Sometimes even the most terrible disasters have serendipitous consequences. Napoleon's disastrous invasion of Russia in 1812 for instance have been said to be a worthwhile "investment" just because of a single chart that was drawn 57 years after. This chart have been said to be a triumph that even the great French general (who was an amateur mathematician himself) would approve of.

As they say, when life gives you lemons...

In our daily lives, there are two things that we can tell: random event, and those due to cause and effect. However some supposedly random things are simply organized in such a way that we can't help by recognising a cause to their non-coincidental effect.

We see it in nature (the Golden Ratio), and constructs by humans (the movement of share prices). But what about in pure numbers? Especially the most mysterious kind: prime numbers.

Pi is one of those constants in the mathematical world. And because of that, it often appears in nature, particularly any that involves curves and ​spirals. But it would be too easy to derive pi from those very things - they are ordered, unchanging, predictable.

But what if pi can be derived from a series of improbable, unpredictable actions?

Nothing and everything. Two mathematical concepts that seems intuitive now, but inconceivable before the invention of zero and infinity. Both of these concepts originates from India, both are linked by the philosophical approach of the civilizations of the subcontinent.

In hindsight, it seems that these two concepts, crucial to the modern world, can only arise from a society that appreciates both.

In Part I we tackled the origins of arithmetic, the most basic and fundamental form of mathematics. Now we look at the more abstract world of geometry brought by the Greeks. It's no coincidence that at the same time they formulate mathematical theorems, they also ponder on philosophical paradoxes.

As we shall see, the Greeks idea of mathematics has more to do with attaining perfection than practical solutions.