The Mathematical Innovations of Father Antonio Spadaro

Nearly fifty years go, my parish secretary, who was elderly even then, kept the parish accounts using an abacus. I gave her the latest kind of electric adding machine, which she used dutifully, but I noticed that she then checked the results with her abacus, an instrument that has been reliable since long before the invention of Hindu-Arabic written numerals. Until then, ten human fingers provided a decimal system.

If we don’t get numbers right, we will not get much else right. This is a point Lewis Carroll made in his Adventures of Alice in Wonderland. An apocryphal story claims that Queen Victoria, having enjoyed the Alice tales, requested a first edition of Carroll’s next book, and was perplexed when it arrived: An Elementary Treatise on Determinants. There is a convincing thesis that Carroll, as an Oxford mathematician, wrote Alice’s Wonderland adventures to satirize new non-Euclidean theories. For instance, when Alice expands to nine feet and shrinks to three inches, she tells the Caterpillar, “Being so many different sizes in a single day is very confusing.” The Caterpillar enjoys the confusion, which is Carroll’s way of saying that Euclidean and hyperbolic geometry, rooted as they are in different axioms, cannot both be true at the same time. The guests at the Mad Hatter’s tea party are very likely symbolic commentaries on the discovery of quaternions by the Irish mathematician William Rowans Hamilton, in 1843.

The abstract algebra, which Carroll thought ridiculous, was the background of Hamilton’s theory of “pure time,” which he seems to have inferred from Kant’s concept of a Platonic ideal of time distinct from chronological time. But this does not deny the existence of time as we know it; and Kant himself was almost neurotically compulsive about timing every action of his day by his clock.

One wonders what Carroll would have thought of Einstein’s Relativity, or Heisenberg’s Uncertainty Principle. But Einstein did not expect that his theory in physics should provide any moral structure, and Heisenberg would not apply a principle of quantum mechanics to theological systems. Since then, many have made such mistakes, the first being the early Modernists and now an increasing number of people even in the heart of Rome, who muddle sciences and hold certainty suspect.

Father Antonio Spadaro, a close associate of Pope Francis, raised eyebrows in July 2017 when he described religious life in the United States, with such confidence that can come only from a profound knowledge of a subject or a total lack of it. Father Spadaro advises the Holy Father, who had never visited the United States before becoming pope. In an essay in Civilta Cattolica called “Evangelical Fundamentalism and Catholic Integralism,” Father Spadaro spoke with disdain of a cabal formed by Evangelicals and Catholics motivated by a “triumphalist, arrogant, and vindictive ethnicism” which is creating an “apocalyptic geopolitics.” Religious fundamentalists behind this plot have included Nixon, Reagan, Bush, and Trump who is a Manichaean. The co-author of this imaginative literary exercise was a Protestant minister, Marcelo Figuero who is editor-in-chief of the new Argentinian edition of L’Osservatore Romano to which office he brings the rich systematic theology of Argentinian Presbyterianism. The two authors were rhetorically florid in denouncing Yankee racism, obscurantism, and fascism, so unlike the temperate history of Spadaro’s own peninsula and Figuero’s Argentinian utopia. If they want to condescend to the USA, they need a loftier platform.

Then in October 2017 Father Spadaro said in Boston, “It is no longer possible to judge people on the basis of a norm that stands above all.” The suggestion is that a mathematical principle of uncertainty also applies to theology where all is in flux and subjective.

Later, in a well publicized comment on “Twitter” which operates according to stable and constant principles of applied engineering, Father Spadaro typed: “In theology 2 + 2 can equal 5. Because it has to do with God and the real life of people…” To put a charitable gloss on that, he may have simply meant theology applied to pastoral situations where routine answers of manualists may be inadequate. But he has made his arithmetic a guide to dogma, as when he said in his Boston speech that couples living in “irregular” family situations “can be living in God’s grace, can love and also grow in a life of grace.” Yet, despite his concern for freedom of thought and expression, Father Spadaro has recently expressed sympathy for calls to censor Catholic television commentators who insist that 2+2 = 4.

There are two things to consider here. First, some clergy of Father Spadaro’s vintage grew up in a theological atmosphere of “Transcendental Thomism.” Aquinas begins the Summa Theologica asserting in the very first Question, four times, that theology has a greater certitude than any other science. While it gives rise to rhymes and song, it is solid science, indeed the Queen of Sciences. Transcendental Thomism was Karl Rahner’s attempt to wed Thomistic realism with Kantian idealism. Father Stanley Jaki, theologian and physicist, called this stillborn hybrid “Aquikantianism.” But if stillborn, its ghosts roam corridors of ecclesiastical influence. This really is not theology but theosophy, as romantic as Teilhard de Chardin, as esoteric as a Rosicrucian, and as soporific as the séances of Madame Blavatsky. The second point is that not all cultures have an instinct for pellucid expression. The Italian language is so beguiling that it can create an illusion that its rotundity is profundity, and that its neologisms are significant. When it is used to calling you a “Cattolico Integralista” or a “Restauratore” the cadences almost sound like a compliment. Even our Holy Father, who often finds relief from his unenviable burdens by using startling expressions, said on June 19, 2016: “We have a very creative vocabulary for insulting others.”

In saying that 2+2=5, Father Spadaro preserves a familiar if deluded intuition, and trailing behind him is a long line of children who in countless schoolrooms have been made to stand in corners for having made that mistake. A famous use of it was in George Orwell’s Ninety Eighty-Four speaking of its dystopia: “In the end the Party would announce that two and two, made five and you would have to believe it. It was inevitable that they should make that claim sooner or later; the logic of their position demanded it … the very existence of external reality, was tacitly denied by their philosophy.”

Malleable arithmetic has its consequences in the solid world. There is Stalin’s consoling wisdom for apparatchiks: “One death is a tragedy; a million is a statistic.” Unlike Orwell’s dystopia, the Third Reich was a fact, and in it, any science that was not ideological was bourgeois. In 1934, the senior German mathematician David Hilbert was asked by the Nazi minister of education, Bernhard Rust, “How is mathematics at Göttingen, now that it is free from the Jewish influence?” Hilbert answered, “There is no mathematics in Göttingen anymore.” Imagine mathematics free from Catholic influence. To name but a few devout Catholics who transformed mathematics while confident that 2+2 = 4 instead of 5, even in theology, Father Spadaro notwithstanding, there are: Fibonacci, Grosseteste, Albertus Magnus, Bacon, Lully Bradwardine, Oresme, Brunellescchi, Nicholas of Cusa, Regiomantanus, Widmann, Copernicus, Tartaglia, Cardano, Ferrari, Descartes, Pascal, Formati, Saccheri, Cauchy, and Bolzano. My favorites are Pope Sylvester II who revived the decimal numeral system a thousand years ago, and the pioneer woman in mathematics, Maria Agnesi (d. 1799) who refined differential and integral calculus.

The Incarnate Christ subjected himself to his own laws of nature, including solid arithmetic. He kept count. He insisted that the Twelve not be eleven or thirteen. If 2+2 were 5 for him, he might have said: “When 2 ½ or 3 ¾ are gathered together, I am in the midst of them.” When he multiplied the loaves, he might have fed 5000 instead of 4000 with 8 ¾ baskets leftover, and after 6250 were fed instead of 5000, there might have been 15 baskets left over. And we would have a longer workweek, because God rested on the 8.75th day.

The late Vietnamese cardinal Nguyen Van Thuan said that in a certain sense, Jesus actually was a bad mathematician: “A shepherd had 100 sheep; one of them strayed. Without thinking, the shepherd went in search of it, leaving the other 99 sheep. When he found the lost sheep he put it on his shoulders (Luke 15: 4-5). For Jesus, 1 equals 99, perhaps even more…” The cardinal could say that without distorting reality because he spent thirteen years in a Communist prison, nine of them in solitary confinement. Those are the real numbers of real years not spent in Wonderland.

Fr. George W. Rutler


Fr. George W. Rutler is pastor of St. Michael's church in New York City. He is the author of many books including Principalities and Powers: Spiritual Combat 1942-1943 (South Bend, IN: St. Augustine’s Press) and Hints of Heaven (Sophia Institute Press). His latest books are He Spoke To Us (Ignatius, 2016) and The Stories of Hymns (EWTN Publishing, 2017).