What’s the Real Secret Magic in the Magic Square?

Text copyright © Aug 27, 2012 Dr. Elizabeth A. Garner, All Rights Reserved




Dürer’s Melencolia I is the most debated image in all of art history, one of his most magical, and one of his most heavily encoded.


Durer's Melencolia and the secret code in the magic square
The 1514 Melencolia I

One of the fascinating symbols in Melencolia is what is known as the Magic Square, which is found in the upper right hand corner of the print on the wall, under the bell, above the winged woman.

The Magic Square



Example of magic square
An example of a numeric magic square

Numeric Magic Squares consist of a series of numbers arranged in a square in such a manner that the sum of each row, each column and of both the corner diagonals adds up to the same amount, which is called the Magic Constant.

Numeric Magic Squares may be divided into two categories:

  1. “Odd” Magic Squares, which means that there is an odd number of cells on each side of the Magic Square.
  2. “Even” Magic Squares, which means that there is an even number of cells on each side of the Magic Square. “Even” Magic Squares may be further divided into two sub-categories:
    • “singly even” Magic Squares, which means that the number of cells on each side of the Magic Square is evenly divisible by two, but not by four (e.g. 6 x 6 and 10 x 10 Magic Squares)
    • “doubly even” Magic Squares, which means that the number of cells on each side of the Magic Square is evenly divisible by both two and 4 (e.g. 4 x 4 and 8 x 8 magic squares)
The Magic Square
The magic square

Dürer’s magic square is a doubly even 4 x 4 square whose magic constant is 34. Dürer’s magic square has the additional property that the sums in any of the four quadrants, as well as the sum of the middle four numbers, are all 34 (Hunter and Madachy 1975, p. 24). It is thus a gnomon magic square. In addition, any pair of numbers symmetrically placed about the center of the square sums to 17, a property making the square even more magical.


Here’s a YouTube video link that explains it in more detail.  Unfortunately the math teacher did not know the difference between a painting and an engraving.


Anyone who has ever commented on Dürer’s magic square seems to believe that it’s inclusion in this composition has something to do with alchemy or Freemasonry or some occult phenomenon.

Dan Brown’s inclusion of Dürer’s magic square as part of the symbol clues in his book the Lost Symbol was fiction. Nothing could be further from the truth.  The Lost Symbol was a great FICTION story but it has done nothing but confuse the real coding that is held in Dürer’s Magic Square.


Do you like to play Sudoku or do you know someone who does?  Of course you do!  People in the Renaissance loved to play games as much as everyone does today.


Sudoku Puzzle
Example of a sudoku puzzle

Magic squares were common in medieval times and everyone loved them and many people owned them.  They were sold at market fairs all over Europe, and their availability was common.  They were considered amulets against disease, which was rampant in Europe. They were manufactured in tin for the masses and in silver or gold for the wealthy.

But the most important point is to understand that anyone who saw the magic square in this print in Dürer’s lifetime would not have connected the symbol with alchemy or something arcane.  They were games and amulets and fun.  Pilgrims often bought them, they were commonplace and would attract buyers.

Durer's Depiction of Medieval Pilgrim
One of Dürer’s famous depictions of a medieval pilgrim.

And anyone who saw the magic square in the print Melencolia was not going to suspect that Dürer was using steganography, the art and science of hiding messages in plain sight, to get a message across about what Melencolia is really about.

Dürer did do something unusual with the numbers in this magic square, which gives us a hint as to the message he was giving.  He rearranged the numbers from their usual order.  Agrippa (http://en.wikipedia.org/wiki/Marcus_Vipsanius_Agrippa) wrote much about magic squares in his Occulta Philosophia and claimed that the Tabula Jovis (http://www.scribd.com/doc/65262304/Adam-McLean-Dr-Rudds-Treatisse-on-Angel-Magick) had magic properties.  The Tabula Jovis configuration of the 4 x 4 square was as follows:


4  14  15 1

9    7   6  12

5  11  10  8

16    2    3  13

We can see that Durer changed his configuration dramatically from Agrippa’s.


The first thing that we must know about the Melencolia magic square is that Dürer originally created this composition with the “9” in the third row backwards.  We know this because there is one existing copy of the backwards “9” magic square in the British Museum.

Based upon how many copies of Melencolia are still existent, we can assume that Dürer changed his mind very quickly about how obvious the clue of the backwards “9” really was, and changed the copper plate to represent a forward “9.”

People don’t often understand that artists made mistakes and were very competent at fixing errors in woodblocks or copperplates in the Renaissance.  No one was perfect.  In woodblocks, the mistake would be cut out and a plug would be inserted and the correction made.  In engraved copperplates, the area would be buffed out and re-engraved.

So it wasn’t that big of a deal for Dürer to change the backwards “9” to a forwards “9.”


Look closely at the “6” under the correction of the “5” in the first box at left, third row from bottom. The “6” is clearly visible under the “5.”

But no one pays attention to the correction of the “5” above the “9.”  Dürer had originally place the number “6” into that block and historians seem to think that OOPS, he made a mistake.  Not likely.  Dürer was also known as a famous scientist and mathematician during his lifetime, so the likelihood that this master of math and master of engraving just happened to OOPS! Put a “6” where a “5” should go is somewhat ludicrous.

What IF Dürer was actually leaving us a message with this “mistake?”  What if he meant to have the image of the “6” visible to all when he corrected it to a “5?”  What IF THAT WAS THE MESSAGE:  whatever the #6 represented was somehow hidden?  If this is true, we don’t truly have a magic square, because another number has been entered into the equation.

But it’s a great way to hide a message!  Something that most people in his lifetime would just ignore, being delighted with “magic” of the numbered square adding up to 34.


And what no one has ever contemplated is this:  HOW is this magic square to be read?  Do we start at the upper left hand corner?  The lower left?  The upper right?  Or the lower right?  If Durer is passing a message steganographically, e.g. hidden in plain sight, the people who are supposed to get the message have to know how to read the code.

The reading of the magic square starts at the lower left hand corner.  What does that tell you?

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29 thoughts on “What’s the Real Secret Magic in the Magic Square?

  1. Durer’s magic square is upside down with respect to Agrippa’s.
    In the original backwards 9 square it appears to me that the backwards 9 would have originally been a 5 and likewise the 5 a correction of a frontwards 9.
    My question is if he did make not a mistake, then his engraving would have to have started with the 5 or 9 which, I presume begs another unanswerable question.

    Really enjoying your blog, I have only “discovered” it this evening.

  2. I surfed on dis topic only cuz i read Dan brown’s book however i dont understand how he deciphered d letters to d nos. can anybody pls. explain tat 2 me. Thanks .And great info. Keep it up.

    1. Thank you for your comment but you are totally wrong. The secrets to any of the what appears to be geometrical ssumbol in that print are purposeful deflections on the Duerer’s part and arrogance in showing hw completely adept they we at sung agh symbols in new ways t get OTHER messages across. in that print a noting to do with agh per se. But the mathmethetcians don’t like giving up their paradigms either. I would be in tereting i f you identified who this “great olver: is, for i was in deep discussion with someone who wha looking to publish stubbornly hs theory, and we just didn’t see yet to ey , biceasue i could prove he was wrong in the thesis, an he would have none f that.

      Please do identify this great solver.as I suspect I know who this person callus to be, I’m sure the rest of us would like to know what reigns as truh as published here with evidence and what and those of them are trying to remain with old paradigms dressed up with new sins



    1. Thank you so much!
      we are for truth in this world when most has become lies and total manipulation. And don’t miss the marvelous videos on my Youtube channel created by the marvelous Joe Kiernan. We add even more into those videos. My Channel is Elizabeth Garner but it would be good to search for Elizabeth Garner Durer on Youtube because there are otter Elizabeth Garners there 🙂

      1. This mathematician lived 32 year only😞😞
        Otherwise ….mathematics is a game for him.
        The GREAT MATHEMATICIAN OF INDIA.I salute him.

  3. Hi ive been following this blog with great interest!
    When one draw lines following the numeric order it actually gives one the freemason sign ?

    1. Therer are SO many mathematical and conspiracy theories about what is the real secret in the magic square and in the entire Melenoclia prime. IT HAS NOTHING TO DO WITH DEPRESSION, OF course the art has integral mathematical properies, Albrecth Durerer wanted to be known as a famous mathematician, not a painter, and he was an incredible mathematician, ALL great art follows mathematical principles of composition.

      But NO, Melenocolia has absolutely nothing to do with Freemaseons, I suggest you fid the series I published regarding the Ships of Melencolia to start getting a sense of what that one print is about. WE have found over 500 encodings in Melencolia alone and the print has very grave messages that are being given.

      Enjoy. Muck around the archives, search for all the melenolia articles, you’ll start getting a sense of the incredible things we have found in this print alone.



  4. A reference I have never heard anyone talk about yet. If you add all the numbers, each column 34 * 4 = 136. Now recognize one more number here? Yes the 1 from the title, add it to 136 to get 137. The hidden meaning suddenly turns to astonishing.
    Using two radii to divide a circle according to the golden ratio yields sectors of approximately 137° (the golden angle). Its a number with huge significance to mathematicians and physicists. In physics 137 is the fine structure constant, a dimensionless physical constant, combining three cosmological constants e2/h bar c. WAY way beyond anything remotely known back then… It’s independent of units, its a perfect number to signal intelligence to other intelligent beings! Also used to understand the motion of electrons around atoms. The fine structure constant of physics continues to convince esoterists that the universe has numerological fine tuning and another example the age of the universe could be considered as roughly 137 times the square of a myriad of years. The Bible says that Ishmael lived to be 137 years old. But that’s reaching. Mostly it’s considered among top particle physicists, like Feinmann to be a perfect number, a magic number even.

    1. Dear Opie,

      It never ceases to astonish me how everyone connected with math finds all sorts of new and weird theories about any of the math, and of the perspective, anything that has to do with math stuff in the duress’ artworks, especially with Melencolia. I’ve been working with experts in math for a long time.

      Bottom line, ALL RENAISSANCE ARTISTS had to be experts in math, they couldn’t produce such stunning artworks without being experts in math, they were well aware of the golden mean, etc, and how these were constants in all life forms. Albrecht WAS an expert in math, that’s how he wanted to be remembered, as a famous mathematician, NOT as a painter or an illustrator and he was very angry about that not being his legacy. So was Margret an expert in math. Albrecht bought the Berhard Walters house, the second observatory in all of Europe, specifically for the observatory AND THE ESOTERIC BOOKS ON MATH AND OTHER SUBJECTS in Walters private library, although there is discrepant information as to how many books he did get with the house purchase, since the villain, Wilibald Pirkheimer, his best friend was the City Librarian, and it is claimed that Pirkheimer was in charge of all the Walters library, a spurious coverup. Pirkheimer did much to change the real truth, even after Albrecht was dead.

      I have many articles here about the Durers knowledge of math, how they used it, Albrechts incredible need to find the ultimate Italian teacher in perspective. In NO WAY SHAP OR FORM WERE THE DURERS SIGNALLING TO “OTHER INTELLIGENT BEINGS” IF YOU ARE TRYING to infer space aliens. They were absolutely messaging to very certain and targeted audiences, all who WERE ALSO EXPERTS IN MATH. YOU MAKE ASSUMPTIONS THAT THE DURERS didn’t know the incredible knowledge connected with Pi, Phi, and many other mathematical constructs, for they surely DID have this knowledge, they knew GREEK very well, they both had studied Euclid, Ptlomey, Aristotle, and many other mathematicians but in a context different from what you imply.

      They didn’t have TV and internet, and other distractions, they studied the cosmology of the sky always, they KNEW astrophysics and chemistry except it was called astrology and alchemy back then.
      the ONE from the title is part of the greatest art hoax in history, it’s an inscription, NOT a title AND I’ve published that information here, you just need to go to the archives to find those articles. The fact that the ONE AS YOU CALL IT could never have been used in the way you are suggesting. Albrecht was a master in LETTERING, HE PUBLISHED A TREATISE ON IT, IT’S THE LETTER I (-the Latin letter used to represent the letter J that was not in Latin) thus your theory falls down completely on its face. Sorry. It’s NOT THE NUMBER one, it’s the letter I, and it’s THE mistake that all other researchers in the past have made, that’s it’s a ONE.

      Your hypothesis falls down completely but its a good example of how zillions of people attempt to find these supposed grand new theories, ESPECIALLY IN MELENCOLIA, for it’s fun for all of you-BUT IT’S NOT THE TRUTH And neither is the hooey that mathematicians all over the world attempt over and over and over again to publish and republish about all sorts of math secrets.

      MELENCOLIA HAS OVER 500 HIDDEN ENCODINGS IN IT, IT’S A VERY SPECIALIZED MESSAGING SYSTEM TO, AS I SAID, A VERY SPECIAL TARGETED AUDIENCE SET, WARNINGS! The books and the movies are in process, you’ll find out al the truths then. I’d suggest you specifically look at the Ships of Melencolia, you might get on the right track. In fact, the Durers’ make a mathematical mistake in Melencolia in one of the symbols for they thought one contemporary mathematician had found a very specialized math answer,unfortunately that mathematician has been proven false, but in the Durers time, the target audience would have understood the message that was being given for they were aware of this mathematician also.

      Please come back, I am impressed with your attempt at finding something radically new, and it was well stated, I WISH YOUR ANALYSIS WAS TRUE, IT WOULD HAVE THRILLED ME, BUT WE CAN’T USE FALSE ASSUMPTIONS JUST TO BE AMUSED AND ASTONISHED.

      HOWEVER YOU HAVE GIVEN ME AN INTERESTING IDEA. Since I DO know where all the encodings are, I will now go back and see if I can find an embedded stray ONE that might be there. It would only be in certain places, it’s an interesting challenge, one that WOULD THEN BLOW ME AWAY. If i find it I will publish your comment as being the source of bringing this potentially to the world’s attention and perhaps we might all find out what Bernhard Walters esoteric books did actually contain, of which the Durers might have taken advantage. I promise I will look hard very soon.

      All the Best,


  5. Thank you for your most interesting article. You may also like these tribute squares:
    For information, I have recently come across another blog by Glen Westmore at http://www.glennwestmore.com.au/
    Glen points out that “the numbers 1 and 4 on either side of the year “15 14” correspond to the letters A and D, the artist’s initials.”
    William Walkington recently posted..A MAGIC SQUARE TRIBUTE TO DÜRER, 500+ YEARS AFTER MELENCOLIA IMy Profile

    1. I think if you read all the articles regarding what was hidden in each square one doesn’t have to go into allegory or creating hidden meanings about numbers corresponding to letters.

      1. “Did Dürer Intentionally Show Only His Second-Best Magic Square?” is the title of a paper dated 25th December 2009, written by William H. Press of the University of Texas at Austin: http://numerical.recipes/whp/notes/DurerSquare.pdf

        The paper uses a mathematical approach to suggest that Dürer purposely used the numbers 1 and 4 to indicate his initials AD. Judging from the source and content I would be tempted to take this work seriously.

        Of course, the interpretation of symbols inevitably leads to multiple interpretations, and everyone will have his or her own personal preference.

        Perhaps the positions of the 1 and 4 were quite accidental, or Dürer just wanted to state “Anno Domini” for the date of his creation of Melencolia I? I do not pretend to know for sure, but who can?

        1. Melencolia is THE most written about artwork in all of history. It’s insane what people come up with and everyone with a smidgen of interest or math degrees has analyzed the magic square to death, every pun intended. Everyone loves to think they’ve cracked a mystery. Of course the print can be analyzed mathematically in its construction because the REALLY important part of the mathematics are the slight perspective shifts that indicate the message clues

          There is NOTHING allegorical in Melancholia or any other of the Durers’ artworks. Just isn’t so. Everything is hidden in plain sight or it’s micro engraved encodings that the select audiences to which the messages were targeted would know the meanings. Highly probably these prints were sold with magnifying glasses so the owner could amuse themselves with the microencodings, there was no TV! Staring at stars gets boring after a while. Drinking and carousing didn’t.

          Melencolia has THREE levels of messages and CAN NOT EVER be understood as to the second level, which I have revealed WITHOUT pairing it with the messages given in the St. Jerome in the Study print of 1514.

          The magic square was the SUDUKO of it’s time. Everyone loved it, everyone had a magic square amulet, they were sold at fairs. Silver for the rich, tin for the rest, the peasants, the workers, the pilgrims.

          The Durers purposefully worked this magic square to have the year 1514 in the square. Combined with other clues, which I have written about, it helps to capture the exact time of death of his mother, Barbara, who is the winged woman. We know this from Albrecht’s private diary where he recorded the exact moment of her death.

          Ask yourself: Why would the Durers NEED to encode the initials AD in the magic square. THEY HAVE A MONOGRAM which identifies the creators. Why waste the energy or time doing that when there was so much other information they needed to impart?

          Never ceases to amaze me the ongoing writings about Melencholia that just aren’t true. It’s an industry of blather.



          1. Indeed, the separate AD monogram could suggest that the numbers 1 and 4 do not signify these letters. Nevertheless, it is a question of individual appreciation, and the opinions of William H. Press and Glenn Westmore should be respected as such. My initial comment only intended to add further information and no provocation was meant.

            I was wondering why you always refer to Albrecht Dürer as the Durers? Are you implying that he had a double personality? It is true that the first version of his square used a reversed 9 that he corrected later, and that his first version was unlikely to be a mistake… But we also know that he had a caustic sense of humour, as illustrated by his “Old Bags with Money” sketch which appeared on the reverse side of his “Portrait of a Young Man.”

            In my opinion Melencolia I is not the hoax that you suggest, but almost certainly an art puzzle to be contemplated and interpreted as we wish.

            Hoping that one day you will become reconciled with mathematicians!

          2. Well William

            You apparently DON’T read the articles here or you would know exactly why I refer to the TWO co-artists as the Durers. And the secret of the backwards 9 and why it was corrected.

            You are entitled to your opinions, they are like a certain body part, everyone has one.

            Both Albrecht and Margret had caustic senses of humor, but the artworks are giving specific messages.

            This is not an argument, it’s facts.

            However, many people don’t like facts, they prefer to hold opinions.

            All the best

  6. Thank you for your article that I have just discovered. I am sure that there is always something new to find on Melencolia I. Until now I have been focused on the symbolism of the magic square and the sphere, and have written two pages on the subject that may be of interest.
    The first page was written in French and can be found here:
    A more recent page in English is a magic square tribute to Dürer, 500+ years after the creation of Melencolia I, which includes contributions from several mathematicians:
    Thank you again and keep up your good work!

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