I have often used Indians myself, especially when some PCer says "Arabs invented numbers/Algebra/Zero/etc."
Good
However, Egyptians/Mesopotamians easily PRE-Date those you mention on the Overall question.
5000+ years ago.
About Twice as old as the Upanishads.
Here your use of the word "easily" displays a lack of understanding. You don't know how old the Upanishads are and the age you are trying to assign to them is based on pure conjecture. This type of conjecture was started by an ignorant European, a German by the name of Max Mueller. You see Mueller was a Christian, and although he was somewhat sincere, he ignorantly believed that the Earth was created about 4000 years before the birth of Christ. As a result, he simply could not accept the Vedic scholars assertion concerning the age of Vedic knowledge and his dating was influenced by his ignorant belief. Since he was respected European scholar, his ideas influenced subsequent thinking in modern times. According to Vedic scholars, the great Vyasa compiled the Vedic knowledge that had been preserved in an oral tradition for thousands of years before that. He taught the Puranas and the Upanishads to students, who
commented and
expanded on them. As a crude analogy consider
2x + 3x = 5x
Now I can comment on that and say x's are like apples, oranges, or anything else in that two apples plus three apples equals five apples. So that is a
comment on a core algebraic statement.
Going further, consider the fundamental distributive property
a * (b + c) = (a * b) + (a * c)
Accepting this as true, someone could come along and say, guess what, then
(a + d) * (b + c) = (a * b) + (a * c) + (d * b) + (d * c)
Because if you let
a = u + v
then
u * (b + c) = (u * b) + (u * c)
and
v * (b + c) = (v * b) + (v * c)
Which most certainly implies that
(a + d) * (b + c) = (a * b) + (a * c) + (d * b) + (d * c)
So from the core statement a * (b + c), an
expanded statement was derived.
Similarly, the core knowledge of the Upanishads came from Vyasa and was
commented and
expanded on by his students and their subsequent students. But all of them, without exception, credit the understanding to Vyasa who himself said that he was stating what had been preserved in oral tradition extending back thousands of years. European scholars simply cannot accept this and as a result they try to base their dating of the Upanishads on conjecture and get confused when they see references to chronological events mentioned in the different Upanishads. What you have done here is merely regurgitate their confused statements.
You see Indian mathematicians were doing far more than counting on bones for a long, long time. Way before people like Newton and Leibniz were doing calculus, Madhava had already done extensive research on such advanced mathematical topics as the behavior of infinite series
For years, English scientist Isaac Newton and German philosopher Gottfried Leibniz both claimed credit for inventing the mathematical system sometime around the end of the seventeenth century.
Now, a team from the universities of Manchester and Exeter says it knows where the true credit lies — and it's with someone else completely.
The "Kerala school," a little-known group of scholars and mathematicians in fourteenth century India, identified the "infinite series" — one of the basic components of calculus — around 1350.
.....
"The beginnings of modern math is usually seen as a European achievement but the discoveries in medieval India between the fourteenth and sixteenth centuries have been ignored or forgotten," he said. "The brilliance of Newton's work at the end of the seventeenth century stands undiminished — especially when it came to the algorithms of calculus.
"But other names from the Kerala School, notably Madhava and Nilakantha, should stand shoulder to shoulder with him as they discovered the other great component of calculus — infinite series."
He argues that imperialist attitudes are to blame for suppressing the true story behind the discovery of calculus.
"There were many reasons why the contribution of the Kerala school has not been acknowledged," he said. "A prime reason is neglect of scientific ideas emanating from the Non-European world, a legacy of European colonialism and beyond."
Calculus created in India 250 years before Newton: study - Technology & Science - CBC News
According to these early mathematicians they have merely commented and expanded on what was passed down in oral tradition for thousands of years. But Europeans can't accept that because of their egocentric arrogance.