CALCULUS Understanding Its Concepts and Methods

Galileo Galilei (1564--1642) --- Historical Sketch

When Galileo's name is mentioned, many people think only of astronomy, his advocacy of the Copernican system, the Inquisition, his trial and prison sentence, and so on. How many think of his contributions to mathematics?

Galileo Galilei was born in 1564 near the ancient city of Pisa when it was under Florentine rule. His father was a music teacher, and Galileo was his mother's first child. Galileo was sent to a monastery for his early education, and he quite liked the monastic life. However, his father wanted the boy to enter the field of medicine, so Galileo went to the University of Pisa for that purpose. But he was indifferent to such studies, preferring courses in mathematics and physical science. From 1582 to 1585, Galileo was a medical student in name but a mathematics student in fact---studying Euclid and Archimedes. He left the university without completing a degree.

Studying mathematics on his own and through correspondence with established mathematicians, and trying unsuccessfully to be appointed to teaching positions, Galileo was appointed in 1589 to the chair of mathematics at the University of Pisa in 1589, when he was but 25. Three years later, Galileo was appointed to a much more lucrative professorship of mathematics at the University of Padua, where he taught Euclidean geometry and geocentric astronomy to medical students (who needed it as a foundation for the astrology they would use in medical treatments).

During his early years at Pisa and Padua, Galileo discovered the isochronal behavior of a pendulum (the time it takes for one swing a pendulum is independent of the length of the swing), invented the hydrostatic balance to measure the specific gravity of solids, demonstrated that bodies of different weights fall with equal velocity (the story that he dropped weights from Pisa's leaning tower are probably apocryphal), showed that the path of a projectile is parabolic (if air resistance is disregarded), built a telescope, observed mountains on the Moon, the satellites of Jupiter, sunspots, the phases of Venus, and discovered that the Moon shines from reflected sunlight. His telescopic discoveries were rewarded with an appointment as mathematician extraordinary at the University of Florence. In 1637, Galileo became totally blind.

You can see that Galileo was mainly concerned with physics and astronomy. He considered himself the creator of the subject of dynamics because he had given to the study of dynamics a mathematical precision it had not had before. His work with astronomy brought to life one of the ancient conics: the orbits of planets as realizations of the ellipse. He was also taken by ideas of the "infinitely small" and the "infinitely large". He pointed out the paradox that there are as many square integers as there are integers.

Though much of Galileo's work can be simplified by calculus as we know it today, he did use thought processes that might be labeled precalculus. Is it significant that Galileo died on the day that Newton was born?

Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.