All: since the title was baiting some people into nationalistic arguments, which are off topic here, we replaced it with representative language from the article explaining what it is about. This is a great HN submission! Please don't let the thread slide back into bickering.

The earliest use of the decimal system in Hindu mathematics is in the Yajurveda Samhita, where there is a list of numerical denominations given: eka(1), dasha(10), shata(100), sahasra(1000), ayuta(10000), nryuta(100000), ... all the way to 10^12. The list, with slight modifications and additions, is repeated in other Vedic texts [1]. The Yajurveda Samhita dates back to between 2000BCE - 1000BCE.

The earliest use of zero as a symbol in Hindu mathematics actually occurs between 300BCE - 200BCE in a work called Chandah Sutra by Pingala. It is used in figuring out the number of combinations of long and short syllables in a verse containing n syllables [2].

The earliest written manuscript that uses zero as a symbol predates both Brahmagupta and Aryabhatta, and is found in the Bakhshali manuscript that is dated between 224CE-383CE [3].

Here are some of the problems tackled in the Bakhshali manuscript [4]:

a) Problems involving systems of linear equations

b) Indeterminate equations of the 2nd degree

c) Arithmetica progressions

d) Quadratic equations

e) Approximate evaluations of square roots

f) Problems of the type x(1-a1)(1-a2)...(1-an)=p

1. https://archive.org/stream/in.ernet.dli.2015.81882/2015.8188...

2. https://archive.org/stream/in.ernet.dli.2015.81882/2015.8188...

3. https://en.wikipedia.org/wiki/Bakhshali_manuscript

4. https://archive.org/stream/in.ernet.dli.2015.189295/2015.189...

The book mentioned in the comments is very interesting https://www.amazon.com/Money-Changes-Everything-Civilization...

"William H. Goetzmann in “Money changes everything”, a history of the influence of finance on civilisation from Babylonian times onwards, also credits Leonardo of Pisa with introducing the concept of what we now call Net Present Value in one of his Liber Abbaci problems."

When we say "India" in an historical context, realize that we're not talking about the place we know today. S. Asian history contains many varying political entities and cultures each covering varying sub-regions of the region covered today by India, Pakistan, and Bangladesh. For much of of the time (I don't remember enough to say how long off the top of my head), the main divide has been between (northern India + Pakistan) and (southern (Tamil?) India), for geographical reasons. Heck, the Indus river, after which India is named, is now in Pakistan. The current countries and their borders date only to 1971, and are unresolved in some places.

(The vagueries of history and its crazy etymologies are hardly limited to the subcontinent: Look at the "West Indies" and Native American "Indians" as easy examples. And every piece of real estate in the world has been controlled by more than one political entity, and periodically one of the former owners claims someone else's land on some historical basis.)

For those interested in more, it's hard to find a good one-volume scholarly history of the region in English, at least last I looked. Here's the best I found, IMHO:

India: A History by John Keay

https://www.harpercollins.com/9780007382392/india-a-history

EDIT: a few enhancements

I’ve always been amused that they are called “Arabic” as a cursory glance at the shapes of European and Hindu digits shows the connection while the Arab scripts use such different forms. But the again this is how we get terms like the foods “turkey” and “orange” so there’s no reason to complain.

India did also have a (presumably) Babylonian-inspired sexagesimal system as well, as seen for example in the pre-decimalized currency. There was extensive trade between India, the Middle East, and Eastern Africa stretching back thousands of years, and cultural as well as physical goods clearly went both ways.

A lot of Indians got annoyed that they are double barrelled as Hindu Arabic, when the original source was India. The arabs then took it and created other concepts. Its like calling English alphabet English-American.

islamic culture cultivated and gathered lots of knowledge, includign that of roman, indian, some african and other cultures. in my opinion their translation efforts have saved a lot of, and furthered a lot of science and research. As europe was plunged into the dark ages, the islamic culture saw an age of light where knowledge was power and there was a big effort for about 1000 years to cultivate and improve understanding of the world around us. alchemy, algebra, algorithm, a lot of words which came from there. though some of the underlying knowledge was gained from translating texts of other cultures, credit goes to these islamic scientists for recognising the importance of these works and improving upon them.

Title of the link is inaccurate. The post refers to the Arabic numerals, not the decimal system - and after all the Roman numerals (which was widely commonal) also follow the decimal system. It should be “the path that Arabic numerals [or Hindu-Arabic numerals] took from India to medieval Europe.”