10

India did not "lag behind". It was the ancient Greece, its successor Hellenistic states, and Renaissance Western Europe where Math jumped ahead. (More precisely, one can say, one Hellenistic state:-)) India was not much different in comparison with most of the rest of the world. The correct question would be "Why in ancient Greece and renaissance Europe ...


8

(I started writing this answer from memory, but on a second look at some sources it turns out to answer the question for the statement of a rotating earth rather than that of a spherical earth... but I'll leave it here; hope the other question is still interesting to you.) The most notable statement of a spherical rotating earth, in Indian astronomy, is by ...


7

At one time, India led rather than lagged. The Indo-Arabic numerals that are now used worldwide originated in India. We count 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, ... Note that I made 0 (zero) bold. The concept of representing nothing with something is uniquely Indian. The world owes a lot, a whole lot, to India and to Brahmagupta in particular. The ...


6

No. In The bridge between the continuous and the discrete via original sources in Study the Masters: The Abel-Fauvel Conference, Pengelley writes that In the 6th century B.C., the Pythagoreans knew about the formula for $\sum n$. In the 3rd century B.C., Archimedes figured out the formula for $\sum n^2$. In the 1st century A.D., Nichomachus figured out the ...


6

According to The Hindu Business Line, quoting the scholar TA Sarasvati Amma: It was only in the 18th century, nearly 2,000 years after active contact of Indians with the Greeks, that Euclid’s Elements were translated into Sanskrit and even then perhaps the example of the Arabs provided the inspiration. TL/DR; Concerning Indian mathematics at about the time ...


6

In the discussion of how different cultures developed mathematics, it is important to remember that patterns of cultural exchange influenced this development. Mathematics did not just independently pop up in Greece, then India, then Europe; rather, the legacy of mathematics was inherited, refined, and passed on to descendants and neighbors in mostly ...


6

I touched upon this in my answer here, near the end. This source indicates that one of the earliest known instances - if not the earliest known instance - is a carving on a tablet discussing gardens in the town of Gwalior. The page says: We have an inscription on a stone tablet which contains a date which translates to 876. The inscription concerns the ...


5

Etymology Quite a few sources say that Aristotle was the progenitor of the term, after his use of energeia (a Latin transliteration of ἐνέργεια). However, one source notes that Heraclitus used a similar word, en-ergon, years prior. Heraclitus wrote: "En-ergon is the father of everything, king of all things and, out of it, all forms of contrast originate. ...


4

You make a fair amount of valid points however you need to see the progression of what was happening at the time. If we assume that Indian math developed independently you'd see they were at the forefront of a lot of "inventions" and "discoveries" in math. Here are a few in as close chronological order as possible from Aryabhatta to Bhaskara II and Madhava ...


4

In ancient Indian texts like Vedas and puranas there are so called philosophies or concepts of energy. Actually vedas and puranas are considered as religious texts, but these texts contain many hidden facts and knowledge(I doubt how many of you agree with this statement. Some of the examples of science in Vedas are, Vedic mathematics, Astrology, ...


3

You can find a brief discussion in : Eli Maor, The Pythagorean theorem : A 4000-year history (2007), page 66-67. See also Ch.8 : Ancient Indian Mathematics, page 311-on of : George Gheverghese Joseph, The Crest of the Peacock Non-European Roots of Mathematics (2011). See also Ch.IV on Geometry, page 155-on, of : T.S. Bhanu Murthy, A Modern Introduction ...


3

The textbook you quoted is that of high school and probably written by high school/college teachers. Most of these side notes are often traditional hearsay. As a good scientist of future, do not trust whatever appears in books and Wikipedia should be your last resort to verify historical facts. Are they all true? If yes, did they have any effect on other ...


3

The interpretation is derived from "stretching" the natural interpretation of product as repeated sum. $3 \times 2 = 6$ because $3 \times 2 = 3+3$. The same for $(−3) \times 2 = (−3) + (−3) = −6$. Starting from this, we may interpret $a \times (−2)$ as "repeated subtraction" : we have to "subtract" twice the quantity $a$. If $a$ is a negative quantitiy,...


2

The Iron Age in India began around 1200 BCE. The Pillar of Delhi was created around 400 CE, 1600 years after Indians had first learned to melt iron. Alloys weren't impossible. In fact, Indians had learned to make steel (not just wrought iron) by 200 CE, and possibly as early as 300 BCE.


2

Weight is an old concept related to energy that was discussed both in not-so-Ancient China, Ancient India, or the Islamic Golden Age. It meets each and every of your criteria : Conservation of weight: the belief appeared in all of these cultures that weight was to be conserved on a global scale. ("Pudgala" for the Jain, just "matter" of al-Tusi) ...


1

Amir Aczel has a new book ["Finding Zero"]. There he finds zero on an inscription from 7th century Cambodia. Perhaps this is earlier than in India. (My remark copied from that other question.)


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