Oh my god!! Where do I begin?? To put it in a very simple way, Indians invented/discovered almost everything in every field imaginable!! India was the centre of the world for every century except the 18th, 19th and 20th century. Let us go through SOME of their important inventions/discoveries, cuz it would be impossible to mention all of them cuz they made so many:
1) Mathematics: They invented zero, the number system, (these 2 in particular are probably the greatest inventions made in the history of mankind!) the place value and the decimal system, algebra, trigonometry, calculus, the value of pi and almost every other concept in mathematics.The largest numbers the Greeks and the Romans used were 106 whereas Indians used numbers as big as 10*53 (i.e. 10 to the power of 53) with specific names as early as 5000 B.C.during the Vedic period.Even today, the largest used number is Terra: 10*12(10 to the power of 12). Here is a quote from Albert Einstein:
"We owe a lot to the Indians, who taught us how to count, without which no worthwhile scientific discovery could have been made."
2) Medicine: Sushrutha is the father of medicine. He was the first person in human history to perform surgeries like kidney stone removal, facial reconstruction surgery and plastic surgery. Indians invented the art of performing surgeries and also discovered the use of Anesthesia. Indians also invented the first school of medicine, namely Ayurveda. Detailed knowledge of anatomy, embryology, digestion, metabolism, physiology, psychology, etiology, genetics and immunity is also found in many ancient Indian texts.
3) Metaphysics/Astronomy: Ancient Indians had a very profound knowledge of the origin of the universe and man, the circumference of the earth and other planets, the age of the universe and the earth,the theory of relativity and also the law of gravity! (It was a man by the name of Brahmagupta who first discovered gravity, it wasn't Isaac Newton). Bhaskaracharya rightly calculated the time taken by the earth to orbit the Sun hundreds of years before the astronomer Smart. According to his calculation, the time taken by the Earth to orbit the Sun was 365.258756484 days.
4) Random: Indians also invented Yoga, martial arts, (it spread from India to other parts of the world) Chess, Snakes and Ladders, buttons, high grade steel manufacturing, the art of navigation, playing cards, gymnasiums, the first university and the first university to admit women, rocket artillery, almost every geometrical instrument, cultivation of cotton, cultivation of jute, mining, the concept of HDI and GDP. Four of the world's major religions originated in India: Hinduism, Sikhism, Buddhism and Jainism.
India's literary, artistic and philosophical contribution to the world is greater than any other civilization in history.
ALL THIS IS JUST THE TIP OF THE ICEBERG.
Here are some quoted to further illustrate my point:
"Almost all the theories, religious, philosophical, and mathematical, taught by the Pythagoreans were known in India in the sixth century B.C."
-H. G. Rawlinson (English Historian)
"I like to think that someone will trace how the deepest thinking of India made its way to Greece and from there to the philosophy of our times."
-John Archibald Wheeler (American scientist)
"Besides the discoverers of geometry and algebra, the constructors of human speech, the parents of philosophy, the primal expounders of religion, the adepts in psychological and physical science, how even the greatest of our biological and theologians seem dwarfed! Name of us any modern discovery, and we venture to say that Indian history need not long be searched before the prototype will be found on record. Here we are with the transit of science half accomplished, and all our Vedic ideas in process of readjustment to the theories of force correlation, natural selection, atomic polarity and evolution. And here, to mock our conceit, our apprehension, and our despair, we may read what Manu said, perhaps 10,000 years before the birth of Christ: The first germ of life was developed by water and heat. Water ascends towards the sky in vapors; from the sun it descends in rain, from the rains are born the plants, and from the plants, animals."
- Louis Francois Jacolliot (French diplomat & author)
"I shall now speak of the knowledge of the Hindus...of their subtle discoveries even more ingenious than those of the Greeks and Babylonians - of their rational system of mathematics or of their method of calculation which no word can praise strongly enough - I mean the system using the nine symbols. If these things were known by the people who think that they alone have mastered the sciences because they speak Greek, they would perhaps be convinced that every folk, not only Greeks, but men of a different tongues, know something as well as they."
- Severus Sebokbt (Syrian astronomer)