Re: Naturally,

Etymonline has this to say, quoted verbatim:

matrix
1373, from O.Fr. matrice, from L. matrix (gen. matricis) “pregnant animal,” in L.L. “womb,” also “source, origin,” from mater (gen. matris) “mother.” Sense of “place or medium where something is developed” is first recorded 1555; sense of “embedding or enclosing mass” first recorded 1641. Logical sense of “array of possible combinations of truth-values” is attested from 1914.

Merriam-Webster agrees with the etymology, and has quite a few other meanings that seem to stem much more naturally from it.

Special bonus for playing:

meconium
“fecal discharge from a newborn infant,” 1706, from L. meconium “excrement of a newborn child,” from Gk. mekonion, lit. “poppy-juice, opium,” dim. of mekon “poppy” (cognate with O.C.S. maku, Ger. Mohn “poppy”). So called by classical physicians for its resemblance

Re: That’s definitely weird

For your first point, allow me to quote Tom Lehrer. I think it adequately explains everything:
“some of you may have had occasion to run into mathematicians and to wonder therefore how they got that way, and here, in partial explanation perhaps, is [this] story”.

As for your second point – no, please don’t. I never appreciated that word in the first place and I really don’t feel like hosting it in my LJ.

Re: Pregnant Animal?

I’ll elaborate then. The earlier meanings of Matrix revolve around “something within or from which something else originates, develops, or takes form” – whether we’re talking about soil in which crystals are formed, extracellular substances in which cells are embedded, or machine-wrought pods in which humans dream their dreams of a lost civilization. The mathematical concept of matrices is a much later formation. I’m not sure how the jump was made, but I’m guessing the mathematical definition of matrix – “a rectangular array of mathematical elements that can be combined to form sums and products” – is a hint. The matrix exists only to give birth to new sums and products.