men-dheh₁-₂
“to fix in mind, remember”memory, memoir, commemorate
Compound giving Latin memoria, English memory, memoir, commemorate, memorial, immemorial.
Discussion
The PIE compound *men-dheh₁- (to fix in mind, to set one's thought upon) combines the root *men- (to think, to remember) with *dʰeh₁- (to put, to place), yielding the literal meaning "to place in the mind" — to remember, to learn, to fix knowledge in memory.
Greek manthánein (μανθάνειν, "to learn") continues the compound, with the derivative máthēma (μάθημα, "that which is learned, a lesson") giving English mathematics — literally "the things learned," the discipline par excellence of learned knowledge. The word polymath ("one who has learned many things") and the suffix -mathy/-mathic preserve the learning sense.
The connection between "placing in mind" and "learning" is transparent: to learn IS to place knowledge in the mind, to fix it there by repeated placement. The PIE compound captured the cognitive act of memorisation as a physical metaphor: the mind is a surface, knowledge is an object, and learning is the act of placing the object on the surface.
The base root *men- independently gave Latin mēns (mind), mentor (a counsellor — from the Homeric character Mentor), mental, mention, monument (a thing that causes remembering), and the combining form -ment (the result of a mental/active process). English mind (OE gemynd) descends from a related Germanic formation.
Sanskrit medhā́ (wisdom, intelligence) continues the compound in Indo-Iranian, appearing in Vedic texts as a central intellectual virtue.
The word's most famous descendant — mathematics — encodes a remarkable claim: that mathematics is the paradigm case of learning, the knowledge that is most thoroughly "placed in the mind." The ancient Greeks who named their most abstract discipline after the PIE compound for "mind-placing" were making a philosophical statement that still defines mathematical education.