Independent, unconnected reinvention of the same notation for the same problem is a general, well-documented pattern in mathematics and physics — not something specific to blind mathematicians

history-of-notationhcinotationindependent-inventiongeneral-theory

Zhang, Zamfirescu-Pereira, Glassman, Masson and Arawjo's 2026 comparative-historical study of notation development ("How Notations Evolve," arXiv:2602.01525) documents that ordinary, sighted mathematicians and physicists have repeatedly, independently invented notation for the same problem with no transmission between them: Newton and Leibniz's rival calculus notations; Feynman–Dyson diagrams alongside Koba & Takeda's contemporaneous "transition diagrams," developed independently in Japan for the same purpose; and Dalton's atom diagrams alongside Berzelius' chemical formulas. The paper's account is that a notation emerges to manage complexity and coordinate action, so a recurring, unmet need can prompt independent, sometimes-contemporaneous invention wherever it recurs.

This bears directly on the vault's own recurring pattern among blind mathematicians — claim-blind-mathematicians-independently-reinvented-private-notation, claim-salinas-and-nemeth-independently-invented-braille-math-codes — which had been held as [unverified-historical] partly because no parallel from sighted mathematics had been found to test whether the recurrence was blindness-specific or a general property of notation (see item 3 of question-why-blind-math-notation-doesnt-transmit-while-method-does). On this evidence, independent invention itself is not distinctive to blindness — it looks like a general pattern wherever a real need recurs before any shared apparatus exists. What the sighted parallels do not settle is the blind-mathematician cases' duration of non-transmission. Zhang et al. document the fact of independent invention but attach no transmission-delay figures to these examples; their Stage 2 account says only that dispersion "typically follows an initial publication in the form of a book, academic journal, or mass media release." The blind-mathematician codes are reported staying unknown even to other blind mathematicians for years — whether the sighted parallels travelled faster, slower, or comparably is a question this source does not answer, and Newton's own fluxional notation is the obvious case to check first, given how long the priority dispute with Leibniz turned on what had and had not appeared in print.