Faith in mathematics

The title of this section should give us pause.

Our culture instills respect for other religions and our faith requires respect for people who practice other religions; nevertheless, I was dismayed when I saw an idol—an actual metal effigy—being worshiped. We who are children of Abraham by adoption may have something to learn from our Jewish and Muslim siblings concerning the vehemence of God’s abhorrence of idolatry. God demands our faithful faith.

Christianity in its early years confronted in Hellenistic culture not only pagan idolatry but a refined strain of religious thought in philosophy. In Fides et Ratio we read, concerning Greek philosophy, “Superstitions were recognized for what they were and religion was, at least in part, purified by rational analysis.”11 Let us pay close attention to the phrase “at least in part”.

Mathematics as we know it originated with Pythagoras, and Pythagoras founded a religion in which numbers played a central role. For the Pythagoreans, the numbers were an infinite, real, uncreated world of beings, and most mathematicians retain that faith today. With no training in history, philosophy, theology, Greek, or Latin, I can only listen as others speak of the early encounter of Christianity with Pythagoreanism. Elaine Pagels writes movingly of Justin’s conversion to Christianity after a previous unsatisfactory experience with a Pythagorean teacher who required him first to learn mathematics before he could be enlightened.12 Perhaps the Holy Spirit had implanted in Justin what today is called “math anxiety”.

I must relate how I lost my faith in Pythagorean numbers. One morning at the 1976 Summer Meeting of the American Mathematical Society in Toronto, I woke early. As I lay meditating about numbers, I felt the momentary overwhelming presence of one who convicted me of arrogance for my belief in the real existence of an infinite world of numbers, leaving me like an infant in a crib reduced to counting on my fingers. Now I live in a world in which there are no numbers save those that human beings on occasion construct.

The Pythagorean religion is no longer practiced. But Pythagoras strongly influenced Plato, and through Plato us. The numbers of Pythagoras are the type of Platonic ideas. What are Platonic ideas? Are they created—contingent and subject to change? Are they uncreated— as they were in the beginning, are now, and ever shall be? Or are they constructs of human thought which we come perilously close to idolizing? For us, men and women from the world of learning, to reify abstract ideas, even to base morality on them, is a temptation more insidious than the worship of metal effigies, and more corrupting.

During my first stay in Rome I used to play chess with Ernesto Buonaiuti. In his writings and in his life, Buonaiuti with passionate eloquence opposed the reification of human abstractions. I close by quoting one sentence from his Pellegrino di Roma.

“For [St. Paul] abstract truth, absolute laws, do not exist, because all of our thinking is subordinated to the construction of this holy temple of the Spirit, whose manifestations are not abstract ideas, but fruits of goodness, of peace, of charity and forgiveness.”

Source: Mathematics and Faith by Edward Nelson (Department of Mathematics Princeton University)

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