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Here is a list of other systems:

  • Babylonian numerals
  • Egyptian numerals
  • Aegean numerals
  • May numerals
  • Chinese numerals

These system are far older than the current system. How did it get to be known and used internationally by nearly every cultures these days?

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  • $\begingroup$ I think a good answer will be rather long. Perhaps you should instead seek reference materials (books and articles) on the subject. $\endgroup$
    – pjs36
    Jun 7, 2016 at 19:42
  • $\begingroup$ that be a a lot of reading. $\endgroup$ Jun 7, 2016 at 19:46
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    $\begingroup$ This is probably better suited for the History of Math & Science Stack Exchange site. $\endgroup$ Jun 7, 2016 at 19:48
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    $\begingroup$ @pjs36: The Babylonian system had one serious drawback: they had no analogue of the decimal point (or comma). It’s as if our $15$ could represent $0.15,1.5, 15, 150$, etc. The Maya system, so far as I know, was modified only when used for the calendrical Long Count and was otherwise genuinely vigesimal. $\endgroup$ Jun 7, 2016 at 20:35
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    $\begingroup$ @ritwiksinha: If you feel like it. I didn't think it was that confusing, but the generalization is not quite wholly right. $\endgroup$
    – Brian Tung
    Jun 7, 2016 at 21:37

3 Answers 3

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First of all, the Egyptian and Aegean systems are "agglutinative" rather than positional. I'm looking at the Unicode Aegean numbers block and I see that they have a specific symbol for ninety thousand. What if you need to represent one hundred thousand? Do you just invent a new symbol for it?

Scientists estimate the universe has $10^{80}$ particles. Wolfram Alpha tells me the next prime number after $10^{80}$ is $10^{80} + 129$. If we had some way to indicate exponents in the Aegean number system, we would be able to express both these numbers with that system. But both the Aegean and Egyptian systems are inherently handicapped.

The Babylonian numerals don't have that limitation, but the choice of base is a little unwieldy. And the Europeans didn't even know about the Mayans until after Columbus thought he had discovered a shortcut to India, so the practicality of their system (or lack thereof) was moot.

That leaves the Chinese numerals, and I think the Europeans knew about the Chinese before they knew about the Mayans. But could they use a system that was so intrinsically tied to the Chinese language? Even today I would doubt that.

So as a result of circumstance, we have the Hindu-Arabic numeral system as our primary system of numeration. But do give credit to the Romans: we still use their numerals for some things even today.

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For short, positional numeral systems offer the great advantage to have efficient algorithms for the computation of sum and products, easy to use in everyday life. The base $10$ is more or less accidental (besides we having $10$ fingers, on average): for instance, there would be many efficient divisibility tests in base $60$ (since $60$ has a lot of divisors), but $60$ figures are hard to memorize, while in base $2$ "everyday numbers" tend to have too long representations. Base $10$ is a good compromise, even if base $12$ would have probably been better.

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    $\begingroup$ (+1) for "on average," and for mentioning that a numeric alphabet of sixty characters would be cumbersome at best. $\endgroup$
    – anonymouse
    Jun 7, 2016 at 20:02
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    $\begingroup$ Imagine learning the multiplication table in base 60, a nightmare! Also Mayan base 20 would be quite boring! $\endgroup$
    – egreg
    Jun 7, 2016 at 20:43
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    $\begingroup$ The Babylonian sexagesimal system was not at all hard to remember, it's more fair to describe it as a hybrid base combining 6 and 10, and the characters are extremely regular: en.wikipedia.org/wiki/Sexagesimal#Babylonian_mathematics. I still wouldn't want to be forced to memorize the base 60 multiplication table :). $\endgroup$
    – Erick Wong
    Jun 7, 2016 at 22:43
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For some history of the Hindu-Arabic system, see e.g. this article and this article. This system was introduced to Europe in the Middle Ages: one of the early influential texts was "Liber abaci" by Fibonacci. See also Wikipedia.

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