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I was taught that the numerals {0,1,2,...,9} are from the Arabic alphabet. But they look completely different from today's Arabic letters. I wonder what is the origin of Arabic numerals?

Edit: The web page of the above link claims that Arabic numerals were developed in ancient India first and then spread to Arabia, and later to Europe and the rest of the world. This only means numerals themselves as symbols, not the arithmetical system for numerical computations.

Note that there are two distinct concepts: arithmetic and numerals. Arithmetic is a number system (often in decimals) that allows easy operations for numbers. Numerals mean symbols for the representation of numbers.

Numerals without arithmetic are very inefficient for numerical computations compared to arithmetic. One example is Roman numerals. The widely used numerals with arithmetic today are Arabic numerals.

Arithmetic was discovered originally in several countries as early as the 1st century AD. For example, Chinese discovered arithmetic with the decimal system of numbers and rules of numerical operations (Chinese numerals) in "The Nine Chapters on the Mathematical Art" in the 1st century AD. Chinese numerals are in Chinese characters, e.g. 〇, 一, 二, 三, 四, 五, 六, 七, 八, 九 (for $0,\cdots,9$ respectively), and 十, 百, 千, 万, 亿 (for ten, hundred, thousand, ten thousand, a hundred millions). Thus they are not widely known to the rest of the world.

As in the answer by @AChem below, it seems that recently there are many web pages that have highly inaccurate and even wrong information to give India unfair credit for many works in mathematics and science (ancient and modern). Be aware of this situation and do not readily believe this claim from some webpages.

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  • $\begingroup$ The linked Wikipedia article has a subsection Evolution of symbols that answers your question. $\endgroup$
    – Conifold
    Apr 1, 2019 at 4:16
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    $\begingroup$ You can see : Louis Charles Karpinski and David Eugene Smith, The Hindu-Arabic Numerals. $\endgroup$ Apr 1, 2019 at 12:19
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    $\begingroup$ See also F.Cajori, A History of Mathematical Notations, para 74-90 for details and useful tables summarizing the complex evolution of the numerals from Boethius and on. $\endgroup$ Apr 1, 2019 at 12:25
  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$
    – Danu
    Apr 17, 2019 at 0:42

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The problem with very old historical stuff including the origins of a certain concepts and giving due credit where it is due is one of the most difficult questions in history. The truth is that we may never know the correct picture behind the question who invented the modern number system? No matter what Wikipedia says. Anyone who is serious scholar of scientific history, Wikipedia should be their last resort to provide a proof. It must have been a very slow progress based on cross-cultural exchange of knowledge. About a thousand years ago, Middle east and central Asia were the center of knowledge just like today's Europe and North America. Some scientific words from Arabic origin still linger in modern mathematics and chemistry, such as algebra (named after a treatise with this title), algorithm (named after an Arabic mathematician), alcohol, boron, chemistry, alkali, natron etc. This shows that translation of Arabic into Latin was an active process in Europe. Translation is a sign of a progressive society.

For instance, OED entry for Arabic numerals traces the word usage history:

Designating the system of numerals written 0, 1, 2, 3, 4, etc.; of or relating to this system. Chiefly in Arabic numeral. Contrasted with Roman. Arabic numerals reached western Europe through Arabia by c1200, but probably originated in India

The earliest usage goes back to 1750s:

1756 Gentleman's Mag. May 239/1 The learned are not quite agreed when the Arabic numerals were first brought into use in this nation.

which clearly shows that nobody was even sure when these numbers were brought to Europe. Also note the word probably. Some falsely imply that these medieval Arab scholars were mere translators of Greek and Indian works. This is a fabricated story as well because as stated above, translation of scholarly work is a part and parcel of science.

Civilization near the Indus valley (now India, Pakistan) have 3000-4000 year old culture and they had their system of weights for trading. Certainly, they knew how to count as well. China had its own set of philosophers. Since the languages of these cultures was so different, it is extremely difficult to trace the ancient history of science. There is very little primary source of information. Today we can look up 18th century articles and say that this and that person is behind this concept but this does not apply to older works. If the Egyptians could build such huge pyramids thousands of years ago (predating all) which still startle modern civil engineers, can we say that they knew trigonometry very well? Nobody knows, because they did not leave anything which we can understand yet. Who knows how much knowledge was lost with time and then re-invented.

Recently, there are series of rather ridiculous claims in History of Science and Mathematics, and even Physics that everything originated in ancient India. Claims range from invention of alegbraic formulae, sine, cosine, numbers, astronomy, distance between Earth and Sun, ancient aircrafts, stem cell research and above all close relationship of German and Sanskrit. Usually Wikipedia and other dubious sources are quoted. BBC even made a report on it, sadly this is being propagated by some obscure university professors. One can only imagine how many students are misled. Perhaps these awed students are posting a series of these questions all over the web.

India: scientists dismiss Einstein theories

The moral of the story is that paper never refused ink. Web is worse, because everyone can propagate false ideas. Our job is to filter junk vs. good work.

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The first 3 digits can be easily explained by the rapid tracing of strokes without lifting the writing stylus from the surface of the paper. If you look at the Chinese characters for 1, 2 and 3: 一, 二, 三, you see these represent obvious numbers of strokes. If you write 二 quickly without lifting the pen, this becomes Z, and from there 2. The same goes for 三 to become 3.
The digit 4 derives from Brahmi script, where it was represented as a +, possibly a representation of 4 lines or 4 directions. This is reminiscent of the Kharoṣṭhī script, where it was represented as a X. A slanted stroke was added to + to become 4 for aesthetic and stylish reasons.
Digit 0 is the representation of an empty space.

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    $\begingroup$ All assertions need references. $\endgroup$ Feb 2, 2020 at 1:17
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    $\begingroup$ I got this from "The Triumph Of The Alphabet: A History Of Writing" by Alfred Charles Moorhouse $\endgroup$
    – Leo
    Feb 2, 2020 at 8:06
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You can see the origin of modern numerals and zero from Sanskrit, carved in granite, also at

https://youtu.be/pElvQdcaGXE?t=101

in a Temple for zero in a talk by Marcus du Sautoy who looks at the contribution of Ancient Indians like Aryabhata, Brahmagupta, Bhaskara, Madhava, etc

Programme: BBC - The Story of Maths Presenter: Marcus du Sautoy

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    $\begingroup$ These videos mean nothing. Do you have some peer reviewed articles to back these claims. I've watched and read that indians invented and discovered trigonometry, algebra, calculus, gravitation, the laws of mechanics, real analysis, etc. Also many indians claim online that without them there will be no technology, no satellites, no space exploration... This wave has to stop; who's feeding them these lies?! $\endgroup$
    – user5402
    May 21, 2019 at 18:54
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    $\begingroup$ Not at all. In Figure 2. A folio from the Bakhshali manuscipt, copied from G R Kaye's 1930 edition. In the middle are two large numbers, with some part on the right missing, forming numerator and denominator of a fraction. It is part of a verification and the fraction is reconstructed to be 50,753,383,762,746,743,271,936 / 7,250,483,394,675,000,000 Courtesy: Bill Casselman The birch bark plate is shown in ias.ac.in/article/fulltext/reso/017/03/0236-0246 $\endgroup$ Jul 19, 2019 at 23:32

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