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normalis already meant right-angled in classical Latin; for example, angulus normalis appears in the first century text De institutione oratoria (volume XI, paragraph 3.141) by Marcus Fabius Quintilia …

The suffix "-oid" means the same as "quasi", so "resembling", "like". A groupoid is a quasi-group, like a group. There are hundreds of words in that category, covering many scientific disciplines. In …

I found this footnote on page 195 of Fricke and Klein's Vorlesungen über die Theorie der automorphen Functionen (1897): Translation: The term "homomorphic" seems more appropriate than the previously …

The name of the curve is cochleoid (= shell-shaped rather than cardioid = heart-shaped). I compare the two below (gold = cochleoid, blue = cardioid). The distinction shell/heart refers to the addition …

Let me address the question "what happens if some name it has already been used but you don't agree with the choice?", by giving a recent example from (mathematical) physics. The 2012 experiment that …

Free objects were first defined* by MacLane in Duality for Groups. That paper gives "free" a curious political context, I quote from page 486: Call the dual (in this sense) of a free (nonabelian) …

Well, Riemann himself says "I denote this function by $\zeta(s)$" ("Die Function [...] bezeichne ich durch $\zeta(s)$"), so I would think the choice of which letter to use for this function was his. …

An extensive discussion of the origin of "Menge" is given in Earliest Known Uses of Some of the Words of Mathematics (scroll down to "Set and Set Theory"). Cantor's (1880) Über unendliche linear Punkt …

The name of an $n\times n$ matrix with positive real elements satisfying $a_{ij}=1/a_{ji}$ for all $i,j\in\{1,2,\ldots n\}$ is reciprocal matrix. A consistent reciprocal matrix has elements of the for …

There may be an earlier source, but Adolf Hurwitz 1897 is one upper bound: A. Hurwitz, Über die Erzeugung der Invarianten durch Integration, Nachr. Ges. Wiss. Göttingen (1897), 71–90. Hurwitz’s paper …

This answer refers to what is probably the first appearance of an $R$-matrix in the context of quantum mechanical scattering theory. Quite possibly the later appearances in the context of the inverse …

It's the same function. I checked with Maple 15: $r := RiemannTheta([0.5+I, 2 I], Matrix(2, 2, [[I, 0], [0, I]]), [])$ $evalf(r)$ $-6.586149971*10^6-2.132900065*10^{-8} I$ Mathematica 8 gives $N[ …

This echos the 2017 comments, but since the question has now been bumped to the front page it might be helpful to give the actual source in Maslov's book [1]. [1] V.P. Maslov, Perturbation Theory …

The name was coined by Barry Simon in this 1982 article (page 487): The Ten Martini Problem: The almost Mathieu operator has a Cantor spectrum. The name comes from the fact that Mark Kac* has …

I guess you'll find much of what you would like to know in this 2004 paper by Jacques Carette (published here): We give the first formal definition of the concept of simplification for general …