Freemasonry, Mysticism, and Mathematics

Of all of the great scientific minds throughout history, our fraternity chose one in particular to mention in our esteemed rites – the name of Pythagoras of Samos.  Pythagoras was a Greek philosopher, mystic and mathematician from the Ionian tribe who is believed to have lived between 495 BCE and 570 CE, but many of us may remember his name from early schooling when we were taught the “Pythagorean theorem.”  The concept that

“…in a right-angled triangle the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides…”  [1]    

But why do Freemasons honor this man in their rites?  Is it simply a reference to his role in one of the “seven liberal arts”?   Is it because he was the leader of a fraternity much like our own in which there were initiation rites and formal degrees?  What about his reputed reputation as a mystic?  Is there a relationship that exists between mysticism and mathematics?

A detailed study of this last question would fill a library, and although you may never have considered mathematics to be a spiritual pursuit, there are many written essays that do just that.  There is a beauty to mathematics, and while I cannot, in this short essay, do justice to this exploration, I will do my best to urge you on to further study.

I personally believe that Pythagoras is mentioned in our rites not simply because of his mathematical acumen, but specifically because of his belief that “All things are numbers.”[2] Pythagoras felt that there was an affinity between numbers and reality that directly pointed to a higher power (or as we say, to the GAOTU).  By the way, another great scientific mind mirrored this same thought; Galileo himself wrote that the “grand book” of the universe “…is written in the language of mathematics, and it’s characters are triangles, circles and other geometric figures without which it is humanly impossible to understand a single word of it.”[3]

“That mathematics, in common with the other humanities, can lead us beyond ordinary existence, and can show us something of the structure in which all creation hangs together, is no new idea.”[4]  “The ability of mathematics to provide frameworks of reality and of action, and its ability to change our perception of what is, is very great.”[5]  But what is more important is the fact that “Mathematical truth is independent of human judgment.  Mathematical reality is there to be discovered or observed.”[6]    Math is true and does not depend upon judgment, that is, 1 + 1 is always 2.  The square root of 25 is always 5.  29 is a prime number, 27 is not.  And despite the ever-changing appearances of reality, mathematics serves as a stalwart marker of reality.  It is the fixed point within a circle. 

So mathematics appears to be an unchanging reflection of reality – a map used by the GAOTU for us to discover and reflect upon  – a mystical endeavor open to anyone who cares to consider it. Is this what Pythagoras meant when he said that “All is numbers”?  I believe so, and I believe that here too is the reason that he is given such recognition in the Masonic rites.  Mathematics is more than a tool used to count, or a way to record dimensions.  Mathematics is a signpost for anyone who wishes to better understand their world, and their own reality. 

Freemasonry is a fraternity that is veiled in allegory.  Its rituals reflect man’s passage through life leading from birth to his ultimate reconnection with the Great Architect.  In our second degree we are advised to study the seven liberal arts – which includes mathematics.  Perhaps we should consider that this suggestion is not a simple directive to know how to calculate, but how to better know that there is “something more behind the curtain.”

Respectfully submitted,

Bro. Tavit Smith    

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[1] http://en.wikipedia.org/wiki/Pythagoras

[2] http://www.mathopenref.com/pythagoras.html

[3] Vico, Opere, ed. R. Parenti (Naples, 1972), I 83. “Vico’s Concept of Knowledge”, in his against the Current (New York, 1980), pp. 111-19.

[4] Essays in humanistic Mathematics, ed. Alvin M. White, The Mathematical Association of America/ Notes Number 2.  1993

[5] Ibid, pg. 10

[6] Ibid, pg. 29.