The Distinction Between Euler’s Method and the Rowaymian List of 144: Clarifying a Common Misconception

Prologue

In certain non-specialist writings, and even in the output of some AI language models, a methodological confusion often arises between what is historically known as Euler’s method of construction on the one hand, and my own Rowaymian List of 144 on the other.

Because this conflation recurs and leads to inaccurate conclusions, I find it necessary to provide this clarification. Euler did not leave behind any fixed list of magic squares; he only proposed a constructive method. By contrast, my classification of 144 squares is an independent work built upon entirely different criteria.

I. Euler’s Method

Attribution: Leonhard Euler (1707–1783), Swiss mathematician.

Contribution: Euler did not produce a list of magic squares with a fixed number. Rather, he developed a constructive method based on the superposition of two orthogonal Latin squares, which in some cases can generate magic squares (particularly of doubly even order).

Limitations: Euler’s method produces only a subset of magic squares, not the full universe.

Important note: Nowhere in the scholarly record is there mention of an “Eulerian list” of 144 (or any fixed number). Such a claim is a later projection without peer-reviewed basis.

II. The Rowaymian List of 144

Attribution: Abu Rowaym (contemporary).

Origin: Derived from Frénicle’s complete catalog of 880 fundamental 4×4 magic squares.

Methodology: I applied specific criteria of fixation and structural classification, grounded in geometric symmetries and internal properties of the squares—not in Euler’s method.

Result: From this filtering process emerged a distinctive subset of 144 squares that form a coherent structural classification.

Significance: This list is an original, independent contribution. It is not a translation, reduction, or adaptation of Euler’s work.

III. Sources of Confusion

1. Method vs. List:

Euler introduced a method of construction. My Rowaymian 144 is a classified list.

2. The “All Eulerian” claim:

It is incorrect to say that all 144 are Eulerian. Some may coincidentally align with Euler’s construction, but inclusion in my list is never based on that criterion.

3. Historical projection:

To retroactively link my 144 classification to Euler’s 18th-century method is unsound. There exists no academic or peer-reviewed publication that establishes such a connection.

Conclusion

Euler: Provided a constructive method, not a fixed catalog.

Abu Rowaym (myself): Produced the Rowaymian List of 144 as a structural sub-classification within Frénicle’s 880.

Necessary separation: Any conflation between the two creates historical and mathematical confusion without scholarly foundation.

Thus, I affirm that the Rowaymian 144 are not “Eulerian,” neither in origin nor in methodology, but rather the outcome of my own criteria and contemporary classification.