Indian science and math
Indian water wheel powered by oxen
From the time of the Harappans to the time of the Islamic conquests, Indian scientists and mathematicians were leaders in many different fields. They especially stood out in mathematics and engineering.
The Harappans in 2500 BC had a sewage system at their city of Mohenjo-Daro, and carefully laid out, straight streets. So even though we can't read their writing, we know that the Harappans understood a lot of geometry.
A severe climate change halted development at Harappa around 2000 BC. The Aryan invasion of 1500 BC also seems to have stopped scientific advances for a while, but it did bring military advances to India in the form of horse-drawn war chariots. Around 800 BC, when the Aryans in northern India learned to smelt iron from the Assyrians in West Asia, this gave them another military advantage.
Around 500 BC, thanks to Persian influence, the city of Taxila (in modern Pakistan) became a great scientific center. Atreya, a great botanist (plant specialist) and doctor, was working at Taxila about this time. Around the 300s BC, Indian farmers seem to have been using water wheels to lift water for irrigation - the earliest water wheels in the world, though these don't provide power - they're powered by oxen turning them.
About 500 AD, the great astronomer Arya Bhata wrote a book.
In the 600s AD, Indian mathematicians may have been responsible for inventing the numeral zero, and the decimal (or place) system (or it is possible that they got this idea from Chinese mathematicians). This made it a lot easier to add and multiply than it had been before. Indian mathematical ideas soon spread to West Asia and from there to Africa and Europe.
Indian advances in iron-working led to some new ideas in the 1000s and 1100s AD. First, Indian architects were the first to use iron beams to replace wooden beams for building big temples. Second, Indian blacksmiths discovered a kind of iron that made a very strong and flexible kind of steel, called wootz steel.
To find out more about Indian science, check out these books from your local library or from Amazon:
Science in Ancient India, by Melissa Stewart (2002). Written for kids.
Eyewitness India, by Manini Chatterjee (2002). Written for kids.
Ancient India, by Virginia Schomp (2005). Written for middle schoolers. Very good for reports.