Look, gnomes fill a role in D&D that is more important than all the mythic characters that might or might not be gnomes (because, honestly, if you're looking for a consistent definition of words, myths are not going to back you up on things -- they defy definition by their very nature as stories about magical things).
They fill a
trope.
Hero = Human (or half-elf): They are the spunky can-do heroes who overcome their frail mortality to save the day for a cause greater than themselves!
Lancer = High Elf (or tiefling, or half-orc): They are ancient and arrogant and all-knowing and quite peaceful and kind of badass, but certainly better than you.
Smart Guy = GNOME (or eladrin, or halfling sneaky-style): They are clever and smart and tricky and sneaky and genius.
Big Guy = Dwarf (or half-orc, or dragonbobs): Tough and strong and noble and boisterous and affectionate.
The Chick = Halfling (hobbit-style, or gnome): They believe in the mission, pull the team together, compliment the hero's fortitude and really believe in the cause!
What REALLY happened, in the history of the game, was that halflings, in scrounging about for a trope that wasn't "the chick" (as Bilbo and Frodo and Sam most certainly were, and was determined in 3e to be a race of creatures that didn't go on adventures), landed on the physical counterpart to the gnome's magical Smart Guy, and promptly the gnomes were forgotten about, since they were never drawn in skintight leather rogue-wear with a come-hither gaze like
certain halflings, and, well,
sex sells.
Okay, there's a lot of alternate folks vying for that trope, and this certainly isn't the Definitive Word on it (tropes, like myths, resist a codified and immutable definition). Certainly a lot of folks legit love the "sneaky tricksy halfling" archetype in ways that the "intelligent, wise, smart-ass gnome" archetype never quite got (for whatever...reasons...).
But some of my favorite characters have been gnomes, from the 2e illusionist/thief who stole and tried to ride a pig, to my 4e gnome assassin who delighted in the remains of his enemies, to my character starting tomorrow: a gnome artificer in an Eberron game that gets along better with machines than she does with people.
PS: Bonus Round:
The Sixth Ranger = Kobold (or gnome, or half-orc)