It turns out that according to a recent discovery in an ancient manuscript, calculus might first have been discovered not by Newton or Leibniz in the 1700s but by Archimedes a millenium earlier:
For seventy years, a prayer book moldered in the closet of a family in France, passed down from one generation to the next. Its mildewed parchment pages were stiff and contorted, tarnished by burn marks and waxy smudges. Behind the text of the prayers, faint Greek letters marched in lines up the page, with an occasional diagram disappearing into the spine.
The owners wondered if the strange book might have some value, so they took it to Christie’s Auction House of London. And in 1998, Christie’s auctioned it off—for two million dollars.
For this was not just a prayer book. The faint Greek inscriptions and accompanying diagrams were, in fact, the only surviving copies of several works by the great Greek mathematician Archimedes.
The kind of mathematics that Archimedes was doing look a lot like standard problems on integration that Calculus II students mutter about today — finding the areas of curved figures, finding the volumes of solids via cross-sectional area sums, and so on.
The article goes into depth about what makes Archimede’s work such a breakthrough, namely the willingness to work with “actual infinity” instead of “potential infinity”. Contemporaries like Aristotle believed that actual infinity didn’t exist; instead, the world is full of potential infinities. For example, lines that are infinitely long do not exist, only lines which are finite but could be extended, hypothetically, to infinite lengths. The article points out that today, we don’t use actual infinity but rather potential infinity, which is the basic underpinning of the concept of the limit which in turn is what all of calculus is based on.
This is a major discovery — the kind that makes you think about the what-if questions of how the world might have turned out differently if calculus had taken off 700 years prior to Newton. And it’s somehow fitting that high-tech microscopic methods, developed no doubt using the very calculus that Archimedes must have envisioned, were used to extract Archimedes’ handwriting from the copied-over manuscript.