The Bible and Society

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God and Mathematics

Posted by Mats on 12/01/2009

Faith By Numbers. When Ratzinger Puts on Galileo’s Robes

From the star of the Magi to the “intelligent structure” that governs the universe: the pope’s reply to the scientists who reject God. A survey among mathematicians reveals that many of them are believers. And some are even theologians

by Sandro Magister
<!– p class=”gee-didaimg”>chiesa magi epifania</p–>

ROMA, January 9, 2008 – In his homily for the feast of the Epiphany, Benedict XVI returned to a topic very close to his heart, the relationship between faith and science.

As his point of departure, the pope took the star of the Magi, who – he noted – “were in all likelihood astronomers,” as Galileo Galilei was. But he invited his audience to look beyond a simple contemplation of the starry sky. “The stars, the planets, the whole universe,” he said, “are not governed by a blind force, they do not obey the dynamics of matter alone.” Above everything, there is not “a cold and anonymous engine,” but the God whom Dante described in the last verse of the Divine Comedy as “the love that moves the sun and the other stars,” the God who became flesh among men, and gave them life. In the “symphony” of creation, the pope continued, there is a “solo” that gives meaning to everything: and this “solo” is Jesus.

2009 is the 400th anniversary of Galileo Galilei’s first observations at the telescope, and will be celebrated all over the world as the year of astronomy. It will also be a year specially dedicated to Charles Darwin and to the cosmological theories that he inspired. Pope Joseph Ratzinger gives the impression of being well prepared for this twofold appointment.

This was demonstrated in part by a key passage in the annual address that he delivered to the Roman curia last December 22:

“Faith in the creator Spirit is an essential element of the Christian creed. The fact that matter carries within itself a mathematical structure, or is full of spirit, is the foundation upon which the modern natural sciences are based. It is only because matter is structured in an intelligent way that our spirit is capable of interpreting it and of actively remodeling it. The fact that this intelligent structure comes from the same creator Spirit who also gave spirit to us brings with it a duty and a responsibility. It is in faith concerning creation that the ultimate foundation of our responsibility for the earth is found. This is not simply our property, which we can exploit according to our interests and desires. It is, instead, a gift of the Creator who designed its intrinsic order, and in this way provided the instructions for us to consult as administrators of his creation. The fact that the earth, the cosmos, reflect the creator Spirit also means that their rational structures that, beyond mathematical order, become almost palpable in experimentation also bear within themselves an ethical orientation. The Spirit who shaped them is more than mathematics: he is Goodness in person, who, through the language of creation, shows us the way of the just life.”

What is striking about this passage is the pope’s repeated insistence on the mathematical structure of the universe.

Mathematics, in fact, is an exact science that today is often opposed to God, as if it were his “scientific,” definitive refutation.

Scientists of worldwide fame, like Richard Dawkins of England and Piergiorgio Odifreddi of Italy, insistently link mathematics with the profession of atheism. Spread through conferences, articles, and best-selling books, their theories aspire to become a common language and philosophy.

In simple terms, the objections to these atheist mathematicians are the ones expressed by a 17-year-old Roman high school student, Giovanni, during a question-and-answer session with the pope in St. Peter’s Square, crowded with young people on April 6, 2006:

“Holy Father, we are often led to believe that knowledge and faith are each other’s enemies; that it was through mathematical logic that everything was discovered; that the world is the result of an accident, and that if mathematics did not discover the theorem-God, it is because God simply does not exist.”

Benedict XVI responded to these objections as follows:

“The great Galileo said that God wrote the book of nature in the form of the language of mathematics. He was convinced that God has given us two books: the book of Sacred Scripture and the book of nature. And the language of nature – this was his conviction – is mathematics, so it is a language of God, a language of the Creator.

“Let us now reflect on what mathematics is: in itself, it is an abstract system, an invention of the human spirit which as such in its purity does not exist. It is always approximated, but as such is an intellectual system, a great, ingenious invention of the human spirit. The surprising thing is that this invention of our human intellect is truly the key to understanding nature, that nature is truly structured in a mathematical way, and that our mathematics, invented by our human mind, is truly the instrument for working with nature, to put it at our service, to use it through technology.

“It seems to me almost incredible that an invention of the human mind and the structure of the universe coincide. Mathematics, which we invented, really gives us access to the nature of the universe and makes it possible for us to use it. Therefore, the intellectual structure of the human subject and the objective structure of reality coincide: the subjective reason and the objective reason of nature are identical. I think that this coincidence between what we thought up and how nature is fulfilled and behaves is a great enigma and a great challenge, for we see that, in the end, it is ‘one’ reason that links them both. Our reason could not discover this other reason were there not an identical antecedent reason for both.

“In this sense it really seems to me that mathematics – in which as such God cannot appear – shows us the intelligent structure of the universe. Now, there are also theories of chaos, but they are limited because if chaos had the upper hand, all technology would become impossible. Only because our mathematics is reliable, is technology reliable. Our knowledge, which is at last making it possible to work with the energies of nature, supposes the reliable and intelligent structure of matter. Thus, we see that there is a subjective rationality and an objectified rationality in matter which coincide. Of course, no one can now prove – as is proven in an experiment, in technical laws – that they both really originated in a single intelligence, but it seems to me that this unity of intelligence, behind the two intelligences, really appears in our world. And the more we can delve into the world with our intelligence, the more clearly the plan of Creation appears.

“In the end, to reach the definitive question I would say: God exists or he does not exist. There are only two options. Either one recognizes the priority of reason, of creative Reason that is at the beginning of all things and is the principle of all things – the priority of reason is also the priority of freedom –, or one holds the priority of the irrational, inasmuch as everything that functions on our earth and in our lives would be only accidental, marginal, an irrational result – reason would be a product of irrationality. One cannot ultimately ‘prove’ either project, but the great option of Christianity is the option for rationality and for the priority of reason. This seems to me to be an excellent option, which shows us that behind everything is a great Intelligence to which we can entrust ourselves.

“However, the true problem challenging faith today seems to me to be the evil in the world: we ask ourselves how it can be compatible with the Creator’s rationality. And here we truly need God, who was made flesh and shows us that he is not only a mathematical reason but that this original Reason is also Love. If we look at the great options, the Christian option today is the one that is the most rational and the most human. Therefore, we can confidently work out a philosophy, a vision of the world based on this priority of reason, on this trust that the creating Reason is love and that this love is God.”
* * *
Two elements stand out in the argument by Benedict XVI just cited. The first is that mathematical reasoning cannot disprove God, but it also cannot prove him. Nonetheless, it draws close to him. And it demonstrates that God is distinctly “an excellent option.” This touches upon the invitation to live “veluti si Deus daretur,” as if God exists, an invitation that Ratzinger has repeatedly issued “to nonbelieving friends” as well, as Pascal did before him.

The second element is that mathematical reasoning cannot say everything about God, because God “is also Love.” In the question-and-answer session with young people in 2006, Benedict XVI limited himself to simply stating this idea. But in order to see how it is developed, all that is needed is to read his entire homily for Epiphany of this year.
* * *
The question remains: is denial of God really so widespread among scientists today, and among mathematicians in particular?

Judging by the series of interviews that “Avvenire,” the newspaper of the Italian bishops’ conference, has been publishing for a month, the answer is no.

“Avvenire” is interviewing some eminent mathematicians on the topic of “Numbers and faith,” meaning the compatibility between mathematical reasoning and faith in God. The picture that emerges is one of a scientific environment that is much more open to faith than the one depicted in the “vulgate” of the media.

The following mathematicians have been interviewed so far:

– on December 11, 2008, Antonio Ambrosetti, for many years a professor of mathematical analysis at the Normale di Pisa, now at the International School for Advanced Studies in Trieste;

– on December 16, Giandomenico Boffi, algebra professor at the University of Chieti and Pescara;

– on December 24, Marco Andreatta, professor of geometry and dean of the faculty of sciences at the University of Trent;

– on January 6, 2009, Giovanni Pistone, professor of probability at the Polytechnic University of Turin;

Pistone is a member of the Waldensian Evangelical Church, and holds a degree in theology, while the others are Catholic. The survey by “Avvenire” is limited to Italy, but the answers by the interviewees make frequent reference to other countries. Fervent men of faith are among the other masters they cite, in particular Ennio De Giorgi, one of the most illustrious mathematicians of the twentieth century.

The survey continues. And it’s an easy bet that the upcoming interviews will include Giorgio Israel, a Jewish professor of complementary mathematics at the Rome University “La Sapienza,” and a great admirer of Benedict XVI.


The newspaper of the Italian bishops’ conference, with the survey on “Numbers and faith,” conducted by Luigi Dell’Aglio:

> Avvenire


Benedict XVI’s homily for Epiphany of this year:

> “Cari fratelli e sorelle, l’Epifania…”


English translation by Matthew Sherry, Saint Louis, Missouri, U.S.A.


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