After the Greeks, it’s almost as if we stopped exploring the universe, both the Platonic and the Aristotelian. Looking back, it seems rather incredible that such a long span of time could have passed before we picked up the baton (by we, I refer to all of us that have been born under the aegis of the scientific method) and continued where they left of.
The incredible thing about mathematics is that it holds true, throughout all time, throughout all possible universes. It is a landscape whose known boundaries can only be drawn back. Its truths are eternal.
I find it a wonder that the discoveries of Apollonius, a millennia and a half before the Renaissance, could reach out across time, freeing us from an era of geocentricism, into the age of space exploration. His text, inscribed on a piece of animal skin, endured and fell into the hands of Kepler, who, along with his contemporaries, gave us modern astronomy. It it likely possible that he, or someone else of his time, would have unveiled the laws of planetary motion without Apollonius’s work on conic sections; but so strongly was the Renaissance inspired by the spirit of Greek Antiquity that it is impossible to imagine one without the other.
What is even more incredible is that in between Apollonius and Kepler, a highly plastic form of numerical representation was codified and popularised. The re-discovery of zero and other mathematical concepts, which spread from India and the Middle-East to Europe, through their usefulness in economic matters, eventually reached the Renaissance scientists. These new concepts unlocked the entire universe to us. The discovery, or non-discovery, of symbolic numerical representation and the concept of zero is a civilisational filter.
Apollonius couldn’t know the applications of his theory when he wrote them down. He was simply exploring the world and charting what he saw. Only over a millennia later, did their applicability become apparent. Conics was a fragment that held the future, that lead to the discovery of relativity, black holes, anti-matter and all manner of wonderful beasts.
We cannot even begin to imagine all that is possible, with what we know today. I find that incredible.