To mathematician Amir Aczel the most important number of all might just be zero. Zero—nothing—may sound boring, but without it our entire number system and the world of mathematics it enables could not exist. In his new book, Finding Zero: A Mathematician’s Odyssey to Uncover the Origins of Numbers (St. Martin’s Press, Palgrave Macmillan Trade, 2015), Aczel searches for, and finds, the earliest known artifact bearing a representation of zero.
The object, an inscription on a stone slab, was originally found in the 1930s in the ruins of a seventh-century temple in Cambodia. It was lost over the years and scholars feared it was destroyed during the 1970s reign of the Khmer Rouge. But Aczel finally tracked it down and reintroduced this important milestone into the historical record.
Scientific American spoke to Aczel about his quest and why the number zero is so fascinating.
[An edited transcript of the conversation follows.]
Why don’t we know the origins of zero?
The mystery is there because of time and space and the lack of information. You have to go back in time many hundreds of years and you also go through space—geographical areas that are immense. You have the first known zero in [A.D.] 683 in Cambodia. The next one is in India so many miles away and hundreds of years later.
I think people haven’t spent enough of an effort trying to look for artifacts with earlier zeros. The history is pretty spotty. Think of this zero I found—it was just thrown away somewhere instead of being catalogued and studied in context. Is this the earliest zero? Likely there’s something earlier, maybe in India.
Why is zero so important?
To me it represents something immense because it’s the human understanding of the concept of nothingness, which is a hard concept to accept. Why would nothing be a number? If it’s nothing, then it shouldn’t be number, but the nothing is really very important. It’s the empty set.
And as a position holder it’s equally important because if you want to write something in a way that’s very efficient, not like Roman numerals, you need something like a zero. It allows us to let the numerals repeat themselves so you can use 1 through 9 again and again—and that’s the only device that allows this. The fact that 101 can be a number, just using the numerals for 1 and 0, is very condensed notation. Had we not had zero as a placeholder it wouldn’t work. How would you distinguish 11 from 101? It seems trivial but it’s not—it’s really a deep concept.
How were you able to recover the “zero” artifact?
It was very touch and go. You spend lots of time talking to people on the phone and sending e-mails and asking, “Do you happen to know where I might find this artifact that was studied in the ‘30s and then disappeared?” The real break was when I found this guy, His Excellency Hab Touch, the director general of the Ministry of Culture and Fine Arts in Cambodia. He found out this stone with the first zero was brought somewhere, and then I had the feeling I would probably find it, although there was the possibility [that] it was destroyed by the Khmer Rouge. Ultimately it was siting in a location among thousands of discarded artifacts. It was just a matter of spending some time looking for it.
What does this object tell us about the history of zero?
It’s a waypoint. It tells us that the zero existed at least in the year 683 A.D. It was probably invented earlier but we don’t know how much earlier.
In this particular artifact zero is a dot; later it became a circle. The next artifact we have is from almost two centuries later. That one is a circle, and the zero we have today in the West is a circle, but the Arabs use a dot just like the Cambodian one. There are a lot of mysteries there.
Where is the stone slab now?
The battle that started at the end of the book is still continuing for me. It ended up in the lab of an Italian archaeologist because she liked it and didn’t want to give it up. In the last chapters I go back to Cambodia and try to convince Hab Touch to take it from the archaeologist and put it in a museum.
Recently my sister died in Israel and left me some money. My sister is the one who got me to go to Cambodia originally. I thought I would take some of the money I inherited from her and I’d pay to move this artifact into a museum. Now everybody will be able to see it—it won’t be hiding in a lab. There are many others who are fascinated by the history of mathematics, and for all of us it’s really important to see the actual object. It’s like the Rosetta Stone.