Nicholas of Cusa

1401-1464

German Mathematician and Philosopher

Nicholas of Cusa is a figure difficult to assess within the context of mathematics. Certainly he wrote extensively about the subject, in particular on the properties of circles, but it is primarily as a philosopher and mystic that he is remembered. On the one hand, he held firmly to mindsets associated with the medieval world, in particular with his belief that all knowledge has its roots in theology. On the other hand, he displayed an openness to new ideas more characteristic of the Renaissance and the modern age that lay beyond it.

Born Nicholas Krebs in the German town of Kues in 1401, Cusa studied law and mathematics at the University of Padua in Italy. He later received his doctorate in canon law before moving to Cologne in the 1420s. There he took an interest in the philosophical writings of the ancients, particularly Plato (427-347 B.C.), and began forming the foundations of his own mystical philosophical system.

In 1431, a year after he entered the priesthood, Nicholas took part in the Council of Basel, convened in an attempt to shore up the church against the rising tides of dissent that would culminate in the Reformation. Six years later, he took part in a failed mission of reconciliation between the Western and Eastern churches, travelling to Constantinople—which, unbeknownst to anyone at that time, would fall permanently into Muslim hands in less than two decades' time.

Despite the mission's lack of success, Nicholas won recognition for his diplomatic work, and was ultimately granted the position of cardinal. He gained even greater favor with the papacy when an old friend, Italian humanist Enea Silvio Piccolomini, assumed St. Peter's throne as Pius II in 1458. Two years later, Nicholas settled permanently in Rome.

By then he was just six years away from the end of his life, and had long since formed his rather idiosyncratic philosophical system. Though he had an interest in mathematics far beyond that of a typical medieval, mathematical knowledge in Nicholas's mind served to increase the mystery in the world rather than to unravel it. Certainly he was not the first to see the discipline in those terms: Pythagoras (c. 580-c. 500 B.C.), who he greatly admired, was perhaps the most notable of all mathematical mystics.

Among Cusa's mathematical interests were the ideas of infinity and of squaring the circle—that is, mapping the area of a circle onto an equally large square, using only a ruler. In his mind, these concepts were linked, because an infinitely large circle would be the same as a square—and, as he noted, would have neither a center, a radius, nor a diameter.

In the realm of astronomy, Nicholas anticipated Copernicus (1473-1543) by many years in saying that the center of the universe was the Sun rather than the Earth. He also suggested that many stars in the universe had their own worlds revolving around them; however, even these scientific statements were heavily laced with Nicholas's mysticism, and his belief that the center of the universe is God. He died on August 11, 1464, in the town of Todi—then part of the Papal States—near Rome.