Why Newton uses geometry full of complexities in his book

The original version of “Principia” written by Isaac Newton, a leading scientist at the pinnacle of classical physics, is filled with ovals, straight lines, circles and any other kind of shapes that you may be able to imagine, which makes it different from other physics books of our time. Physical theories explained by Newton’s geometric shapes can be replaced with simple equations. Then, this begs the question: Why the math genius wrote “Principia” not based on algebra but based on geometry?

Starting from this simple question, Professor Kim Min-hyeong at Edinburgh University describes from a macroscopic viewpoint how European history has separated from that of the Islamic world since the Battle of Lepanto in 1571. Kim majored in mathematics in Seoul National University to graduate early, later joining the ranks of the most renowned mathematicians in the world to become the first South Korean to teach math at Oxford University.

Professor Kim explains that algebra flourished in the Islamic region while geometry prospered during the ancient Greek era. For example, as early as the 11th century, Islam scholars systemized the cubic equation by adopting the Arabic numerals, which makes it easier to handle multiplication than the Roman ones. By contrast, ancient Greece made outstanding achievements in geometry such as the Pythagorean Theorem in the 6th century BC. Around the end of the Middle Age, Europe accepted algebra and geometry of the ancient Greek era via the Islamic world to get them prepared before the Renaissance in the 14th century.

Following the fall of Constantinople by the Ottoman Empire in 1453, the Battle of Lepanto in 1571 divided the Mediterranean east-west with the Islamic world on one side and Europe on the other side. It is around the 15th to 16th century when the divide of Western and Eastern civilizations came about. That is why geometry during the ancient Greek period bases Newton’s “Principia” rather than algebra acquired from the Islam world, according to the author’s analysis. He emphasizes that socio-cultural needs can have a great influence on scientific evolution.


Sang-Un Kim sukim@donga.com