In De sectionibus conicis, 1655, Wallis wrote let this be the sign of an infinite number and used a sideways eight, then reused it through his Arithmetica Infinitorum. He left no rationale. Candidates: the Roman numeral for 1,000, CIƆ, which doubled as many, attested on a hand abacus in Paris; or lowercase omega, the alphabet's last letter, a standing metaphor for the ultimate. Euler later used an open variant for absolute infinity. Bernoulli had named the curve lemniscate, ribbon, decades earlier, for a different shape entirely.
The tilted eight appears in alchemical usage before Wallis, standing for eternity, and rode tarot's Magician card into the twentieth century as a spiritual icon before the jewelry industry adopted it wholesale. One lineage even claims the infinity sign derives from a double-looped ouroboros, the serpent looped once before eating its tail. Mathematics borrowed a symbol the mystics had already worn out, and the mystics promptly borrowed it back.
The claim: infinity's mark conquered because its author left it blank, a symbol with no documented meaning is infinitely assignable, and Wallis's silence functions like the symbol itself: unbounded. Verdict: compare the peace sign, whose designer explained everything and lost control anyway, and the swastika, whose meaning was fixed and then stolen. Meaning is always assigned by the loudest later user. Wallis just made the assignment easy by dying quiet.
If the symbol's origin is a blank, what are all the necklaces actually citing?