The Power of Geometric Progression: From Ancient Sumerians to Exponential Growth

Some time ago I made a little-known episode about how many people have ever been born. On one hand, it’s more of a life question than a mathematical one. On the other hand, the answer might truly surprise you — especially when you compare it to the world’s current population.

What’s fascinating is that at the heart of this seemingly simple calculation lies geometric progression. This straightforward tool from middle school math is the key to understanding our world, exponential growth and decay — phenomena found everywhere: from population growth to the spread of viruses, from financial strategies to space exploration.

What Makes Geometric Progression So Powerful

The answer is simplicity and universality.

Each successive element is obtained from the previous one by multiplying by a fixed number — the common ratio. Any term can be expressed through its index, the ratio, and the first term. And perhaps most remarkably, the sum of an infinite geometric progression (a decreasing one, of course) is found simply by dividing the first term by one minus the common ratio.

The Ancient Origins of Geometric Progression

What’s no less astonishing is that unlike a smartphone or a computer, we have been using geometric progression for nearly 5,000 years. At least the foundational principles emerged that long ago.

The history of geometric progression begins with the Sumerians, who lived around 2900 BC. They used sequences with a base of 3 and a multiplier of 1/2 to count supplies and distribute resources. Later, in the 3rd century BC, Euclid explored the properties of progressions in his landmark work Elements, applying them to the analysis of volumes and geometric figures. In the Middle Ages, mathematicians continued this work — the Indian scholar Brahmagupta used progressions to solve complex equations — and in the 18th century, Thomas Malthus applied them to explain the exponential growth of human population.

Geometric Progression Applications That Are Still Reshaping the World

And so a simple yet powerful tool emerged, with universal applications across many fields. But there is one more remarkable application of geometric progression worth knowing about. It came into existence exactly 16 years ago. And you will almost certainly be surprised by what it is and how it continues to change the entire world.

From it grew a multi-trillion-dollar industry. It has affected hundreds of millions of people across the globe and laid the foundation for what may become the world of the future. But more on that in the next episode, coming in just a couple of days — stay tuned. In the meantime, you can revisit the question of just how many people have ever been born throughout all of human history.