Computing Science through the ages ;

The Chinese started writing the open circle we now use for zero.
The Hindus depicted zero as a dot.

Additional resources

Scientific American: The Origin of Zero
Yale University: The History of Zero
American Mathematical Society: All For Naught

Q:where can we access these articles ? at the end of the article below;;; Q: can they be accessed directly from here as well?[];;; no ::: needs to be copied and executed there ;;;

https://www.livescience.com/27853-who-invented-zero.html

Zero in the Americas
Six hundred years later and 12,000 miles from Babylon, the Mayans developed zero as a placeholder around A.D. 350 and used it to denote a placeholder in their elaborate calendar systems. Despite being highly skilled mathematicians, the Mayans never used zero in equations, however. Kaplan describes the Mayan invention of zero as the "most striking example of the zero being devised wholly from scratch."

India: Where zero became a number
Some scholars assert that the Babylonian concept wove its way down to India, but others, including those at the Zero Project, give Indians credit for developing numerical zero independently. "We are of the view that in ancient India are found numerous so-called 'cultural antecedents' that make it plausible that the mathematical zero digit was invented there," said Gobets, whose organization is composed of academics and graduate students devoted to studying the development of zero in India. "The Zero Project hypothesizes that mathematical zero ('shunya', in Sanskrit) may have arisen from the contemporaneous philosophy of emptiness or Shunyata," said Gobets. If philosophical and cultural factors found in India were important to the development of zero as a mathematical concept, it would explain why other civilizations did not develop zero as a mathematical concept, said van der Hoek.

>>> If philosophical and cultural factors found in India were important to the development of zero as a mathematical concept, it would explain why other civilizations did not develop zero as a mathematical concept, said van der Hoek.<<<

According to the book "The Crest of the Peacock; Non-European Roots of Mathematics," by Dr. George Gheverghese Joseph, the concept of zero first appeared in India around A.D. 458. Joseph suggests that the Sanskrit word for zero, śūnya, which meant "void" or "empty" and derived from the word for growth, combined with the early definition found in the Rig-veda of "lack" or "deficiency." The derivative of the two definitions is Śūnyata, a Buddhist doctrine of "emptiness," or emptying one's mind from impressions and thoughts.

"From this philosophy, we think that a numeral to use in mathematical equations developed," said van der Hoek. "We are looking for the bridge between Indian philosophy and mathematics."

"Zero and its operation are first defined by [Hindu astronomer and mathematician] Brahmagupta in 628," said Gobets. He developed a symbol for zero: a dot underneath numbers. "But he, too, does not claim to have invented zero, which presumably must have been around for some time," Gobets added.

An inscription on a temple wall in Gwalior, India, dates back to the ninth century, and has been considered the oldest recorded example of a zero, according to the University of Oxford. Another example is an ancient Indian scroll called the Bhakshali manuscript. Discovered in a field in 1881, researchers thought it also had originated in the ninth century. However, recent carbon dating has revealed that it was probably written in the third or fourth century, which pushes the earliest recorded use of zero back 500 years.

Marcus du Sautoy, a professor of mathematics at the University of Oxford, said, "Today we take it for granted that the concept of zero is used across the globe and is a key building block of the digital world. But the creation of zero as a number in its own right, which evolved from the placeholder dot symbol found in the Bakhshali manuscript, was one of the greatest breakthroughs in the history of mathematics.

"We now know that it was as early as the third century that mathematicians in India planted the seed of the idea that would later become so fundamental to the modern world. The findings show how vibrant mathematics have been in the Indian sub-continent for centuries."

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Who Invented Zero?
By Jessie Szalay - Live Science Contributor September 18, 2017
https://www.livescience.com/27853-who-invented-zero.html

recall Ramanujan's number ( also called Hardy-Ramanujan number ) 1729 = 10^3 + 9^3 = 12^3 + 1^3 , which is the smallest number which can be expressed as sum of two cubes in two different ways ; and , also recall problem of solving Nx^2 + 1 = y^2 in integer x and y for a given N ; in respect of the later problem namely that of solving Nx^2+1 = y^2 in integers , if N=2 , then x=2 and y=3 ; that is a solution --- --- Q: isn't it ?[ ] ; for a specified N such as N = 61 , Fermat's challlenge , the problem is clearly non-trivial ; for N = 61 the solution is x = 226 153 980 , y = 1766 319 049 ; Q: is there a solution for every N , Eh ?