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You will not find any Indian invention around you. Your car, fridge, TV, oven, phone and pen- none of them. But, Indians of present day are good in putting stake for the achievers. Just because one's name is Indian, or that he was born in Mumbai or that he visited his great grand father in Ahmedabad for the first time whole India will be proud of him for his invention! Ancient Indians never looked outwards to make some sort of electronic or mechanical toys, but they postulated great theories. Aryabhata(476BC) was the first to discuss spherical astronomy and calculate position of planets, eclipse points and the circumference of earth. He postulated heliocentric theory even 1000 years earlier to Copernicus. The very words Geometry and Trigonometry are derived from Sanskrit words geomiti and trikonamiti. Salva sutra describes Paithogorus theorem. Brahma gupta (628AD) postulated that any integer divided by zero yields infinity. Albert Einstein has said, "We owe to the Indians for they taught us to count without which no scientific discovery was ever possible". Indians discovered calculations in decimals and fractions, pi value, square and cube roots while their contemporaries were struggling to write 83(LXXXIII is roman notation for 83!).
SCIENCE, PHILOSOPHY & ARTS IN ANCIENT INDIA
The Gregorian calendar on your desk simply adds on one day for every 4 years and is not in coherence with the movement of sun. But, Hindu calendar is in coherence as the short fall is corrected in the month itself by adding Adhikamasa as postulated by Maharshi Vishwamitra. Rig Veda 1.164.1, 2, 14 and 15 describe sun's motion, ritus and colours of spectrum. Kalyana varma, Varahamihira, Jaimini, Vidyanatha Deekshita, Kalidasa, Mantreshwara, Satyacharya, Venkatadri, Parashara, Ramadayalu and Garga have immensely contributed for the development of Hindu astrology. Kanada (6th BC) had propounded that Paramanu (atom) forms dwinuka (molecules) He also discovered that the density of molecules is peculiar to each matter and so an object weighs less in water than in air, even earlier to Archimedes

Ancient Indians had good knowledge of chemistry. Dyes, perfumes and bhasmas (for medical use) were also prepared. Iron Pillar erected by Raja Chandra Verma in Delhi stands rust-free for more since 1500 years. Such metal treatment was not known to western world till the discovery of stainless steel. Sushruta describes surgical techniques and tools. Also, he conduced surgery for bladder stone removal, cataract and plastic surgery. Nyayashastra by Goutama, Natya shastra by Bharata Muni, Artha shastra by Koutilya give the glimpses of the culture of ancient India..
My friend  - Sri C.S. Sastry, a successful IT specialist and entrepreneur of www.vicisoft.com who has travelled extensively in US, Europe & other countries,  has this so say:

FACTS TO MAKE EVERY INDIAN PROUD:
We Indians are the wealthiest among all ethnic groups in America, even faring better than the whites and the natives. There are 3.22 millions of Indians in USA (1.5% of population). YET, 38% of doctors in USA are Indians. 12% scientists in USA are Indians. 36% of NASA scientists are Indians. 34% of Microsoft employees are Indians. 28% of IBM employees are Indians. 17% of INTEL scientists are Indians. 13% of XEROX employees are Indians.

QUOTES ABOUT INDIA:

We owe a lot to the Indians, who taught us how to count, without which no worthwhile scientific discovery could have been made. --Albert Einstein.

India is the cradle of the human race, the birthplace of human speech, the mother of history, the grandmother of legend and the great grand mother of tradition. -- Mark Twain.

If there is one place on the face of earth where all dreams of living men have found a home from the very earliest days when man began the dream of existence, it is India. --French scholar Romain Rolland.
Music that is distinctive from the western was well developed. Ancient Indians were good navigators and the very word navigation is derived from Sanskrit root 'nowka'. Yet, they never invaded neighboring land nor subjugated other cultures.

Most of the Indian works are related to philosophy. Kapila, Patanjali, Badarayana, Vyasa, Sri Shankara, Madhvacharya, Ramanujacharya and all the rishis mentioned in Vedas and Upanishads have contributed towards this. Panini devised the first ever grammar treaties. Indian philosophy is not founded by a single person's teachings nor by someone's certain sacrifice but it encourages quest for knowledge. It does not implore to believe in the name of faith.
India conquered and dominated China culturally for 20 centuries without ever having to send a single soldier across her border. --Hu Shih, (former Chinese ambassador to USA) .

ALL OF THE ABOVE IS JUST THE TIP OF THE ICEBERG, THE LIST COULD BE ENDLESS. BUT, if we don't see even a glimpse of that great India in the India that we see today, it clearly means that we are not working up to our potential and that if we do, we could once again be an ever shining and inspiring country setting a bright path for rest of the world to follow. Work towards the welfare of INDIA . Say proudly, I AM AN INDIAN.

Sri. Sastryji, thanks a lot for your valuable input.
"Do question as you like. If known will tell everything, said the rishi". - sloka2, prathamadyaya,  Prashnopanishad. There have been attempts to decode veda mantras to the numeric form (like ja stands for 8). The location of chakras in the body have been acknowledged by Dr. Motoyama of Japan and Dr. Sergekyev of Russia. Anuvaka3, sukta 11 mandala 7 of Rig Veda says-"O Agni, we know you have wealth to give 3 times a day to mortals". This is seen as the reference to the Gamma ray showers that occur about 3 times a day. I have not included these, as the research is not yet conclusive.  Our ancient poets Amara simha, Vyasa, Valmiki, Kalidasa, Bana, Bhasa, Bharavi, Vishnu Sharma, Sudraka, Bhartruhari and works like Mahabharata, Ramayana are no less than Shakespeare, Words worth, Milton and Keats.

We are being taught about Archimedes, Neils Bohr, Rutherford, Paithogorus and Ptolemy since our early childhood. A general knowledge book by a reputed Indian publishing house (Maharaj, it is not a foreign one - we can not blame West for all our misfortunes!) which also owns a vernacular daily and an English weekly, sketched vivid details cosmology of Babylonians, Greeks, Arabs and Europeans but the Indian contribution is summed up merely as --"Aryabhatta, Bhaskaracharya, Varahamihira etc.," in two lines. When my purohit friend puts forth pseudo-scientific reasons for performance of Achamana, Shraddha, it pains me much. We have forgotten our heritage and our achievements but grope in darkness for a reason to be proud of.