10,000 has an old, specific English name that's fallen almost entirely out of literal use but survives as a common word with a shifted meaning: a myriad. The term comes directly from the ancient Greek "murias" (μυριάς), meaning precisely ten thousand — not a vague "a lot," but a specific counting unit, the largest single named quantity in common use in classical Greek arithmetic, since Greek numeral notation of the era had no easy, compact way to represent numbers meaningfully larger than this without resorting to combinations of myriads.
That specific limitation is exactly what motivated one of the more famous applications of the term in the history of mathematics: Archimedes' treatise The Sand Reckoner (3rd century BCE), in which he set out to estimate — and demonstrate that it was possible to meaningfully name — a number large enough to count every grain of sand that could fit in the entire universe as the Greeks understood its scale. To do this, Archimedes had to invent an extended numbering system built on myriads of myriads (a "myriad myriad" being 100,000,000, itself used as a new base unit for counting still-larger quantities), specifically because the existing Greek numeral system topped out functionally at a single myriad and had no built-in mechanism for anything larger. It's a genuinely early and sophisticated example of a mathematician recognizing a real limitation in existing notation and constructing a systematic extension to solve it, roughly two thousand years before modern scientific notation solved the same fundamental problem in a different way.
The English word "myriad" survives today almost exclusively in its looser, adjectival sense — "a myriad of options," meaning simply "very many," rather than the precise ancient numeral value of exactly 10,000. This shift from a precise counting term to a vague intensifier is a common pattern in language generally (similar drift happened with words like "hundred" in some older usages), and it's worth knowing the word's original, exact mathematical meaning specifically because it illustrates how a genuinely precise ancient counting unit can survive in modern language purely as a figure of speech, stripped of its original numerical specificity.
As a plain integer, 10,000 = 10⁴, the fourth power of ten, factoring as 2⁴ × 5⁴ — a clean, symmetric factorization reflecting its status as a round power-of-ten milestone, giving it twenty-five divisors total via the standard formula ((4+1)×(4+1)=25). It's a perfect square (100² = 10,000) and, notably, also expressible as a perfect fourth power (10⁴ directly), a genuinely double status shared by every whole power of ten with an even exponent.
10,000 also marks a specific naming threshold in the traditional East Asian numbering systems used in Chinese, Japanese, and Korean — where large numbers are grouped in units of 10,000 (万/万/만, "wan"/"man") rather than the Western convention of grouping by thousands, a structural difference that means the natural "next big milestone word" after a thousand in these languages arrives at ten thousand rather than at one million, a genuinely different linguistic grouping convention worth knowing when translating large numbers between these systems.
This grouping difference has a real, practical consequence worth flagging: translating a number like "one million" directly between English and Chinese, Japanese, or Korean isn't simply a matter of substituting the equivalent word, since these languages naturally express one million as "one hundred wan/man" (100 × 10,000) rather than having an equally common single native word occupying exactly the same conceptual slot as the English "million" — a genuine structural mismatch between numbering systems that translators and financial documents crossing between these language groups have to account for deliberately, rather than a simple vocabulary substitution.
Archimedes' Sand Reckoner, which put the myriad to such ambitious use, is also historically notable for containing one of the earliest known serious scientific estimates of the size of the observable universe as understood at the time — using his extended myriad-based numbering system specifically to express that estimate in a single coherent number, rather than resorting to a vague qualitative description of "an enormous quantity," a genuinely early example of mathematics being pressed into service to make an otherwise unspeakably large concept concretely nameable — an ancient ancestor, in spirit if not in specific method, of the same impulse behind modern scientific notation's handling of astronomically large and small quantities today.