# How We Discovered the Number Zero

of all the №s that exist, there’s something spesh bout zero. we can find real-realm exs of other №s, be it \$1, 99 red balloons, 100 yrs of solitude or any other thing we care to tabul8. but it’s difficult to find exs of nothingness — even the supposed vacuum of space is disturbed by faint gusts of hydrogen atoms.

perhaps that’s why zero is a fairly recent invention. while it popped up in ≠ forms in various places, the concept of nothing as a № is just a few thousand yrs old, atta most. and sometimes it never seems to ‘ve existed at all. both the egyptians and romans didn’t appear to use zero.

nonetheless, zero is quite primordial to us tody. the concept plays a foundational role in calculus, as we calcul8 derivatives converging upon zero. it’s also used in coordinate systems on graphs, which begin atta point (0, 0).

ancient civilizations found use in zero swell, 1st as a component of numerical systems and l8r as a mathematical tool. the sumerians are thought to be the 1st to ‘ve recognized the idea of nothing (although not til l8r did they come up witha symbol for zero). the maya, likewise, developed the idea of zero indiely. the concept of nothingness l8r traveled from the middle east to india, china and elsewhere.

€an civilizations were fairly l8 to the nothing game, incorporating zero into their cultures 1-ly after the mathematician fibonacci brought the indo-arabic numeral system to € after travels inna middle east and africa. there, as elsewhere, zero ‘d prove to be a revolutionary concept, inspiring thinkers of the middle ages and renaissance to primordial insites bout mathematics na realm.

## counting to nothing

the discovery of zero doesn’t seem to ‘ve come all at once, but rather in stages. scholars think it began w'da concept of nothing as a placeholder while counting. this is how the babylonians employed zeros some 4,000 yrs ago. when counting, they divided their №s into columns, much as we do tody, a concept called positional notation. for us, the № 115 has 3 columns with place vals — ones, tens and hundreds. there’s a 5 inna ones column, a 10 inna tens column and a one inna hundreds column. to write, say, 105, we nd'2 show that there’s nothing inna tens column, something accomplished witha zero tody.

though the babylonians used a ≠ № system than we did, they counted in much the same way using positional notation. when they needed to show dat a' column had nothing in it, the babylonians came up w'da idea of simply leaving a space there — nothing inna truest sense. it’s our 1st real ex of an acknowledgment of the concept of nothing.

babylonian cuneiform numerals. (credit: josell7/cc by-sa 4.0/wikimedia commons)

over 1,000 yrs l8r, under the seleucid empire, the babylonians appear to ‘ve begun using glyphs shaped like wedges in place of spaces — somd' 1st graphical representations of zero. but, even so, the babylonians don’t seem to ‘ve extended their concept of zero to include it as an actual №. a stone tablet of mathematical sums, for ex, includes the calculation “20 – 20,” but cutouts the answer blank — an undefined sum.

the maya applied zero in much the same way. when writing dates, they needed a means of putting a zero in columns when appropriate. for ex, the date that corresponds to the beginning of wha’ they believed was the realm’s current era was written 13.0.0.0.0 in maya notation and corresponded to 3114 b.c. cause the maya had no contact with eurasia til long after these glyphs were written, it’s clear that the maya invented the concept of zero indiely.

maya numerals. (credit: !original:neuromancer2k4vector: bryan derksen/cc by-sa 3.0/wikimedia commons)

the maya appear to ‘ve used several ≠ glyphs for zero, though a shell was most common. the shell glyph also appears to ‘ve been used to indicate the concept of nothing + generally. a transl8d verse in maya text mourning a fallen leader, reads, in pt, “no pyramid, no altar, no earth/cave.” the same shell glyph that stands for zero in their № system appears here in a + abstract sense, signifying nothing.

## zero onna move

from babylon, zero began to spread sloly to other regions of the realm. it turns up in greece round the 4th century b.c., probably brought back by alexander the gr8 after he conquered the babylonian empire in 331 b.c. here, we begin to see traces of the modern oval that we use tody to represent zero. greek astronomers like ptolemy made use offa hollo circle when calculating trigonometric figs, often adding a bar or line across the top. this, argues robert kaplan onnis book the nothing that is: a natural history of zero, indicates they probably thought of zero as something closer to a punctuation mark tween real №s, rather than a № in and of itself.

for a true appreciation of zero’s place inna № line, we must venture to india. there, researchers see the 1st solid evidence of zero, called “sunya” by the indians, bein’ used in mathematical calculations. it’s a sign that mathematicians there conceived of zero as a unique numerical entity. likely the 1st to make this logical leap was a man named brahmagupta, a foundational fig in indian mathematics. onnis mathematical treatise brahmasphutasiddhanta, written in a.d. 628, brahmagupta provides rules for doin’ calculations with zero that mirror wha’ we cogg tody.

“when zero is added to a № or subtracted from a №, the № remains unchanged; and a № multiplied by zero becomes zero,” he writes.

this represents a profound logical leap, argues neurosci andreas nieder in a 2016 paper.

“for a brain that has evolved to process sensory stimuli (something), conceiving of empty sets (nothing) as a meaningful category requires high-lvl abstraction. it requires the ability to represent a concept beyond wha’ is perceived,” he writes.

khmer numerals from sambor inscriptions dated to 683 a.d., found in present-dy cambodia. some say this № system includes the earliest use of zero. (credit: paxse/cc by-sa 3.0/wikimedia commons)

the true origins of zero are still a subject of debate among historians and mathematicians. for ex, the № zero may ‘ve shown up in wha”s now cambodia even earlier than in india, argues amir aczel. the mathematician undertook a yrs-long search for the origins of zero, ending up in a shed near the ancient city of angkor wat. there, a tablet dated to the 7th century a.d. bears wha’ he argues tis 1st real zero. as he writes in finding zero: a mathematician’s odyssey to unc’oer the origins of №s, that ‘d move the 1st true zero from india to cambodia, and push back our timeline of the № by bout 200 yrs.

wherever twas 1st discovered, our present-dy zero — the one we write witha hollo oval — didn’t make it to the western realm til the 13th century. that’s when fibonacci, best known tody for an eponymous № set, introduced € to the indo-arabic zero onnis text liber abaci. the book, published in 1202, brought our modern № system to the continent, including its foundational zero. the №s caught on, and mathematicians carried the zero inna'da renaissance and beyond.

in €, as wherever else zero was discovered or introduced, it appears that the № never fell out of fashion. once nothing appears, it’s there to stay.

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