Some Facts which must be known:

First Indian women to obtain a medical degree - Anandi Gopal Joshi.

Based on her life a novel was return, Caroline Wells Healey Dall wrote Anandibai's biograhpy and a serial was aired on Doordshan named Anandi Gopal.(At the same time another interesting serial Discovery of India based on Nehru Book was also aired).

More Information:
http://en.wikipedia.org/wiki/Anandi_Gopal_Joshi.
The article states “It was common for Brahmins in those times to be proficient in Sanskrit;”, which makes us to realize that we need to known the importance of learning sanskrit which is one of the foundation and part of India tradition. :

Srinivasa Ramanujan.

With almost no formal training in pure mathematics, made extraordinary contributions to mathematical analysis.
http://en.wikipedia.org/wiki/Srinivasa_Ramanujan

The first Telugu Mathematician - Pavuluri Mallana: .

http://en.wikipedia.org/wiki/Pavuluri_Mallana

First Highest Civilian awardee - Sarvepalli Radhakrishnan.

http://en.wikipedia.org/wiki/Sarvepalli_Radhakrishnan

Works by Sarvepalli Radhakrishnan

1. Indian Philosophy (1923) Vol.1, 738 pages. Vol 2, 807 pages. Oxford University Press.
2. The Hindu View of Life (1926), 92 pages
3. An Idealist View of Life (1929), 351 pages
4. Review: E.A. Burtt (Cornell University), The Philosophical Review, Vol. 44, No. 2, (Mar., 1935), pp. 205–207
"Those who have read the author's previous volumes or have heard him speak are accustomed to associate with him warmth and vigor of style, penetrating flashes of keen analysis, and detailed familiarity with past and present philosophies in both east and west. In these respects none will find the book disappointing."
5. Eastern Religions and Western Thought (1939), Oxford University Press, 396 pages
6. Religion and Society (1947), George Allen and Unwin Ltd., London, 242 pages
7. The Bhagavadgītā: with an introductory essay, Sanskrit text, English translation and notes (1948), 388 pages
8. The Dhammapada (1950), 194 pages, Oxford University Press
9. The Principal Upanishads (1953), 958 pages, HarperCollins Publishers Limited
10. Recovery of Faith (1956), 205 pages
11. A Source Book in Indian Philosophy (1957), 683 pages, Princeton University Press
12. Review: E.A. Burtt (Cornell University), The Philosophical Review, Vol. 67, No. 3, (July 1958), pp. 411–412
"I believe this is the first time I have written a review when no negative criticism of any kind seemed to me warranted. ... No one interested in Indian thought who does not expect to master the original materials can dispense with this book."
13. Religion, Science & Culture (1968), 121 pages

The legend of Bhishma's.

http://en.wikipedia.org/wiki/Bhishma