Is the pope a mathematician? Yes, actually – and his training may help him grapple with the infinite

Humans are limited beings with finite brains and interactions during their lifetimes. However, humans possess the remarkable ability to grasp the concept of infinity. This capacity is evident in various aspects, such as Euclid’s proof of infinite prime numbers and the belief in infinite gods by many people.

The connection between mathematics and theology is evident in the life of Pope Leo XIV, who had a background in mathematics before joining the church. Infinity plays a crucial role in both disciplines, with mathematical objects forming infinite collections and theologians describing God as an absolutely infinite being.

Historically, mathematicians and theologians have had different perspectives on infinity. While mathematicians accepted the existence of infinitely many numbers, they rejected the idea of the absolute infinite. This led to paradoxes like Galileo’s paradox, highlighting the complexities surrounding infinity in mathematics.

The mathematician Georg Cantor revolutionized the concept of infinity in the 19th century by introducing transfinite set theory, which allowed for the exploration of absolute infinities in mathematics. Cantor’s theory laid the foundation for modern mathematics and provided a unified understanding of the infinite.

Cantor’s theory demonstrates that not all infinite sets are of the same size, with real numbers being larger than integers. The introduction of transfinite numbers, denoted by Aleph, expanded the understanding of infinity and its measurement in mathematics.

Cantor, a devout Christian, believed that his theory of absolute infinities was divinely inspired and sought to reconcile it with Catholic theology. His correspondence with Pope Leo XIII reflected his efforts to show that his theory did not challenge the uniqueness of God as an infinite being.

The intersection of mathematics and theology in Cantor’s work highlights how profound changes in mathematics can be intertwined with religious considerations. Pope Leo XIV’s choice of pontifical name in honor of Leo XIII, influenced by this mathematical connection, underscores the intricate relationship between mathematics, theology, and the concept of infinity.