the answers, as I see them, into one short paper. It would be

impossible to go into each one fully, and, in process of condensation, the answers will

overlap; but I will try to state them as simply as possible and I hope I may succeed in

making the general outline, at least, clear.  It can only be an outline, for that which must

ultimately be sought is beyond form, formless.  It can never be filled in fully in words.

The connection with Freemasonry will, I think, make itself clear, if we attempt to answer

the other three questions.


First, then, just who was, or rather in, Pythagoras.  As the most famous of Greek

Philosophers, he was born at Samos about 586 B.C. His father was Mnesarchuss, a

man of learning and of noble birth. As a boy, Pythagoras had every advantage of

education and, later, seems to have travelled all over the world and to have formulated

his philosophy upon basic principles culled fron the various systems to which he gained

access. Thus he studied Astronomy and Astrology both in Chaldea and in Egypt, and

the Esoteric Sciences among the Brahmans of India. To this day his memory is

preserved in India under the name of Yavanacharya, the Ionian Teacher. Returning to

Europe, he settled at Crotona, in Magna Grecia, where he established a School, to

which were attracted all the best intellects of the civilized world.  He left no writings

himself, so we have to piece together the details of his philosophy from the writings of

his followers. To him we owe the word Philosopher. He was the first to teach the

heliocentric system in Europe and no one of his time was so proficient in Geometry.

Not only was he the greatest mathematician, geometer and astonomer of historical

antiquity, but he also held highest place among scholars and metaphysicians. His fame

cannot perish.  He taught much of the Ancient Secret Wisdom, the truth of

re-incarnation, the necessity for return to a natural system of diet, the rule of Justice in

the whole Universe and the certainty of ultimate attainment of perfection by all beings.

He realised that the solution of the great problem of Eternity belongs neither to religion,

to superstition not to gross materialism.  The harmony and balance of the two- fold

evolution - of Spirit and of Matter, - have been made clear only in the Universal

Numerals of of Pythagoras, who built his whole system entirely upon the so-called

"Metrical Speech" of the Vedas.  In both Pythagorean and Brahman Philosophy the

esoteric significance is derived from numbers. One of the few commentators who have

paid just tribute to the high mental development of the old Greek and Latin writers,

Thomas Taylor, says "Since Pythagoras, as Iamblichus informs us, was initiated in all

the Mysteries of Byblus and Tyre, in the sacred operations of the Syrians and in the

Mysteries of the Phoenecians, and also that he spent two and twenty years in the adyta

of the Temples in Egypt, associated with the magicians of Babylon and was instructed

by them in their venerable knowledge, it is not at all wonderful that he was skilled in

Magic, or theurgy, and was therefore able to perform things which surpas merely human

power, and which appear to be perfectly incredible to the vulgar."


For entrance to the School ot Pythagoras the qualifications were high and rigorously

enforced and, once entered, the candidate came under very strict rules as regards diet,

exercise and study. Besides this outer discipline there were pledged disciples who were

expected to pass through three degrees, during a probation of five years. Of the outer

disciples, leading an ordinary family social life, G.R.S. Mead says, "The authors of

antiquity are agreed that this discipline had succeeded in producing the highest

examples, not only of the purest chastity and sentiment, but also a simplicity of

manners, a delicacy and a taste for serious pursuits which was unparalleled. This is

admitted even by Christian writers".  The three degrees of the Inner School were:


HEARERS, who studied for three years in silence.


MATHEMATICI, learning Geometry and Music, the nature of Number, Form, Colour,



PHYSICI, who learned to master Cosmogony and Metaphysics. They were then

prepared for the Mysteries.


The School at Crotona was closed at the and of the sixth century B.C., being

persecuted by the Civil Power; but other communities carried on the tradition.  Mead

says that Plato intellectualized it to protect it from profanation, which was on the

increase, and the Mysteries of Elusis, although they had lost its spirit and substance,

still preserved some of its rites.


The root of all such teachings seems to have lain in Central Asia, whence Initiates

spread to every land, carrying the same doctrines, using the same methods, working

towards the same final goal. There was a common language and symbolism which

served for intercommunication. Pythagoras in India received a high Initiation and later,

Appolonius of Tyana followed in his steps. Typically Indian are the dying words of

Plotinus, noblest of the Neo-platonists "Now I seek to lead back the self within me to the

All-self." One great teacher has said, "The end of knowledge is to know God - not only

believe; to become one with God - not only to worship afar off." We gain a hint in the

Kathopanishat (V1- 17) "Let a man with firmness separate it (the soul) from his own

body, as a grass stalk from its sheath," to which point we will return later.


Pythagoras gave the "knowledge of things that are" to his disciples and his knowledge

of Music is said to have been such that he could use it to control men's wildest

passions and to illuminate their minds. Iamblichus quotes instances and advises

Porphyry to remove from his thoughts the image of the thing symbolised and to reach

its intellectual meaning. Of the use of symbols Proclus remarks, "The Orphic method

aimed at revealing divine things by means of symbols, a method common to all writers

of divire lore." Great stress was laid upon the fact that numbers should be studied for

the better comprehension of life, and not or use in commerce.


I am tempted to think that Pythagoras is a title, rather than a real name and it is

significant that his father Mnesarchus, the nearest translation of which is "Ruler of

Memory."  Pythagoras, as a title, is identical, in root meaning, with Hiram Abif and with

the Egyptian Thoth-Hermes.  The root Pytha is the Sanscrit Pitta and the Latin Pater and

the Greek, , all meaning Father.  It is again the same root as the Egyptian Phtha, one

of the names of Thoth and Abif also means Father.  Goras is the Sanscrit root Guru

meaning Teacher, and the same root is found in Huram or Hiram. The Egyptian root is

ChR Horus.  ChR-Mes or Horus-Moses means Son of Horus.  We may note here that

Mercury, the latin equivalent of the Greek Hermes is a corruption of the

Syrian Mar-Kurios meaning Son of the Lord.


The Pythagorean system of Cosmology is based upon the Decad, 10, or to use the

name of the symbol associated with its name, the Tetractys.  This Tetractys is

represented in United Grand Lodge of England by a single great Hebrew Yod, or "I,"

placed immediately over the Grand Master's Throne, Yod being the tenth letter of the

Hebrew alphabet and that also being its numerical value. The "pillar and circle," also 10,

the perfect number of the Pythagoreans became later, among th Jews, a pre-eminently

Phallic number, among whom it represented Jehovah as Male-Female.  This Decad,

representing the Universe and its evolution out of Silence and the Unknown depths of

spirit, was presented to the student in Dual Aspect. It applied first to the Macrocosm,

from which it descended to the Microcosm. To-day, upon four-square bases, we have,

in our Lodges, or should have, two pillars, each bearing aloft a circle in perpetuation of

this symbolism.


Both the purely intellectual and metaphysical, or "inner science" and the purely

materialistic or "surface science", can be expounded by, and contained in, the Decad,

study being by the deductive method of Plato or by the inductive method of Aristotle.

Plato commenced with Divine Comprehension, and multiplicity proceded step by step

from Unity, the digits appearing only to be returned to the Circle of the All-pervading

Absolute.  Aristotle started with perception by the senses, the Decad being regarded

either as the unity which multiplies or as the matter which differentiates, its study being

limited to two dimensions, to the Cross, or the 7; proceeding from the 10, the perfect

number, on Earth as in Heaven.  The whole conception apppears originally in India, but

we cannot go into that now.  The Western Teacher who first formulated it was



Primarily numbers are symbols of the beginning and development of a universe, so the

simplest way of bringing home to you their significance will be to take the first cycle of

Creation, leading to full manifestation of the ultimate physical atom, and the building

therefrom of matter, as we  know it.  I shall run through the stages very rapidly and

leave it to you to go more fully into the subject should it appeal.


First, then, we have the Zero, nought, the Circle appears the Point at the Centre,

potentiality, showing the Circle as not barren. In Arithmetic "0" is nothing, but, added to

other numbers, is all things. Without it multiplicity cannot go beyond 9. This

Circle-potential is the first number of the Cosmos, symbol of the Unknown, the

Illimitable, containing all numbers as possibilitiss, as sunliqht contains all colours in



The 0 the Circle or Ovum is Passive, and requires vivification before it can fructify and

produce.  The  point, or centre, then becomes active and from it arises the Line, - the

diameter which bisects the Circle, thereby polarising it.  This is the Monad, the First

Power of the Universe creating Polarity, opposites in Unity.


Some ancient philosophers spoke indiscriminately of Monad and One, but the Platonists

drew sharp distinction, speaking of the Monad as that containing distinct yet profoundlly

united multitude, whereas the One is the "sumnit of the Many" and simpler.  One is the

first of a series, nonexistant unless followed by other numbers, whereas the Monad

includos all numbers, holds division in check.  One is the apez of all numbers which

spread fron it to the base, 10.  Pythagoras realised the fundamental basis of numbers

as Rhythm. In it was based the generation of all things.  Numbers, to Pythagoras, were

names and descriptions of Cosmic Ideas and Happenings.  One writer quotes him as

saying, "There is a mysterious connection between the gods and numbers, on which

the science of arithmancy is based.  The soul is a world that is self moving; the soul

contains in itself, and is, the quaternary, the tetractys, the perfect cube, and another

says "Pythagoras is not reported as saying that the gods are numbers, or that all things

are numbers, as some of his followers and critics affirm."  Everything with the

Pythagoreans, ideas, injustice, separation, mixture and even man and his horse, were

all numbers" according to Aristotle. When speaking of the Monad or One, they actually

referred to that which was before Creation, and, if philosophically minded, referred to

it as the "Primordial Cross," if religiouis, as God, both understanding the same thing.

They had many names for such number.  Their One corresponds to the Advaitya, the

one without a second of the Hindoos, creator and cause of all numbers.


The Duad, 2, is termed the cause of dissimilitude, matter. It is considered to be

feminine, as the matrix or all things, and is the symbol of growth.  Two cannot be

produced from One, so duality is considered as the actual begining of manifestation;

It is the drawing apart of God as Life and God as Substance, 1 X 1 is l and nothing but

1 so 1 needs 2, as Life needs Substance for manifestation and multiplication.

1 entering into relation with 2 gives rise to 3. Life, 1, ensouling Form, 2, becomes linked

to it, 3, after being polarised, 2, from itself, 1.  Opposites are essential to any creative

purpose. 2 is therefore called the "First Number".  Cornelius Agrippa calls it so because

"it is the first magnitude and the common measure of all numbers, or, as the

Pythagoreans term it, a confusion of unities.  Thus, God, as One, the producer and

clause of Persistence, polarizes, His Unity and draws apart from His substance,

Subsistence, and, then vivifies it, producing Existence. 1 is potentially 2 for polarity is

everywhere, as are pairs of opposites.


Avicebron of Cordova (1021-70) speaks of the affinity between "to be" and numbers and

says 3 is tte root of all things; for Spirit, 1, and Matter, 2, linked by Will, the bond

between, form the Triad.  He ways, "All existing things are constituted after the nature

of numbers.....The Highest Abstract God is the indivisible, metaphysical unity". So 3, as

relating the action of the two opposites is rightly considered the number of true

beginning, without which no production is possible. One, potential, like a ring of

magnetized steel, is powerless until broken, or polarized, and the opposites are

themselves useless until there is a relation between them. 3 is then the number of active

growth and production. There are three distinct steps to be taken by the student before

he can enter the "outer court" of the Mysteries:-


1. He must collect together his forces and prepare to learn.

2. He must eliminate and subtract gross matter.

3. He must amalgamate or synthesise the result.


or in more familiar words


1. He must come of his own free will and accord.


2. He must be deprived of all metals and material valuables.


3. He must be properly prepared.


The third step of apprenticeship gains approbation from a master and leads the student

to a position where he can grasp the work with his whole nature.


The number 3 is most important and, masonically, so far as the Craft is concerned,

must be studied in conjunction with 5 and 7.  I will return to this point.


The idea of the fundamental Trinity presupposes a condition of being before the worlds

were created.


4 is significant of system and order.  Plutarch states that it is because of 4 that every

body has its origin. It is Foundation, and does not relate to the building of physical

forms and bodies, which is the function of 8, but to that of the Cosmic stones, the

ultimate atoms out of which these forms will be built.  Philo says it is the first number

to show the nature of solidity. Mathematically it is Foundation, for, without it, no

progression beyond 6 is possible, but with it completion in 10, that is, the complete

cycle, can be reached.  Three components blending equally gives 6 and no more but

predomination of any one of them would lead to 7 or more, for 1 plus 2 plus 3 equals

6 and also 1 X 2 X 3 equals 6 each of which requires the addition of 4 to complete the

cycle (or circle).


5 has a root meaning of "harvesting", the arranging in sheaves of produced substance,

hitherto potential, now becoming matter. Five forms are combined in the foundation of

the chemical atoms. It is a matter of rebirth and actual material commencement.  That

matter should be ensouled is not sufficient. Both matter and life must be qualified that

gradation and diversity may result.  Each chapter of the first ten chapters of Genises is

said to refer to one of these numerical steps and it should be noted that chapter V

contains a description of all emanated things and is devoted solely to generation.

D'Olivet reads it as a story of Cosmic generation. The Pythagorean name was cardiatis

or cardialts, as the heart of things manifest, change of quality, the fire which "changes

all things triply extended or which have length, breadth and depth into the sameness

of a sphere and producing light." It is eminently a "circular number" and spherical,

restoring itself in every multiplication. Note here the F.C's steps. By 5 arranging matter

ready for use, three fundamental qualities are produced in the prepared matter and the

three aspects of Diety find reflection in them, Will or Strength to Create, Love or Wisdom

to Preserve, and activity or Beauty to Transmute or to send forth Creation, producing

6, representing that period in the creative process in which Triple spirit enters into

Matter, already prepared as a triplicity to receive it. The double triangle is its symbol.

Allendy defines it as a static correspondence between two analagous terms and not a

transitory action or passage from one state to another. It is the instrument of

progression but not the progression itself."


7 represents the progressive atomization of matter, without which building is

impossible. The ancient Greeks called it Justice and represented it as a pair of scales,

the bar pivoting about a point and supporting two hemispherical pans, each supported

by 3 chains. 7 is to 3 as 3 is to 1. As 3 represents the development of a principle, so

does 7 represent it doubly represented, that is to say not only manifested but objectively

realised. Everywhere in nature we find this 7, in ourselves, in colour, music, the Arts, in

healing and so on, balancing three on the life side against three on the form side with

one giving synthosis.


Now, I think we may stop here, for this is the point to which the Craft of Freemasonry

brings us.  To complete the major cycle one has to consider the Holy Royal Arch and

the Installation of W.M. which leads to it.


Before passing to one last point I want to take up, let me give the parallels briefly:-


In the making of a Freemason there must first be the man himself, the Circle,

No-number. Next comes that preparation in the heart which makes him the

Circle-potential. The Unknown God, transcendent within-all men has become immanent

in him. Then he takes his first step towards the door of the Lodge, The First step of a

Series, he separates himself from the vulgar crowd and becomes a free unit, "Free and

of Good Report."  He becomes polarized, realising dimly that to is not only Body but

also Spirit, he gains forward "In Strength."  The E.A. degree is founded upon the number

3, and in it, by the union of his opposites, he makes production possible, he reaches

"Plenty". In the F.C. degree he is able "To Establish" himself upon a sure foundation,

begins to realise his real self.  He gains control of matter and of "Worldly Possessions",

producing multiplication of ports.  The M.M. degree is founded on the number Seven,

which, so we saw represented full atomization.  Here the One Rock of the Quarry has

become the individualized multiplicity of prepared stones, ready for the building. Each

is a complete work in itself but has to die as such in order to reach a reunion with the

companions of its toil and take its place in the building of the Temple, the new cycle of

7 which it inaugurates.


Now for my last point. Several of the ancient Philosophers, including both both Plato

and Aristotle, hint that man is something more than the three-dimensional being that he

appears to be, at first sight. We cannot go into full evidence here, but Plato's beautiful

allegory of the men chained in a cave with the light behind them and seeing only their

own shadows and those of the passersby, thrown upon the flat surface of the opposite

wall, should be called to mind.  He tries to show how difficult it would be for one who

had escaped and returned to his chained companions to bring to them any realisation

of three dimensions. This seems to be a clear hint, and a study of Dimensional Masonry

bears it out.


Before entering the Lodge for the first time, the Candidate is symbolically unaware of

the existence of Spiritual Dimensions: Yes, in this three-dimensional world of ours, he

has reached a stage where the unfolding of spiritual consciousness has become for him

a definite aim.  He has, in this sense, become one-pointed.  So, when he comes to the

door of the Lodge, he enters upon an undimensional Euclidean Point, having neither

length, breadth nor thickness. Only at a later stage, when he has been restored to light,

is it rivealed to him that this point was attachad to and formd part of a straight line, a

one-dimensional instrument, held by a brother whose grip was separated from it by a

cross-piece, which, by its very position, indicated its two-dimensionality. Thus, the

candidate transcended the first dimension of space and became a two-dimensional



Advancing to the E. he passes through a symbolic figure of 9, 12, and 15 units,

indicating the Pythagorean proportion found in Euclid, 1, 47.  Thus he surpases the

second dimension of space and becomes a three-dimensional beinp capable of ruling

and preparing a plate surface by knocking off all superfluous knobs and excrescences,

roughly squaring the faces of the Ashlar in its rough form and preparing it for the hand

of the more expert workman. This stone is placed upon the pedestal of the J.W. and

should appear in the Ceremony in the N.E. corner of the Lodge.


Proceding onwards he enters upon the next stage upon an instrument which, although

it is used upon three-dimensional work, is itself two-dimensional and which can be used

to test the rectangularity of the previous advance. He then advance in a manner typical

of three-dimensional motion.  Under no conceivable circumstances can this advance

take place in less than three dimensions. Now he produces a smooth stone, the Perfect

Ashlar, which has place on the pedestal of tho S.W. ard appears ceremonially in the

S.E. corner of the Lodge.


Once more he passes on his way and enters upon, another stage of his quest, this time

upon an instrument which is used in the depicting and measurement of the three-

dimensional advance he has previously made.  He now reaches the supreme test.

Three stops he takes, each indicating an advance in a different direction and together

showing that conquest of the three-dimensional world has been achieved.  Then, boldly

he marches forward, and indicates, in a very beautiful piece of symbolism, his passage

into a new world, a world almost inconceivable to our untutored finite minds,

the FOURTH DIMENSION of space. The Stone he can now prepare is of a shape

normally outsite our consciousness.


It may be noted here that the W.T.'s in each degree of the Craft, and those of an I.M.,

indicate work in 1, 2, and 3 dimensions, the conquest, in each case, of the three

boundaries of our three dimensional existence, length, breadth and thickness.


This third stone is one over which there has been much wrangling, discussion and wild

speculation, yet its essential qualities would seem to be sufficiently obvious.  Most

writers tacitly accept the Perfect Ashlar as the last possible stage in the preparation of

of the stone, but this is true only of the three-dimensional world. If there are other

dimensions, there will be further stages in the preparation, and it is significant that we

find references to yet another stone, whose true place is on the Master's Pedestal, and,

it its ceremonial position, "With the centre", perpendicular, perpendicular, or perpend,

to three-dimensional space. This is the PERPEND ASHLAR, and the reason why it

cannot be seen in its completeness in the Lodge is that, existing in the Fourth

Dimension, the only part we could perceive would be a perfect cube, suspended in

space, to ever point to which it would be perpendicular. Mr. C.H. Hinton (in "The Fourth

Dimension" calls it the Tessoract.  It is to be noted that each Regular step is rectangular,

taken symbolically at right angles to the last position. We move a point to produce a

line; we move a line at right angles to the previous motion to obtain a superficies.  This

is the First Regular Step and from it we obtain a rectangular plane figure, a square; we

now move our square at right angles to both the former directions of motion and the

result is a solid cube, the Second Regular Step; and now we move this cube at right

angles to all three directions of motion already used, and produce; by our Third

Regular Step, a four-dimensionial figure, the Tesseract.  Even then the journey is

incomplete, for, as an I.M., the zealous brother uses tools belonging to the three

dimensions of our space to prepare himself to work freely in the four-dimensional

atmosphere of the Holy Royal Arch, wherein the whole scheme of Creation of Man as

a reflection or form created by God "in the image of His own Eternity" and the method

of the return of that image into the substance of T.G.A.O.T.U. in unfolded in the

consciousness of the Initiate.


Thus far I have tried to answer the first three questions put at the beginning of this

paper. Pythagoras, is, we have seen, fundamentally involved in our symbolism.  We

have taken a very hurried glance at the relevent portions of his Philosophy, and

we have seen the same fundamentals running through our rituals.


Now, very briefly to answer the fourth question.


We can, I think, say definitely that there is no Royal Road to Perfection. Each must find

a way for himself. But signposts are not wanting, for to those who choose to raise their

eyes from the plane of Matter, they point a clear way. The first and most important

comes early in our Masonic knowledge." This can only come from the age-old three-fold

method of advance being applied; CONCENTRATION, MEDITATION, CONTEMPLATION.

These we must apply daily to some portion of our Ceremonies, Tools and other

Symbols, seeking ever to find their irrer significance.


At no time in the Era of Recorded History has the application of these methods been

more difficult than it is to-day in the Western world, but at no time has so much help

been available to those who conscientiously attempt to apply them.  In this

Machine-tyrranized Age it is difficult to attain the necessary leisure, peace, quiet,

stillness and silence, and the forgetfulness of the rush and hurry of the world in its

search for the transient and worthless.  Yet, even now, there are many signs that the

world is getting tired of its own shallowness and sensationalism and is turning to things

that are more worth while.


Perhaps the time is nearer than we think when men will at last seek the Middle Chamber

of their own Tomple, to find the wages of Truth. Tired of chasing an illusion, thay may

seek the reality within, the Overself, which lies sheathed, as lies a grass-stalk in its husk,

within the husk of Personality, ready to be drawn out into tho Light of T.G.A.O.T.U.


Peace to All Beings, Amen.



History of Science, Mathematics, Technology, #158


Colombia Universite

158.  Cuneiform Tablet. Larsa (Tell Senkereh), Iraq, ca. 1820-1762 BCE. -- RBML, Plimpton Cuneiform 322 (See fuller description below.)
"Plimpton 322" is known throughout the world to those interested in the history of mathematics as a result of the interest that Otto Neugebauer, chair of Brown University's History of Mathematics Department, took in the tablet. In the early 1940s, he and his assistant Abraham Sachs interpreted it as containing what is known in mathematics as Pythagorean triples, integer solutions of the equation a2 + b2 = c2, a thousand years before the age of Pythagoras.

Recently, Dr. Eleanor Robson, an authority on Mesopotamian mathematics at the University of Cambridge, has made the case for a more mundane solution, arguing that the tablet was created as a teacher's aid, designed for generating problems involving right triangles and reciprocal pairs. Mr. Plimpton, who collected "our tools of learning" on a broad scale, would have been delighted with this interpretation, showing the work of an excellent teacher, not a lone genius a thousand years ahead of his time.