Posts Tagged ‘del Monte’

The Jesuits: Pioneers of Mathematics as University Subject

May 8, 2013

There were chairs of mathematics at the Italian Universities from the late fourteenth century onwards. There was a chair of arithmetic in Bologna in 1384-5. When Leo X reformed the University of Rome in 1514 he appointed two professors of mathematics. Pisa had a chair of mathematics in 1484. Galileo was appointed a ‘mathesis praeceptor’ at the University of Pisa in 1589 through the influence of Cardinal Francesco del Monte. Galileo’s own influence on the teaching of mathematics in Italian universities was immense. His pupils Benedetto Castelli and Bonaventura Cavalieri respectively held the chairs of mathematics at Pisa, the Sapienza in Rome, and Bologna. Evangelista Torricelli, one of Castelli’s pupils, succeeded Galileo as the court mathematician of the Dukes of Tuscany. Another of Castelli’s pupils, Giovanni Alfonso Borelli became the mathematics lecturer at Messina in 1635. Malpighi, Borelli and Borelli’s pupil Lorenzo Bellini introduced Galileo’s mathematical programme into biology.

It was the Jesuit Order, which made mathematics an explicit and integral part of the educational curriculum. The Order’s Constitutiones of 1556 stated that the Society’s aim was ‘to aid our fellow men to the knowledge and love of God and to the salvation of their souls’. The principal subject at the Jesuit universities was therefore theology, as the subject best suited to this. A wide range of other subjects were also taught in addition to it, including literature and history, classical and oriental languages, and the arts and natural sciences. These were included because they ‘dispose the intellectual powers for theology, and are useful for the perfect understanding and use of it, and also by their own nature help towards the same end’. St. Ignatius de Loyola himself stated that ‘logic, physics, mathematics and moral science should be treated and also mathematicss in the measure suitable to the end proposed’. The person, who was chiefly responsible for establishing Jesuit policy in mathematics and their achievements in the subject was Christopher Clavius. Clavius held the chair of mathematics at the main Jesuit university, the Collegio Romano from 1565 until his death in 1612. Clavius defended the role of mathematics at the University agains the doubts of other colleagues, establishing a school of mathematics at the Collegio. Clavius lamented the low value many pupils placed on maths and philosophy, noting that

‘Pupils up to now seem almost to have despised these sciences for the simple reason that they think that they are not considered of value and are even useless, since the person who teaches them is never summoned to public acts with other professors’. He also considered it a great shame and disgrace, that members of the order, who had little knowledge of maths, became speechless during conversations with leading men, who were much better educated mathematically. He artgued that a proper grasp of maths was necessary for understanding the rest of philosophy. He stated that

‘these sciences and natural philosophy have so close an affinity with one another that unless they give each other mutual aid they can in no way preserve their own worth. For this to happen, it will be necessary first that students of physics should at the same time study mathematical disciplines; a habit which has always been retained in the Society’s schools hitherto. Folr if these sciences were taught at another time, students of philsophy would think, and understandably, that they were in no way necessary to physics, and so very few would want to understand them; though it is agreed among experts that physics cannot rightly be grasped without them, especially as regards that part which concerns the number and motion of the celestical circles, the multitude of intelligences, the effects of the stars which depend on the various conjunctions, oppositions and other distances between them, the division of continuous quantity into infinity, the ebb and flow of the sea, winds, comets, the rainbow, the halo and other meteorlogical things, the proportions of motions, qualities, actions, passions and reactions etc. concerning which ‘calculatores’ wirte much. I do not mention the infinite examples in Aristotle, Plato and their more celebrated commentators, which can by no means be understood without a moderate understanding of the mathematical sciences…’

Clavius’ influence is strongly shown in the Jesuit ‘Ratio Studiorum’ – educational curriculum – of 1586 and 1599. This was strongly Aristotelian, except where Aristotle conflicted with Christian theology, and included the whole range of Aristotelian natural philosophy and mathematics. The section on mathematics in the Constitutiones argued it was included because

‘without mathematics our academies would lack a great ornament, iindeed they would even be mutilated, since there is almost no fairly celebrated academy in which the mathematical disciplines do not have their own, and indeed not the last, place; but much more because the other sciences also very much need their help, because for poets they supply and expound the risings and settings of the heavenly bodies; for historians the shapes and distances of places; for the Analytics examples of solid demonstrations; for politicians admirable arts for good administration at home and in time of war; for physics the forms and differences of heavenly revolutions, light, discords, sounds; for metaphysics the number of spheres and intelligences; for theologians the main parts of the divine creation; for law and ecclesiastical custom the accurate computation of times; not to mention what advantages redound to the state from the work of mathematicians in the care of diseases, in navigations and in the pursuit of agriculture.’

Dawkins and the other militant atheists have sneered at the idea of people of faith as teachers. But the great pioneers in teaching mathematics at university the level were the Jesuits, who taught it as a vital aid to faith, and as a vital and indispensible tool for the other sciences. They were certainly not unaware that improving the standards of maths teaching in the order would also raise their status in contemporary society. Neverthless, they did much to establish maths as a suitable and necessary subject for Christians to study. Some of these early Jesuit mathematicians were also friends of Galileo. They included Clavius’ pupil and successor at the Collegio, Christopher Grienberger. Despite the aim of the Society to promote Roman Catholic Christianity, Jesuit scientists also co-operated and corresponded cordially with Protestant people of science. Recent Jesuit historians have noted that the Jesuits in West Africa collaborated with their Dutch scientific counterparts in their exploration of the region’s wildlife, and contacted Scandinavian scientists in Norway or Sweden for the scientific information they had. Their science was still strongly aristotelian, but they were despite this able to make valuable contributions to science.


‘Mathematics and Platonism in the Sixteenth-Century *Italian Univrsities and in Jesuit Educational Policy’ in A.C. Crombie, Science, Art and Nature in Medieval and Modern Thought (London and Rio Grande, Ohio: The Hambledon Press 1996).