Abstract: Mathematics had a rich history in ancient and medieval India. Indian mathematicians made original contributions to algebra, number theory, and geometry. In this lecture, we cover some of the highlights of the emergence and development of mathematics and mathematical thoughts in India. We will focus especially on themes related to square roots and the Pythagoras theorem. While Class X mathematics is enough background to follow these topics, the ideas and creativity involved are non-trivial and exciting. It is also illuminating to see how our ancestors absorbed and improved knowledge from our neighbors, and in turn, influenced them.