The roots √UMU and variant √UGU were often assigned a negative sense, either as elaborations on the base root negative √Ū or sometimes (especially in the case of √UGU) serving as its source. The earliest iteration of these more elaborate negative roots was ᴱ√UMU or ᴱ√UVU in the Qenya Lexicon of the 1910s with derivatives like the negative verb ᴱQ. um- or ᴱQ. uv- as well as ᴱQ. ūvanimo “monster” (QL/98); ᴱQ. munta “nothing” from the Qenya Grammar of the 1920s was probably related (PE14/48, 81).
The Etymologies of the 1930s had negative stems ᴹ√UMU and ᴹ√UGU with derivatives like the negative verb ᴹQ. um- as well as ᴹQ. úmea “evil” (Ety/UGU; UMU). This document also had inverted forms ᴹ√MŪ and ᴹ√GŪ, the latter the basis for the negative prefix ᴹQ. ú- with a bad or evil connotation (Ety/GŪ; MŪ). Finally both √UMU and √UGU were mentioned a number of times in later writings in connection to negation (PE17/143, 172; VT49/29). See the entry on negative √Ū and the entry on Quenya negation for further information.
This root was the basis for Elvish words for “counting” for much of Tolkien’s life. The earliest indications of the root are in primitive ᴱ✶notta > ᴱN. noth “number” in Early Noldorin word lists of the 1920s, along with related words like ᴱN. gonod- “count” (PE13/145, 151); the revision of noth “number” to nath may represent some uncertainty on its initial form, but it seems Tolkien restored noth in a marginal note (PE13/150, 151).
The root reappeared as ᴹ√NOT “count, reckon” in The Etymologies of the 1930s with a number of derivatives of similar meaning, the most notable being N. arnœdiad or arnediad “innumerable, countless, endless” (Ety/NOT) as in Nirnaeth Arnoediad “[Battle of] Tears Unnumbered”, a name Tolkien introduced in the 1930s and with minor variations (Nirnaith vs. Nirnaeth, Arnediad vs. Arnoediad) retained thereafter. The root √NOT itself appeared several times in Tolkien’s later writings (PE17/62; PE19/86), most notably as the basis for Q. únótima “numberless” from the Q. Namárië poem (LotR/377).