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How I Rediscovered the Oldest Zero in History

Science & Tech  (tags: ancient, archaeology, concept, design, discovery, humans, history, investigation, research, science, scientists, society, space, study, technology )

- 1130 days ago -
The oldest zero in India with a confirmed date is from the mid-ninth century, and found in the Chatur-bujha temple in the city of Gwalior.

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Kit B. (276)
Saturday May 25, 2013, 6:56 am
Photo Credit: Debra Gross Aczel -- Inscription K-127, from Sambor on Mekong.

Mathematically, the Greco-Roman-Etruscan number system is an endlessly repetitive number system that is inefficient and cumbersome. To write 3333, which we do by repeating the sign 3 four times, a Roman would have had to scribble down MMMCCCXXXIII—three times as many characters. And I challenge anyone to multiply this number by MMDCCCLXXIX—using only the Roman system (meaning without translating these numbers into what they would be in our base-10 number system and then back into Roman numerals). Surprisingly, this clunky old Roman number system, with its ancient Greek and Etruscan roots, remained in use in Europe until the thirteenth century!

Our base-10 system derives its power and efficiency from the fact that we use a zero. The zero here is not just a concept of nothingness (and something every schoolchild learns you are forbidden to divide by), but also a place holder. The zero is a sign we place in a location in a number when there is nothing there—to tell us, for example, that 40 means four tens and no units, or that 405 is four hundreds, no tens, and five units.

Numbers on a dial

The zero thus turns the numerals 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 into what algebraists call the ring Z(10). When you stack such rings one on top of the other, and you let them represent, in turn, the units, tens, hundreds, thousands, ten thousands, and so on, based on each ring’s location, you get the highly efficient number system we have today. Think of each ring as a dial—when it goes around full circle, you get 0 and you add a 1 to the ring above it. As an example, start with the number 5—this means only the lowest ring, that of the units, is nonempty, and has the number 5. Now add to this the number 7. Five units from the 7 will bring the units ring to 0 and make the tens ring jump up to 1. The remaining 2 from the 7 will make the lowest ring (the lowest dial) now show 2. Thus we have that the sum of 5 and 7 is 12. Without the place-holding zero, which makes each “dial” start repeating itself after going through zero, we couldn’t do this.

The ancient Babylonians (preceded by the Akkadians and Sumerians) had a base-60 number system, without a zero. So already 4,000 years ago, people in ancient Babylon understood that it is efficient to make numbers become “circular” or dial-like, in the sense that 60 was like our 10, and 3600 (60 squared) was like our 100, and so on. But the Babylonians didn’t use a place-holding zero, so there were serious ambiguities in their system.

Our number system is far superior to the old Babylonian base-60 system, because our base is much smaller and because we use a zero, and it is also superior to the 3,000-year-old Greco-Roman-Etruscan letter-based system. Zero is the incredible invention that made our number system so efficient. This system was popularized in Europe after the publication, in 1202, of the book Liber Abaci (The Book of the Abacus), by Fibonacci (of the famous Fibonacci sequence). Presumably, Fibonacci learned the use of the 10 numerals with zero from Arab traders, with whom he dealt on behalf of his merchant father, and that is why we often call them the Arabic numerals. But Fibonacci himself refers to them in his book as the “nine Indian numerals” with zero, which he calls zephirum, perhaps originating from the Arab sefir.

The original zero

But who invented the zero, which gives so much power to our number system? We don’t know who invented it, but we are pretty sure that the zero is an Eastern invention. The oldest zero in India with a confirmed date is from the mid-ninth century, and found in the Chatur-bujha temple in the city of Gwalior.

At one point, an older zero was known. In the 1930s a zero from the year AD 683 was found in Cambodia, and its great antiquity allowed a French researcher by the name of Georges Coedes to prove that the zero is of Eastern provenance. This is because, while the Gwalior zero is concurrent with the Arab empire based in Baghdad (the Caliphate), the zero from 683 predates extensive Arab trading. It also comes from a location that is much farther east than India. Its existence thus makes it highly unlikely that the zero was invented in Europe or Arabia and traveled east through Arab traders, as some had believed in the early 20th century. The Cambodian zero proved that zero was an Eastern invention. But this zero disappeared during the Khmer Rouge regime in Cambodia, and no one knew if it still existed.

I felt very strongly that it was important to recover the world’s oldest zero. I spent five years researching its whereabouts and developed various hypotheses about where it might be found. Then last year I was awarded a generous research grant from the Alfred P. Sloan Foundation in New York, which enabled me to travel to Cambodia to search for this precious find. As is well known, Cambodian artifacts have been plundered for decades and sold illegally on the international antiquities markets. During the Khmer Rouge era, while killing 1.7 million of their own people, Pol Pot and his henchmen also looted, vandalized or destroyed more than 10,000 ancient statues or inscriptions.

The location where the oldest zero in the world—on a seventh-century stone inscription—was kept was plundered by the Khmer Rouge as late as 1990. I traveled to that location, not far from the famous Angkor Wat temple, and after weeks of searching among thousands of artifacts, many of them damaged or discarded, I was able to discover the inscription. It is shown in the photo below, taken by my wife.
** See above photo or at VISIT SITE

The zero is the dot in the middle, to the right of the spiral-looking character, which is a 6 in Old Khmer. The numeral to the right of the dot is a 5, making the full number 605. The inscription says: “The Chaka era reached year 605 on the fifth day of the waning moon…” We know that in Cambodia the Chaka era began in the year 78 AD. Thus the date of this zero is 605 + 78 = 683.

I notified the Cambodian Government of my discovery, and His Excellency Hab Touch of the Cambodian Ministry of Culture and Fine Arts, who had helped me in my search, promised me to place this inscription—one of the most important finds in the history of science—in the Cambodian National Museum in Phnom Penh, where it rightly belongs. So anyone interested in the history of science and the birth of numbers should soon be able to see the first zero ever discovered.

By: Amir D Aczel | Discover Magazine | 5/20/2013

Amir D. Aczel writes often about physics and cosmology. His book about the discovery of the Higgs boson, Present at the Creation: Discovering the Higgs Boson, was published in paperback by Broadway Books in November 2012.

Darren Woolsey (218)
Saturday May 25, 2013, 7:23 am
Fascinating stuff this... thanks for sharing it.

Tim C. (2437)
Saturday May 25, 2013, 8:34 am

linda newman (3947)
Saturday May 25, 2013, 8:58 am
awesome info

lee e. (114)
Saturday May 25, 2013, 9:13 am
What amazing stuff, even simplified and with all this additional info - I still suck at math! It's nice to know attempts were made to make it simpler:)

Nyack Clancy (528)
Saturday May 25, 2013, 9:17 am
Very interesting-

I bet there may be even much earlier discoveries to come than that- since nature itself is a repeating patten-

I think once they invented the wheel, they already knew the concept... and I just can't imagine t pyramids being built without a very advanced math that included a zero, tho the marker may not have looked like a zero- that may have evolved.

Kit B. (276)
Saturday May 25, 2013, 9:21 am

Most numbers have their origin in ancient India. People discovered that have a "short hand" for the words that represented numbers made for faster calculations and therefore faster exchanges when trading. I do agree that some form of math including a zero was probably at work in the Pyramids. They most certainly had mastered geometry from an early point.

Sorry Lee, I know that many find math to be a stumbling block.

Bryna Pizzo (139)
Saturday May 25, 2013, 10:19 am
Thanks Kit! I love history even when it involves mathematics. The post is fascinating and the debate following the article was quite entertaining! Giggle Giggle :) History fascinates me. I couldn't get enough of it or literature in school. (n, p, t)

Vallee R. (276)
Saturday May 25, 2013, 11:31 am
that's amazing - thanks Kit - love this stuff!

Angelika R. (145)
Saturday May 25, 2013, 12:04 pm
I agree what an amazing article, though I am surprised at the finding and would have imagined it started in ancient China.. That ambitious Mr Aczel really amazed me, spending years chasing for literally nothing, nil. :-) and he FOUND it, too! How cool is that!
BTW-couldn't we all think of some more locations where absolute zeros are put as place holders..

Kit B. (276)
Saturday May 25, 2013, 12:14 pm

Angelika, there are many ZEROS holding a place in the United States Congress, but unlike the real zero they are completely unnecessary.

Angelika R. (145)
Saturday May 25, 2013, 12:38 pm
..for sure, just holding the place for the necessary ones to take over..

Diane K. (134)
Saturday May 25, 2013, 1:03 pm
This is interesting. A bit of ancient archaeology, that's for sure. thanks Kit

Joanne Dixon (37)
Saturday May 25, 2013, 2:03 pm
Some people swear by base 12, and there are probably some who could do the multiplication in binary (don't look at me! I couldn't!), but neither of these would be possible without the zero either.

Lois Jordan (64)
Saturday May 25, 2013, 2:35 pm
Noted. Thanks, Kit. I feel a little smarter now, even though I could never pass anything more than high school geometry.

Kit B. (276)
Saturday May 25, 2013, 2:38 pm

Maybe it's better to begin geometry and algebra in earlier grades before students learn to fear math.

Kathlene Lentz (30)
Saturday May 25, 2013, 2:42 pm
Very interesting. And I don't think I'd ever try to multiply anything in Roman Numerals, thank you!

Kit B. (276)
Saturday May 25, 2013, 2:51 pm

In binary math one could have a base of 12 or as we know the 1 - 0 that our computers use. I had to laugh when I read the idea of multiplying in Roman numerals. Yet, the Roman numerals stood for many years, and they must have a way of using them in what seemed a practical fashion.

Jae A. (320)
Saturday May 25, 2013, 3:19 pm
Like Angelika I too thought it would have been the Chineese..weird how one can peg a culture as automatically tops in their field regardless of the..time span. Anyway...great ...and an ever so informative... read. As the saying goes....try and learn something evrey day keeps the ol brain tuned,so to say.

Julia R. (296)
Saturday May 25, 2013, 3:47 pm
Fascinating article! So the oldest zero originated in Cambodia and that is what made for our much more efficient number system- the place holding zero! It is amazing how much of our culture, language, mathematics and science came from the East! Thanks, once again, Kit B. for expanding our minds!

Jo S. (618)
Saturday May 25, 2013, 3:50 pm
I am a math nut and tis is awesome!
Thank you so much Kit! Congrats on the new grand baby!
Noted, read,copied & shared.

Birgit W. (156)
Saturday May 25, 2013, 4:14 pm
Interesting, thanks.

Fred Krohn (34)
Saturday May 25, 2013, 6:09 pm
Both the Mesoamericans and the Egyptian Pharaonic culture necessarily had a mathematical notation system that included a zero; their geometry (pyramids) and social systems couldn't have functioned otherwise. Same goes for the creators of Stonehenge. For whatever reason, we've never found their associated records. India and Arabia are known to be the sources of modern higher math; I consider the Roman notation totally unusable and obsolete and reject its use even today. I'd be surprised if the Chinese hadn't developed an independent zero-inclusive math notation, they've had 4500 years or so to do it and have som of the cultural results.

Lisa Zilli (17)
Saturday May 25, 2013, 7:46 pm
Thanks for sharing

Laurie H. (813)
Saturday May 25, 2013, 8:12 pm
Always great to learn something new and keep our minds stimulated!!! Will share this too.Very informative & interesting as always, Kit--So Many Thanks!!~

Colleen L. (2)
Saturday May 25, 2013, 9:18 pm
I've always been into math. Fascinating article. Thanks Kit

june t. (66)
Sunday May 26, 2013, 12:20 am
interesting thanks

Dave C. (239)
Sunday May 26, 2013, 3:03 am

there are 10 types of people in the world....those who find something like this cool (like me) and those who don't.....

Past Member (0)
Sunday May 26, 2013, 4:10 am
Very Interesting

Lindsay Kemp (2)
Sunday May 26, 2013, 6:55 am
Thanks for sharing! Very interesting.

Craig Pittman (52)
Sunday May 26, 2013, 8:36 am
Wonderful Kit. Thank you for sharing this.

Abdessalam Diab (145)
Sunday May 26, 2013, 11:17 am
Thanks Kit for this interesting Article .The question about who invented Zero will be raised may be forever. Some scientists say it has been created independently in different parts of the world such as India,Babylon and in America (Maya).,I have recently read an article titled " Who invented ZERO?"

Theodore Shayne (56)
Sunday May 26, 2013, 2:13 pm
Yes, India and Ramanujan.

Kit B. (276)
Sunday May 26, 2013, 2:21 pm

This reminds of the ever lasting discussion on who discovered America. It sure was not Columbus, but he had the advantage over those who came before him, the printing press. The truth is we can only make educated guesses on just who first used the zero, we have some insights but also don't know which or if all began using it at the same time.

Past Member (0)
Sunday May 26, 2013, 5:20 pm

JL A. (286)
Monday May 27, 2013, 12:13 pm
I love math history

Sherri E. (128)
Tuesday May 28, 2013, 9:37 pm
Very interesting but I think Amir's academia critics reviewing his research was as interesting as his research. Thanks Kit enjoyed this article very much. Noted

BMutiny TCorporationsEvil (429)
Monday August 12, 2013, 4:57 pm
People who didn't have a Zero, could still do computations ON AN ABACUS.
For those of you who haven't seen one, it is like beads on wires, in a frame.
I never learned how to use an Abacus myself, but I have read enough to have a basic understanding of how they work. {But not enough to describe it here!}
However, people who learn use of an Abacus in cultures such as China where it is still used, learn it in school maybe or elsewhere, develop extreme speed and skill.
I read somewhere that an Abacus expert, beat out some of the very early adding machines and computers in complicated calculations. Not any more, I'm sure. But, they beat out people doing calculations "by hand", by a long ways. They rapidly move the beads on the wires... faster than we can write. It is 100% accurate, if you know what you're doing...

BMutiny TCorporationsEvil (429)
Monday August 12, 2013, 5:21 pm
Read the notes after the article - I LOVE it when Scholars have at each other, no-holds-barred, better entertainment for me BY FAR, than watching soccer or wrestling!

I don't see where Egyptian Geometry would need a zero. Egyptian Geometry developed from the need to re-apportion farmers' fields each year, after the yearly flooding of the Nile wiped out all the landmarks every year. All you need is some kind of a "right-angled" square, for square fields, for a grid - and a Standard Unit of Measurement, say like a Yardstick. You get a right angle, by twice bisecting a circle, easy enough. Then you make a right-angled piece of wood or metal or something hard & permanent, to use over & over... Same with your "Yardstick" or Measuring Rod. You decide on the Standard, then make all future Rods to an exact match... not beyond their technology!
With a Right Angle instrument, and a Standard Measuring Rod, you just use simple multiples of the Standard Measure over & over again... You can build a Pyramid or other structure that way, as far as I know, without a zero.... Just simply use a "Metre" or whatever your Standard Measure is, again & again & again & again & again...simple addition... until you have the length you want. Pyramids are kindof uncomplicated, mathematically. It's just the MOVING of all those tons of rock...

In order to calculate how to FEED all those Laborers on the Pyramids, how much bread and BEER {a very important part of their rations!}, they could have used some sort of an multiply... I think those are very early...
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