Mathematics, Science, and the Society of Jesus
Mathematics, Science, and the Society of Jesus
Founded in the year 1540 by St. Ignatius Loyola, the Society of Jesus quickly became one of the preeminent religious orders of Europe and the world. In addition to teaching, the Jesuits considered the acquisition of knowledge to be a source of spirituality because it could help humans to better understand God's universe. Following this philosophy, many Jesuits became mathematicians and scientists, conducting research and teaching at universities as they contributed to man's store of knowledge. This led the Society of Jesus to become perhaps the world's most scientifically prolific religious order as well as some of the world's best teachers, traditions that continue to this day.
In the early 1530s Ignatius of Loyola, a Spanish soldier, was wounded in battle. He experienced a profound religious conversion during his convalescence and, along with six companions, vowed to follow a life of poverty and chastity and to make a pilgrimage to Jerusalem. In 1539, realizing they would not be able to make this journey, the seven men promised to accept any work assigned them by the Pope that would help the Church. In 1539, Ignatius presented the Pope with an organizational outline for a new religious order, the Society of Jesus. Unlike existing religious orders, the Society of Jesus swore an oath of personal loyalty to the Pope. In addition, there was great emphasis placed on flexibility, independent thought, and similar innovations. This resulted in a religious order that was to become important as the Church's emissaries abroad, as teachers, missionaries, diplomats, and the like.
Almost from the start, the Society of Jesus had its detractors. In fact, its familiar name, the Jesuits, was first given as a pejorative nickname, and was adopted by the Society soon after its founding. Because their training emphasized obedience to the Pope and to their hierarchy, education, and a rational approach to religious belief, the Jesuits quickly became Europe's teachers, opening colleges and universities throughout Europe. In fact, at one point Francis Bacon (1561-1626), a prominent Protestant and an opponent of the Catholic Church commented, "They are so good that I wish they were on our side."" In 1556, when Ignatius died, there were 1,000 Jesuits. Seventy years later, the order had over 15,000 members teaching at several hundred colleges and universities, most of which were Jesuit-run.
At that time only royalty, the aristocracy, the clergy, and the upper class of society received much in the way of formal education. The Jesuit's prominence in education in Catholic nations gave them unparalleled access to those in power. This, in turn, helped them to become respected and feared. The universities also gave the Jesuits the impetus to produce scientists of their own, which was encouraged by their admonition to find God in the laws of nature as well as in the Church.
Most Jesuit mathematicians of the sixteenth and seventeenth centuries are referred to as "geometers" and, because of this, it is often assumed that Jesuits concentrated on geometry and the mathematics of classical Greece to the exclusion of other methods. However, it is important to recall that, until Isaac Newton's (1642-1727) invention of the calculus, and the mathematical advances that accompanied this, most mathematical proofs were geometrical in nature. In fact, even Newton used geometry to prove many aspects of his calculus, and it was only in later decades that purely mathematical proofs, without geometry, became accepted. In particular, it is interesting to note that the work of Andre Tacquet (1612-1660) on infinitesimals helped provide the groundwork for the development of the calculus by exploring aspects of limits that were important to understand fully. In this, he ran counter to some religious arguments regarding the nature of infinity, since many felt that God's infinity should not have to accommodate a mathematical infinity. However, Tacquet's work remained important, and was among the first to describe many of the concepts later expanded on by Newton, Gottfried Leibniz (1646-1716), and Blaise Pascal (1623-1662) in their work.
Other noteworthy Jesuit mathematicians of this time included Ignace Pardies (1636-1673), Gregory St. Vincent (1584-1667), Honoré Fabri (1607-1688), and Christoph Clavius (1538-1612). There were, of course, many other Jesuit mathematicians and geometers; in fact, one reference notes no fewer than 631 Jesuits involved in mathematical work in the first two centuries of the order's existence, whose work ranged from mediocre to superb, as well as noted Jesuit astronomers, physicists, biologists, and geologists. All in all, the Society of Jesus has likely contributed more to the sciences than any other religious order in the world. In the next section, we will examine the impacts that this devotion to learning has had on science and on society.
The impact of the Society of Jesus and its priest-scientists can be seen in three primary areas: advances in scientific and mathematical knowledge, the impact of this research on Jesuit-led education, and the effects on the Catholic Church and its followers.
The first and most obvious impact, of course, is that on science itself. Jesuit mathematicians and scientists made a number of significant discoveries that helped expand our knowledge of mathematics, physics, and the world around us. Their discoveries helped pave the way for many of Newton's discoveries, as well as helped to consolidate the intellectual territories he and his contemporaries opened for inquiry. Jesuits were also among the first to differentiate between science and pseudo-science, questioning some of the more dubious claims and "discoveries" made in an era that did not always clearly differentiate between the natural and the supernatural. On the other hand, Jesuits were also in the forefront as the Church attempted to combat the effects of the Reformation, and they often took the role of reactionaries trying to protect the Church from change. This also led, in some cases, to attempts to hew to the status quo, including an emphasis on geometrical proofs as noted above, but it did not preclude Tacquet's work on infinitesimals or Fabri's support of Galileo (which landed him in prison for 50 days).
In addition, Jesuit mathematicians had a significant impact on the mathematics of this era. According to one writer, "One cannot talk about mathematics in the sixteenth and seventeenth centuries without seeing a Jesuit at every corner." Fabri, for example, worked on the problems of tides, optics, heliocentrism (whether the earth or the sun was the center of the universe), and tried to unify all of physics in a manner similar to geometry. Gregory Saint Vincent (1584-1667) developed polar coordinates, which are crucial to solving some types of math and physics problems. He was also important in developing analytic geometry, taught today alongside calculus in most colleges and universities. Pardies investigated problems in a manner that later inspired Newton, and even questioned some of Newton's findings in a way that forced Newton to go back to clarify his thinking on some crucial points. Other Jesuits, particularly those who were born in the sixteenth century, seemed more likely to concentrate on the classical teachings and wisdom of Aristotle, Euclid, and other ancient thinkers, rather than pursuing new avenues of inquiry. However, such teachers and thinkers became fewer and fewer over time, and their impact on society and on science lessened with the passing years.
As important as the Jesuit's research was, they clearly made their most significant contribution to European society through their teaching; and their teaching was, in turn, influenced by their research.
Because of the Jesuit's emerging tradition of intellectual independence and inquiry, their colleges and universities also tended to incorporate these traits into their teachings. There is no substitute for learning from those who are making important discoveries, and many of Europe's leaders were educated by priests who were active in adding to the sum of human knowledge. At the same time, these priests were celebrating the joy and the importance of learning, and teaching that physics, mathematics, and other branches of knowledge were not incompatible with religious beliefs. This combination may well have helped encourage the same spirit of rational inquiry that furthered the Renaissance and led to the Enlightenment, which led in turn to the French Revolution and the revolutions in North and South America.
Finally, and possibly most important, is the effect that all of the above had on European society of the sixteenth and seventeenth centuries. This was the time of the Renaissance, the rebirth of Western civilization after centuries of feudal rule. Although the Medieval period was not necessarily the long centuries of intellectual darkness so often pictured, it was also not the hotbed of new ideas that was to come. Man was beginning to realize that it might just be possible to understand nature and, to some extent, to predict and control it, and this was heady knowledge. It affected philosophy, politics, and religion, and all of these, to some extent, affected all of society.
The two biggest controversies in which Jesuit scientists became embroiled were those regarding the legitimate place of Earth in the universe and the nature of the infinite. In both cases, there were those who felt that science was intruding on God's prerogatives or that science was attempting to dethrone humans and God from their rightful places in the cosmos. The Church came down as squarely opposed to the Copernican solar system (in which the Earth and planets orbit the Sun), just as it was not in favor of mathematical infinities (or their converse, the infinitesimal). And, in both cases, scientists and mathematicians, including some Jesuits, showed the Church to be in error. These were but two steps in a process that continues to this day, in which scientific findings seem to detract from the authority of the Church, weakening it ever so slightly.
It is important, however, to recognize one important fact: most current scientific and religious leaders do not perceive that science and religion are mutually exclusive. While the scientific controversies of earlier years may have fostered this view, it should be obvious by the continuing presence of Jesuit (and other orders) priest-scientists through the centuries that this belief is overly simplistic and, in fact, is just wrong. And this may have been one of the more important societal contributions of Jesuit scientists and mathematicians at the time; their demonstration that a priest could also be a good scientist helped show Europe, recently emerged from superstition, that a good Christian could also believe in science and view the world in a rational way. This realization has served mankind well for over 400 years.
P. ANDREW KARAM
MacDonnell, Joseph. Jesuit Geometers: A Study of Fifty-SixProminent Jesuit Geometers during the First Two Centuries of Jesuit History. The Institute of Jesuit Sources, 1989.
"Jesuit Geometers." http://www.faculty.fairfield.edu/faculty/jmac/sj/sjgeom.html.