Gregory of St. Vincent (1584-1667)    Historical Sketch

This referent is variously known as Gregory of Saint Vincent, as Gregorius Saint-Vincent, or as Gregory St. Vincent, SJ. It seems that the first is the most widely used. Also, he is variously listed as having been born in 1584 in Bruges or Ghent, Belgium, and he became a Jesuit. He taught in Brussels, Antwerp, Louvaine, and Ghent, where he lived out his life, dying in 1667.

Gregory's reputation was that of a brilliant mathematician. Leibniz reportedly included him with Descartes and Fermat as one of the founders of analytic geometry. He is reported to be the first to settle Zeno's Achilles paradox, doing it the way you would do it today---summing an infinite geometric series (see the problem below). This so-called paradox had baffled philosophers for eons (and still seems to baffle people today). He found areas and volumes in pretty much the same way that one does by computing limiting forms of small incremental areas and volumes, i.e., essentially by integral calculus, very much as Archimedes did. Also, he essentially integrated the function f(x) = 1/x, and got to what we today call the logarithmic function. His written mathematical works are contained in a book of some 1250 pages.

Here is Zeno's Paradox in a nutshell: I am in a room and want to leave. I must first cover half the distance from here to the door. Having done that, I must then cover half the remaining distance to the door. Having done that, I must cover half the remaining distance to the door. And so forth, forever, so I cannot get to the door. Solve the so-called paradox by summing an infinite geometric series.