Lately, I've been thinking that the concept of a commutative algebraic theory is really, really important. So I'm curious; who had the honor of first discovering this concept? In particular, I'd like to know:
- Which mathematician was the first to explicitly describe the notion of a commutative algebraic theory?
- What was the name of his/her paper?
The nLab homepage has a focus on higher category theory, and this subject has a long history, certainly not due to just one person, or one paper. The commutativity here is not a new discovery, thinking of the development of, say, commutative algebra, where in particular polynomial rings $K[x_1,\ldots ,x_n]$ and rings of integers $\mathcal{O}_K$ have been studied (for algebraic geometry, resp. algebraic number theory).
The link you have given generalises commutative monoids and abelian groups. The history of group theory and commutative groups has also a long development, and here the name of one particular person is well-known: Niels Henrik Abel. Abelian groups were named by Camille Jordan after Abel, because Abel found that the commutativity of the group of a polynomial implies that the roots of the polynomial can be calculated by using radicals.
The link says the following to your question: The notion of commutative algebraic theory was formulated in terms of monads by Anders Kock (1970).