Zero

The concept of zero was absolutely crucial in the development of mathematics, enabling the development of algebra and latterly, calculus.

It was in India that the notion of zero as representing nothingness first took root.

The Indians were not the first to employ a place value system like the decimal number system we use today. The Babylonians employed such a system and the Mayans independently used one too, and each realised that a marker of some sort needs to be used in such a system to prevent errors. So in a crude sense, you had an idea of a zero as a marker of an empty place, with a very definite and resticted technical meaning. But this would not be the result of, say, subtracting 1 from 1. That result, i.e "nothing", was something the Babylonians and the Greeks who followed them had great trouble with.

The key leap in thought that occurred to ancient Indian mathematicians here was to recognise that this zero could also be used to represent "nothingness". Brahmagupta was the first to hit upon a deep - and unique - insight, that the arithmetical number line could be extended to yield zero and negative integers.

It's only abstractly that one can conceive of speaking of "one apple", "two apples" and consider "no apples" as inhabiting the same thought-space. We take this for granted now but at the time, this was a revolutionary achievement.