Magma is one of those beautiful words of Greek origin (μάγμα) that arouses the child and the wild in me, making me think of volcanoes. I just found out, though, that it is also used in mathematics to mean a type of algebraic structure (a set paired with a binary operation on it)! I am very curious how this name was picked for this particular algebraic structure (which is also called by groupoid). Wikipedia attributes the coining of this term to Nicolas Bourbaki, but does not mention how they arrived at such a name. I have not been able to find the specific etymology of this sense anywhere else. What is its origin?
It may be a pun. Looking up magma in the French wikipedia*, another name for magma in French is groupoïde de Ore†. Here Ore is a Norwegian mathematician, but ore in English is mineral-bearing rock, whereas magma (in both English and French) is molten rock.
Would Bourbaki have based a mathematical term on this pun? I'm not in a good position to judge; maybe somebody else could comment on this.
* Since Bourbaki was a pen name used by a group of French mathematicians, this is the right language to search in.
† There is also a groupoïde de Brandt, also called a groupoid in English, which would explain why Bourbaki felt compelled to coin a new name.
Google says of the etymology of magma
late Middle English (in the sense ‘residue of dregs after evaporation or pressing of a semi-liquid substance’): via Latin from Greek magma (from massein ‘knead’).
I have a hard time imagining an algebraic structure with less structure than a magma, so "residue of dregs" seems fitting. Once you boil away all the structure, you are left with a magma. Historically, I have nothing to suggest that this is accurate.
I am expressing my personal view without a historical excursus. Geological magma associates with a melted, liquid, formless substance. 'Algebraic magma' requires only the closure property: result of an operation applied to a set is in the set. Citation: Bourbaki, N. Elements of Mathematics, Algebra I, Chapters 1-3. Paris: Hermann, Massachusetts: Addison-Wesley, 1974. Paragraph LAWS OF COMPOSITION, p. 1, Definition 1. "Let E be a set. A mapping f of E x E into E is called a law of composition on E. The value f(x, y) of f for an ordered pair (x, y ) [belonging to] E x E is called the composition of x and y under this law. A set with a law of composition is called a magma". As for identity, inverse, associativity, commutativity, then magma does not require them. Pretty unstructured! One begins gradually and in different combinations adding identity and/or other properties. This embeds "some structure": semigroup, monoid, group, ... The 'algebraic magma' is crystalizing! The origin is a "bouillon" from which the crystal of life is growing. I am not sure who has applied the term first time but it is a very impressive comparative image. A poet could envy.
protected by tchrist♦ Oct 28 '17 at 18:54
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