Leaving the question whether math is innate or acquired, by nature or by nurture, there is ample evidence that infants and primitive tribes can count either mentally or using fingers. As per the "Dasama Nyaya" a person counting a group leaves himself out which means counting manually is prone to errors. Between 1911-18 Swami Bharati Krishna Tritha published what is called now "Vedic Mathematics" taught in school all over:
"After a deep study of the Vedas, he extracted 16 Sutras and 13 sub-sutras that form the backbone of Vedic mathematics. These formulas aren't limited to just addition or multiplication they extend to algebra, geometry, trigonometry, calculus, and more."
Besides Ramanujam (1887-1920), who was not a self-admitted vedic scholar, the aforementioned swami was the most celebrated hindu mathematician even though their mathematical intuition is worlds apart. For instance, Ramanujam thought about various kinds of infinity viz. countable, uncountable, ordinal, cardinal, etc. along with intuition of his co-evals in the west that there are more real numbers packed in between zero and one than there are numbers in the entire range of naturals.
My favorite puzzle is when you have a guest appearing at a hotel with infinite rooms that are all occupied, how would you check-him in? One solution is to ask the existing guests to shift by one room and the first vacant room is to be assigned to the new guest.
While it could be that vedic mathematicians didn't ponder over infinity besides the saanti mantra, called metaphysical infinity, which in essence means whether you add or subtract infinity from or to infinity the result is infinity, they deserve credit for zero, a mysterious number connecting the negative and positive numbers on the number axis. Its use in modern binary computers is well known.
For ancient hindus, math is not just an instrument to study reality, like posited by the scientists studying phenomenal laws, but a way to connect with the divine. Nowhere it is more apparent than in jyotish. Starting with sages Parasara and Jaimini (5000 BCE), Arya Bhata (476–550 CE) who was a mathematician-astronomer and author of Āryabhaṭīya and the Arya-siddhanta, Varahamihira (505- 587 CE) who gave us a compendium of Greek, Egyptian, Roman, and Indian astronomy called Pancha-siddhantika (“Five Treatises”), are some of the great jyotishi Bharat ever produced.
In the realm of counting or arithmetic, Bhaskaracharya who gave us Leelavati Ganita in 12th century AD, for sizing up weight, volume, currency, etc. that are commonly called "weights and measures" in modern curricula, Dharma Raja who was an expert in "yaksha hridaya ganita" whereby one could tell the number of leaves on a fully grown tree without counting or the number of horses on a battle-field by a mere glance, besides Ramanujam who said the sum of infinite series of nature numbers adds up to a negative fraction which is more like the destiny of human race, are well known.
With the advent of calculators and computers, though counting fast or efficiently using brain power have taken a back-seat, the challenges posed by infinity are ever present. For example, what is the largest number to represent a nation's GDP or trade deficit that are currently in the range of trillions? What is the largest prime number that can be used to encrypt this message? Is space infinite? And so on.
In Leelopakhyana of Ramayana, Sage Vasishta speculates that within each atom there is an entire universe composed of atoms that have their own universe endlessly. It could be that our universe is the last in that chain. As scientists try to smash atoms in particle accelerators, we miss the big picture the Sage had painted. For example, our puranas say Lord Vishnu "descended" to earth from Vaikuntha. None is any wiser.
Finally there are autistic savants like in the movie Rain Man who could be specialists in counting or arithmetic though cognitively limited when compared to normal people, as there are people who can remember dates while not knowing their street address. Modern AI is made possible by such autistic theory where the "neural networks" specialize in pattern recognition to the exclusion of commonsense. Unchecked, future generations will turn out to be autistic savants much like Sakuntala Devi and Bharatiya chess wizards like Anand had demonstrated.
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